def test_quadrature_tri_mass_mat_monomial():
"""Check that quadrature integration on triangles is exact as designed."""
from hedge.mesh.generator import make_square_mesh
mesh = make_square_mesh(a=-1, b=1, max_area=4 * 1 / 8 + 0.001)
order = 4
discr = discr_class(
mesh, order=order, debug=discr_class.noninteractive_debug_flags(), quad_min_degrees={"quad": 3 * order}
)
m, n = 2, 1
f = Monomial((m, n))
f_vec = discr.interpolate_volume_function(lambda x, el: f(x))
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
vis.add_data(visf, [("f", f_vec * f_vec)])
visf.close()
from hedge.optemplate import MassOperator, Field, QuadratureGridUpsampler
f_fld = Field("f")
mass_op = discr.compile(MassOperator()(f_fld * f_fld))
from hedge.optemplate.primitives import make_common_subexpression as cse
f_upsamp = cse(QuadratureGridUpsampler("quad")(f_fld))
quad_mass_op = discr.compile(MassOperator()(f_upsamp * f_upsamp))
num_integral_1 = numpy.dot(ones, mass_op(f=f_vec))
num_integral_2 = numpy.dot(ones, quad_mass_op(f=f_vec))
true_integral = 4 / ((2 * m + 1) * (2 * n + 1))
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
print num_integral_1, num_integral_2, true_integral
print err_1, err_2
assert err_1 > 1e-8
assert err_2 < 1e-14
def test_quadrature_tri_mass_mat_monomial():
"""Check that quadrature integration on triangles is exact as designed."""
from hedge.mesh.generator import make_square_mesh
mesh = make_square_mesh(a=-1, b=1, max_area=4 * 1 / 8 + 0.001)
order = 4
discr = discr_class(mesh,
order=order,
debug=discr_class.noninteractive_debug_flags(),
quad_min_degrees={"quad": 3 * order})
m, n = 2, 1
f = Monomial((m, n))
f_vec = discr.interpolate_volume_function(lambda x, el: f(x))
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
vis.add_data(visf, [("f", f_vec * f_vec)])
visf.close()
from hedge.optemplate import (MassOperator, Field, QuadratureGridUpsampler)
f_fld = Field("f")
mass_op = discr.compile(MassOperator()(f_fld * f_fld))
from hedge.optemplate.primitives import make_common_subexpression as cse
f_upsamp = cse(QuadratureGridUpsampler("quad")(f_fld))
quad_mass_op = discr.compile(MassOperator()(f_upsamp * f_upsamp))
num_integral_1 = numpy.dot(ones, mass_op(f=f_vec))
num_integral_2 = numpy.dot(ones, quad_mass_op(f=f_vec))
true_integral = 4 / ((2 * m + 1) * (2 * n + 1))
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
print num_integral_1, num_integral_2, true_integral
print err_1, err_2
assert err_1 > 1e-8
assert err_2 < 1e-14
def run_convergence_test_advec(dtype,
flux_type,
random_partition,
mesh_gen,
debug_output=False):
"""Test whether 2/3D advection actually converges"""
from hedge.timestep import RK4TimeStepper
from hedge.tools import EOCRecorder
from math import sin
from hedge.data import TimeDependentGivenFunction
from hedge.visualization import SiloVisualizer
from hedge.backends import guess_run_context
rcon = guess_run_context(["mpi"])
# note: x component must remain zero because x-periodicity is used
v = np.array([0.0, 0.9, 0.3])
def f(x):
return sin(x)
def u_analytic(x, el, t):
return f(
(np.dot(-v[:dims], x) / la.norm(v[:dims]) + t * la.norm(v[:dims])))
def boundary_tagger(vertices, el, face_nr, points):
face_normal = el.face_normals[face_nr]
if np.dot(face_normal, v[:len(face_normal)]) < 0:
return ["inflow"]
else:
return ["outflow"]
mesh = mesh_gen(boundary_tagger)
eoc_rec = EOCRecorder()
if random_partition:
# Distribute elements randomly across nodes.
# This is bad, efficiency-wise, but it puts stress
# on the parallel implementation, which is desired here.
# Another main point of this is to force the code to split
# a periodic face pair across nodes.
from random import choice
partition = [choice(rcon.ranks) for el in mesh.elements]
else:
partition = None
for order in [1, 2, 3, 4]:
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh, partition)
else:
mesh_data = rcon.receive_mesh()
dims = mesh.points.shape[1]
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=dtype)
op = StrongAdvectionOperator(
v[:dims],
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type)
if debug_output:
vis = SiloVisualizer(discr, rcon)
u = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, 0))
ic = u.copy()
if debug_output and rcon.is_head_rank:
print "#elements=%d" % len(mesh.elements)
test_name = "test-%s-o%d-m%s-r%s" % (
flux_type, order, mesh_gen.__name__, random_partition)
rhs = op.bind(discr)
stepper = RK4TimeStepper(dtype=dtype)
from hedge.timestep import times_and_steps
final_time = 1
step_it = times_and_steps(final_time=final_time,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
u = stepper(u, t, dt, rhs)
assert u.dtype == dtype
u_true = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, final_time))
error = u - u_true
l2_error = discr.norm(error)
if debug_output:
visf = vis.make_file(test_name + "-final")
vis.add_data(visf, [("u", u), ("u_true", u_true), ("ic", ic)])
visf.close()
eoc_rec.add_data_point(order, l2_error)
if debug_output and rcon.is_head_rank:
print "%s\n%s\n" % (flux_type.upper(), "-" * len(flux_type))
print eoc_rec.pretty_print(abscissa_label="Poly. Order",
error_label="L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 3
assert eoc_rec.estimate_order_of_convergence(2)[-1, 1] > 7
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
def boundary_tagger(vertices, el, face_nr, all_v):
return ["inflow"]
if rcon.is_head_rank:
from hedge.mesh import make_rect_mesh, \
make_centered_regular_rect_mesh
#mesh = make_rect_mesh((0,0), (10,1), max_area=0.01)
refine = 1
mesh = make_centered_regular_rect_mesh(
(0, 0),
(10, 1),
n=(20, 4),
#periodicity=(True, False),
post_refine_factor=refine,
boundary_tagger=boundary_tagger)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
shearflow = SteadyShearFlow()
fields = shearflow.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = shearflow.properties()
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=2,
gamma=gamma,
mu=mu,
prandtl=prandtl,
spec_gas_const=spec_gas_const,
bc_inflow=shearflow,
bc_outflow=shearflow,
bc_noslip=shearflow,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
# needed to get first estimate of maximum eigenvalue
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-cpu-%d-%d.dat" % (order, refine),
"w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.3,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 10 == 0:
#if False:
visf = vis.make_file("shearflow-%d-%04d" % (order, step))
#true_fields = shearflow.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = shearflow.volume_interpolant(t, discr)
l2_error = discr.norm(op.u(fields) - op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
finally:
vis.close()
logmgr.save()
discr.close()
def optimize_shape_bandwidth(method, state, analytic_rho, exponent):
discr = method.discretization
rec = method.depositor
adv_radius = method.mesh_data.advisable_particle_radius()
radii = [adv_radius * 2**i for i in numpy.linspace(-4, 2, 50)]
def set_radius(r):
method.depositor.set_shape_function(
state,
method.get_shape_function_class()(
r,
method.mesh_data.dimensions,
exponent,
))
tried_radii = []
l1_errors = []
debug = "shape_bw" in method.debug
visualize = set(["shape_bw", "vis_files"]) <= method.debug
if visualize:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
import sys
if debug:
sys.stdout.write("optimizing shape bw (%d attempts): " % len(radii))
for step, radius in enumerate(radii):
if debug:
sys.stdout.write("%d." % step)
sys.stdout.flush()
try:
try:
method.set_ignore_core_warnings(True)
set_radius(radius)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
state.derived_quantity_cache.clear()
try:
try:
method.set_ignore_core_warnings(True)
rec_rho = method.deposit_rho(state)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
tried_radii.append(radius)
l1_errors.append(discr.integral(numpy.abs(rec_rho - analytic_rho)))
if visualize:
visf = vis.make_file("bwopt-%04d" % step)
method.add_to_vis(vis, visf, state, time=radius, step=step)
vis.add_data(
visf,
[
("rho", rec_rho),
#("j", method.deposit_j(state)),
("rho_analytic", analytic_rho),
],
expressions=[("rho_diff", "rho-rho_analytic")],
time=radius,
step=step)
try:
rec.visualize_grid_quantities
except AttributeError:
pass
else:
rec.visualize_grid_quantities(visf, [
("rho_grid", rec.deposit_grid_rho(state)),
("j_grid",
rec.deposit_grid_j(state, method.velocities(state))),
("rho_resid",
rec.remap_residual(rec.deposit_grid_rho(state))),
])
visf.close()
if debug:
sys.stdout.write("\n")
sys.stdout.flush()
if visualize:
vis.close()
from pytools import argmin
min_idx = argmin(l1_errors)
min_rad = tried_radii[min_idx]
min_l1_error = l1_errors[min_idx]
rel_l1_error = abs(min_l1_error / discr.integral(analytic_rho))
if rel_l1_error > 0.1:
from warnings import warn
warn("Charge density is very poorly resolved (rel L1 error=%g)" %
rel_l1_error)
def is_local_minimum(list, i):
if i == 0:
return False
elif i == len(list) - 1:
return False
else:
return list[i] < list[i - 1] and list[i] < list[i + 1]
local_minima = [
idx for idx in range(len(tried_radii))
if is_local_minimum(l1_errors, idx)
]
chosen_idx = max(local_minima)
chosen_rad = tried_radii[chosen_idx]
if "shape_bw" in method.debug:
chosen_l1_error = l1_errors[chosen_idx]
print "radius: guessed optimum=%g, found optimum=%g, chosen=%g" % (
adv_radius, min_rad, chosen_rad)
print "radius: optimum l1 error=%g, chosen l1 error=%g" % (
min_l1_error, chosen_l1_error)
set_radius(chosen_rad)
state.derived_quantity_cache.clear()
if set(["interactive", "shape_bw"]) < method.debug:
from pylab import semilogx, show
semilogx(tried_radii, l1_errors)
show()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context( ["cuda", "mpi"])
if rcon.is_head_rank:
mesh = make_wingmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
wing = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=wing.gamma, mu=wing.mu,
prandtl=wing.prandtl, spec_gas_const=wing.spec_gas_const,
bc_inflow=wing, bc_outflow=wing, bc_noslip=wing,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code"
"cuda_no_metis",
],
default_scalar_type=numpy.float64,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = wing.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.6 * op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("wing-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
from hedge.discretization import ones_on_boundary
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
t += dt
finally:
vis.close()
logmgr.save()
discr.close()
def test_symmetry_preservation_2d():
"""Test whether we preserve symmetry in a symmetric 2D advection problem"""
from numpy import dot
def make_mesh():
array = numpy.array
#
# 1---8---2
# |7 /|\ 1|
# | / | \ |
# |/ 6|0 \|
# 5---4---7
# |\ 5|3 /|
# | \ | / |
# |4 \|/ 2|
# 0---6---3
#
points = [
array([-0.5, -0.5]),
array([-0.5, 0.5]),
array([0.5, 0.5]),
array([0.5, -0.5]),
array([0.0, 0.0]),
array([-0.5, 0.0]),
array([0.0, -0.5]),
array([0.5, 0.0]),
array([0.0, 0.5])
]
elements = [
[8, 7, 4],
[8, 7, 2],
[6, 7, 3],
[7, 4, 6],
[5, 6, 0],
[5, 6, 4],
[5, 8, 4],
[1, 5, 8],
]
def boundary_tagger(vertices, el, face_nr, all_v):
if dot(el.face_normals[face_nr], v) < 0:
return ["inflow"]
else:
return ["outflow"]
from hedge.mesh import make_conformal_mesh
return make_conformal_mesh(points, elements, boundary_tagger)
from hedge.discretization import SymmetryMap
from hedge.timestep import RK4TimeStepper
from hedge.models.advection import StrongAdvectionOperator
from hedge.data import TimeDependentGivenFunction
v = numpy.array([-1, 0])
mesh = make_mesh()
discr = discr_class(mesh,
order=4,
debug=discr_class.noninteractive_debug_flags())
#ref_discr = DynamicDiscretization(mesh, order=4)
def f(x):
if x < 0.5:
return 0
else:
return (x - 0.5)
#def f(x):
#return sin(5*x)
def u_analytic(x, el, t):
return f(-dot(v, x) + t)
u = discr.interpolate_volume_function(lambda x, el: u_analytic(x, el, 0))
sym_map = SymmetryMap(discr, lambda x: numpy.array([x[0], -x[1]]), {
0: 3,
2: 1,
5: 6,
7: 4
})
for flux_type in StrongAdvectionOperator.flux_types:
stepper = RK4TimeStepper()
op = StrongAdvectionOperator(
v,
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type)
dt = op.estimate_timestep(discr, stepper=stepper)
nsteps = int(1 / dt)
rhs = op.bind(discr)
#test_comp = [ "bflux"]
#test_rhs = op.bind(discr, test_comp)
#ref_rhs = op.bind(ref_discr, test_comp)
for step in xrange(nsteps):
u = stepper(u, step * dt, dt, rhs)
sym_error_u = u - sym_map(u)
sym_error_u_l2 = discr.norm(sym_error_u)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test-%s-%04d" % (flux_type, step))
vis.add_data(
visf,
[
("u", u),
("sym_u", sym_map(u)),
("sym_diff", u - sym_map(u)),
("rhs", rhs(step * dt, u)),
#("rhs_test", test_rhs(step*dt, u)),
#("rhs_ref", ref_rhs(step*dt, u)),
#("rhs_diff", test_rhs(step*dt, u)-ref_rhs(step*dt, u)),
])
print sym_error_u_l2
assert sym_error_u_l2 < 4e-15
def run_convergence_test_advec(dtype, debug_output=False):
"""Test whether 2/3D advection actually converges"""
from hedge.mesh.generator import make_ball_mesh, make_box_mesh, make_rect_mesh
from hedge.timestep import RK4TimeStepper
from hedge.tools import EOCRecorder
from math import sin, pi, sqrt
from hedge.models.advection import StrongAdvectionOperator
from hedge.data import TimeDependentGivenFunction
from hedge.visualization import SiloVisualizer
from hedge.backends import guess_run_context
rcon = guess_run_context(["mpi"])
# note: x component must remain zero because x-periodicity is used
v = numpy.array([0.0,0.9,0.3])
def f(x):
return sin(x)
def u_analytic(x, el, t):
return f((numpy.dot(-v[:dims],x)/la.norm(v[:dims])+t*la.norm(v[:dims])))
def boundary_tagger(vertices, el, face_nr, points):
face_normal = el.face_normals[face_nr]
if numpy.dot(face_normal, v[:len(face_normal)]) < 0:
return ["inflow"]
else:
return ["outflow"]
for i_mesh, mesh in enumerate([
# 2D semiperiodic
make_rect_mesh(b=(2*pi,3), max_area=0.4,
periodicity=(True, False),
subdivisions=(5,10),
boundary_tagger=boundary_tagger,
),
# 3D x-periodic
make_box_mesh((0,0,0), (2*pi, 2, 2), max_volume=0.4,
periodicity=(True, False, False),
boundary_tagger=boundary_tagger,
),
# non-periodic
make_ball_mesh(r=pi,
boundary_tagger=boundary_tagger, max_volume=0.7),
]):
for flux_type in StrongAdvectionOperator.flux_types:
for random_partition in [True, False]:
eoc_rec = EOCRecorder()
if random_partition:
# Distribute elements randomly across nodes.
# This is bad, efficiency-wise, but it puts stress
# on the parallel implementation, which is desired here.
# Another main point of this is to force the code to split
# a periodic face pair across nodes.
from random import choice
partition = [choice(rcon.ranks) for el in mesh.elements]
else:
partition = None
for order in [1,2,3,4]:
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh, partition)
else:
mesh_data = rcon.receive_mesh()
dims = mesh.points.shape[1]
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=dtype)
op = StrongAdvectionOperator(v[:dims],
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type)
if debug_output:
vis = SiloVisualizer(discr, rcon)
u = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, 0))
ic = u.copy()
if debug_output and rcon.is_head_rank:
print "#elements=%d" % len(mesh.elements)
test_name = "test-%s-o%d-m%d-r%s" % (
flux_type, order, i_mesh, random_partition)
rhs = op.bind(discr)
stepper = RK4TimeStepper(dtype=dtype)
from hedge.timestep import times_and_steps
final_time = 1
step_it = times_and_steps(
final_time=final_time,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
u = stepper(u, t, dt, rhs)
assert u.dtype == dtype
u_true = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, final_time))
error = u-u_true
l2_error = discr.norm(error)
if debug_output:
visf = vis.make_file(test_name+"-final")
vis.add_data(visf, [
("u", u),
("u_true", u_true),
("ic", ic)])
visf.close()
eoc_rec.add_data_point(order, l2_error)
if debug_output and rcon.is_head_rank:
print "%s\n%s\n" % (flux_type.upper(), "-" * len(flux_type))
print eoc_rec.pretty_print(abscissa_label="Poly. Order",
error_label="L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0,1] > 3
assert eoc_rec.estimate_order_of_convergence(2)[-1,1] > 7
def test_symmetry_preservation_2d():
"""Test whether we preserve symmetry in a symmetric 2D advection problem"""
from numpy import dot
def make_mesh():
array = numpy.array
#
# 1---8---2
# |7 /|\ 1|
# | / | \ |
# |/ 6|0 \|
# 5---4---7
# |\ 5|3 /|
# | \ | / |
# |4 \|/ 2|
# 0---6---3
#
points = [
array([-0.5, -0.5]),
array([-0.5, 0.5]),
array([0.5, 0.5]),
array([0.5, -0.5]),
array([0.0, 0.0]),
array([-0.5, 0.0]),
array([0.0, -0.5]),
array([0.5, 0.0]),
array([0.0, 0.5]),
]
elements = [[8, 7, 4], [8, 7, 2], [6, 7, 3], [7, 4, 6], [5, 6, 0], [5, 6, 4], [5, 8, 4], [1, 5, 8]]
def boundary_tagger(vertices, el, face_nr, all_v):
if dot(el.face_normals[face_nr], v) < 0:
return ["inflow"]
else:
return ["outflow"]
from hedge.mesh import make_conformal_mesh
return make_conformal_mesh(points, elements, boundary_tagger)
from hedge.discretization import SymmetryMap
from hedge.discretization.local import TriangleDiscretization
from hedge.timestep import RK4TimeStepper
from math import sqrt, sin
from hedge.models.advection import StrongAdvectionOperator
from hedge.data import TimeDependentGivenFunction
v = numpy.array([-1, 0])
mesh = make_mesh()
discr = discr_class(mesh, order=4, debug=discr_class.noninteractive_debug_flags())
# ref_discr = DynamicDiscretization(mesh, order=4)
def f(x):
if x < 0.5:
return 0
else:
return x - 0.5
# def f(x):
# return sin(5*x)
def u_analytic(x, el, t):
return f(-dot(v, x) + t)
u = discr.interpolate_volume_function(lambda x, el: u_analytic(x, el, 0))
sym_map = SymmetryMap(discr, lambda x: numpy.array([x[0], -x[1]]), {0: 3, 2: 1, 5: 6, 7: 4})
for flux_type in StrongAdvectionOperator.flux_types:
stepper = RK4TimeStepper()
op = StrongAdvectionOperator(v, inflow_u=TimeDependentGivenFunction(u_analytic), flux_type=flux_type)
dt = op.estimate_timestep(discr, stepper=stepper)
nsteps = int(1 / dt)
rhs = op.bind(discr)
# test_comp = [ "bflux"]
# test_rhs = op.bind(discr, test_comp)
# ref_rhs = op.bind(ref_discr, test_comp)
for step in xrange(nsteps):
u = stepper(u, step * dt, dt, rhs)
sym_error_u = u - sym_map(u)
sym_error_u_l2 = discr.norm(sym_error_u)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test-%s-%04d" % (flux_type, step))
vis.add_data(
visf,
[
("u", u),
("sym_u", sym_map(u)),
("sym_diff", u - sym_map(u)),
("rhs", rhs(step * dt, u)),
("rhs_test", test_rhs(step * dt, u)),
("rhs_ref", ref_rhs(step * dt, u)),
("rhs_diff", test_rhs(step * dt, u) - ref_rhs(step * dt, u)),
],
)
print sym_error_u_l2
assert sym_error_u_l2 < 4e-15
def prepare_with_pointwise_projection_and_basis_reduction(self):
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
min_s_values = []
max_s_values = []
cond_s_values = []
basis_len_vec = discr.volume_zeros()
el_condition_vec = discr.volume_zeros()
point_count_vec = discr.volume_zeros()
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
mode_id_to_index = dict(
(bid, i) for i, bid in enumerate(ldis.generate_mode_identifiers()))
for el in eg.members:
basis = list(zip(
ldis.generate_mode_identifiers(),
ldis.basis_functions()))
eog, points = self.find_points_in_element(el, self.el_tolerance)
while True:
scaled_vdm = self.scaled_vandermonde(el, eog, points,
[bf for bid, bf in basis])
max_bid_sum = max(sum(bid) for bid, bf in basis)
killable_basis_elements = [
(i, bid) for i, (bid, bf) in enumerate(basis)
if sum(bid) == max_bid_sum]
try:
u, s, vt = svd = la.svd(scaled_vdm)
thresh = (numpy.finfo(float).eps
* max(scaled_vdm.shape) * s[0])
assert s[-1] == numpy.min(s)
assert s[0] == numpy.max(s)
# Imagine that--s can have negative entries.
# (AK: I encountered one negative zero.)
if len(basis) > len(points) or numpy.abs(s[0]/s[-1]) > 10:
retry = True
# badly conditioned, kill a basis entry
vti = vt[-1]
from pytools import argmax2
kill_idx, kill_bid = argmax2(
((j, bid), abs(vti[j]))
for j, bid in killable_basis_elements)
assert kill_bid == basis[kill_idx][0]
basis.pop(kill_idx)
else:
retry = False
except la.LinAlgError:
# SVD likely didn't converge. Lacking an SVD, we don't have
# much guidance on what modes to kill. Any of the killable
# ones will do.
# Bang, you're dead.
basis.pop(killable_basis_elements[0][0])
retry = True
if not retry:
break
if len(basis) == 1:
raise RuntimeError(
"basis reduction has killed almost the entire basis on element %d"
% el.id)
if ldis.node_count() > len(basis):
print "element %d: #nodes=%d, killed modes=%d" % (
el.id, ldis.node_count(), ldis.node_count()-len(basis),)
basis_len_vec[discr.find_el_range(el.id)] = len(basis)
el_condition_vec[discr.find_el_range(el.id)] = s[0]/s[-1]
point_count_vec[discr.find_el_range(el.id)] = len(points)
min_s_values.append(min(s))
max_s_values.append(max(s))
cond_s_values.append(max(s)/min(s))
self.make_pointwise_interpolation_matrix(eog, eg, el, ldis, svd, scaled_vdm,
basis_subset=[mode_id_to_index[bid] for bid, bf in basis])
backend.elements_on_grid.append(eog)
# visualize basis length for each element
if set(["depositor", "vis_files"]) < self.method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("rec-debug")
vis.add_data(visf, [
("basis_len", basis_len_vec),
("el_condition", el_condition_vec),
("point_count", point_count_vec),
])
visf.close()
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0]*(len(backend.bricks)+1))
# print some statistics
self.generate_point_statistics()
def prepare_with_pointwise_projection_and_enlargement(self):
tolerance_bound = 1.5
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
cond_claims = 0
min_s_values = []
max_s_values = []
cond_s_values = []
from hedge.discretization import Projector, Discretization
fine_discr = Discretization(discr.mesh, order=8)
proj = Projector(discr, fine_discr)
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(fine_discr)
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
# If the structured Vandermonde matrix is singular,
# enlarge the element tolerance
my_tolerance = self.el_tolerance
orig_point_count = None
while True:
eog, points = self.find_points_in_element(el, my_tolerance)
if orig_point_count is None:
orig_point_count = len(points)
scaled_vdm = self.scaled_vandermonde(el, eog, points,
ldis.basis_functions())
bad_vdm = len(points) < ldis.node_count()
if not bad_vdm:
try:
u, s, vt = svd = la.svd(scaled_vdm)
thresh = (numpy.finfo(float).eps
* max(scaled_vdm.shape) * s[0])
zero_indices = [i for i, si in enumerate(s)
if abs(si) < thresh]
bad_vdm = bool(zero_indices)
except la.LinAlgError:
bad_vdm = True
if not bad_vdm:
break
my_tolerance += 0.03
if my_tolerance >= tolerance_bound:
from warnings import warn
warn("rec_grid: could not regularize structured "
"vandermonde matrix for el #%d by enlargement" % el.id)
break
#from pytools import average
#print average(eog.weight_factors), min(s)
#raw_input()
if my_tolerance > self.el_tolerance:
print "element %d: #nodes=%d, orig #sgridpt=%d, extra tol=%g, #extra points=%d" % (
el.id, ldis.node_count(), orig_point_count,
my_tolerance-self.el_tolerance,
len(points)-orig_point_count)
cond_claims += len(points)-orig_point_count
min_s_values.append(min(s))
max_s_values.append(max(s))
cond_s_values.append(max(s)/min(s))
if max(s)/min(s) > 1e2:
for i in range(len(s)):
if s[0]/s[i] > 1e2:
zeroed_mode = vt[i]
zeroed_mode_nodal = numpy.dot(ldis.vandermonde(),
zeroed_mode)
print el.id, i, s[0]/s[i]
fromvec = discr.volume_zeros()
fromvec[discr.find_el_range(el.id)] = zeroed_mode_nodal
gn = list(eog.grid_nodes)
assert len(gn) == len(u[i])
tovec = numpy.zeros((backend.grid_node_count_with_extra(),), dtype=float)
tovec[gn] = s[i]*u[i]
usevec = numpy.zeros((backend.grid_node_count_with_extra(),), dtype=float)
usevec[gn] = 1
visf = vis.make_file("nulled-%04d%02d" % (el.id, i))
vis.add_data(visf, [("meshmode", proj(fromvec))],
expressions=[
("absmesh", "abs(meshmode)"),
("absgrid", "abs(gridmode)"),
])
self.visualize_grid_quantities(visf, [
("gridmode", tovec),
("usevec", usevec),
],
)
visf.close()
#print s
#raw_input()
self.make_pointwise_interpolation_matrix(eog, eg, el, ldis, svd, scaled_vdm)
backend.elements_on_grid.append(eog)
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0]*(len(backend.bricks)+1))
# print some statistics
self.generate_point_statistics(cond_claims)
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
mesh = make_nacamesh()
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
for order in [4]:
from gas_dynamics_initials import UniformMachFlow
uniform_flow = UniformMachFlow()
from hedge.models.gas_dynamics import GasDynamicsOperator, GammaLawEOS
op = GasDynamicsOperator(
dimensions=2,
equation_of_state=GammaLawEOS(uniform_flow.gamma),
prandtl=uniform_flow.prandtl,
spec_gas_const=uniform_flow.spec_gas_const,
mu=uniform_flow.mu,
bc_inflow=uniform_flow,
bc_outflow=uniform_flow,
bc_noslip=uniform_flow,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip",
)
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
"cuda_no_plan",
# "cuda_dump_kernels",
# "dump_optemplate_stages",
# "dump_dataflow_graph",
# "print_op_code"
],
default_scalar_type=numpy.float32,
tune_for=op.op_template(),
)
from hedge.visualization import SiloVisualizer, VtkVisualizer
# vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = uniform_flow.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import ODE23TimeStepper, LSRK4TimeStepper
stepper = ODE23TimeStepper(
dtype=discr.default_scalar_type, rtol=1e-6, vector_primitive_factory=discr.get_vector_primitive_factory()
)
# stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, add_simulation_quantities, add_run_info
logmgr = LogManager("cns-naca-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1", "Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
# logmgr.add_quantity(ChangeSinceLastStep())
# filter setup-------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(discr, ExponentialFilterResponseFunction(min_amplification=0.9, order=4))
# timestep loop -------------------------------------------------------
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
# max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt,
)
model_stepper = LSRK4TimeStepper()
next_dt = op.estimate_timestep(discr, stepper=model_stepper, t=0, max_eigenvalue=max_eigval[0])
for step, t, dt in step_it:
if step % 10 == 0:
visf = vis.make_file("naca-%d-%06d" % (order, step))
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
# ("true_rho", op.rho(true_fields)),
# ("true_e", op.e(true_fields)),
# ("true_rho_u", op.rho_u(true_fields)),
# ("true_u", op.u(true_fields)),
# ("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
# ("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
# ("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
# ("diff_rho", "rho-true_rho"),
# ("diff_e", "e-true_e"),
# ("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "(0.4)*(e- 0.5*(rho_u*u))")
],
time=t,
step=step,
)
visf.close()
fields, t, taken_dt, next_dt = stepper(fields, t, dt, rhs)
fields = mode_filter(fields)
finally:
vis.close()
logmgr.save()
discr.close()
def compute_initial_condition(rcon, discr, method, state,
maxwell_op, potential_bc,
force_zero=False):
from hedge.models.poisson import PoissonOperator
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import ConstantGivenFunction, GivenVolumeInterpolant
def rel_l2_error(field, true):
from hedge.tools import relative_error
return relative_error(
discr.norm(field-true),
discr.norm(true))
mean_beta = method.mean_beta(state)
gamma = method.units.gamma_from_beta(mean_beta)
# see doc/notes.tm for derivation of IC
def make_scaling_matrix(beta_scale, other_scale):
if la.norm(mean_beta) < 1e-10:
return other_scale*numpy.eye(discr.dimensions)
else:
beta_unit = mean_beta/la.norm(mean_beta)
return (other_scale*numpy.identity(discr.dimensions)
+ (beta_scale-other_scale)*numpy.outer(beta_unit, beta_unit))
poisson_op = PoissonOperator(
discr.dimensions,
diffusion_tensor=make_scaling_matrix(1/gamma**2, 1),
dirichlet_tag=TAG_ALL,
neumann_tag=TAG_NONE,
dirichlet_bc=potential_bc)
rho_prime = method.deposit_rho(state)
rho_tilde = rho_prime/gamma
bound_poisson = poisson_op.bind(discr)
if force_zero:
phi_tilde = discr.volume_zeros()
else:
from hedge.iterative import parallel_cg
phi_tilde = -parallel_cg(rcon, -bound_poisson,
bound_poisson.prepare_rhs(
rho_tilde/maxwell_op.epsilon),
debug=40 if "poisson" in method.debug else False, tol=1e-10)
from hedge.tools import ptwise_dot
from hedge.models.nd_calculus import GradientOperator
e_tilde = ptwise_dot(2, 1, make_scaling_matrix(1/gamma, 1),
GradientOperator(discr.dimensions).bind(discr)(phi_tilde))
e_prime = ptwise_dot(2, 1, make_scaling_matrix(1, gamma), e_tilde)
from pyrticle.tools import make_cross_product
v_e_to_h_cross = make_cross_product(method, maxwell_op, "v", "e", "h")
h_prime = (1/maxwell_op.mu)*gamma/maxwell_op.c * v_e_to_h_cross(mean_beta, e_tilde)
if "ic" in method.debug:
deposited_charge = discr.integral(rho_prime)
real_charge = numpy.sum(state.charges)
print "charge: supposed=%g deposited=%g error=%g %%" % (
real_charge,
deposited_charge,
100*abs(deposited_charge-real_charge)/abs(real_charge)
)
from hedge.models.nd_calculus import DivergenceOperator
bound_div_op = DivergenceOperator(discr.dimensions).bind(discr)
d_tilde = maxwell_op.epsilon*e_tilde
d_prime = maxwell_op.epsilon*e_prime
#divD_prime_ldg = bound_poisson.div(d_prime)
#divD_prime_ldg2 = bound_poisson.div(d_prime, maxwell_op.epsilon*gamma*phi_tilde)
from hedge.optemplate import InverseMassOperator
divD_prime_ldg3 = maxwell_op.epsilon*\
(InverseMassOperator().apply(discr, bound_poisson.op(gamma*phi_tilde)))
divD_prime_central = bound_div_op(d_prime)
print "l2 div D_prime error central: %g" % \
rel_l2_error(divD_prime_central, rho_prime)
#print "l2 div D_prime error ldg: %g" % \
#rel_l2_error(divD_prime_ldg, rho_prime)
#print "l2 div D_prime error ldg with phi: %g" % \
#rel_l2_error(divD_prime_ldg2, rho_prime)
print "l2 div D_prime error ldg with phi 3: %g" % \
rel_l2_error(divD_prime_ldg3, rho_prime)
if "vis_files" in method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("ic")
vis.add_data(visf, [
("phi_moving", phi_tilde),
("rho_moving", rho_tilde),
("e_moving", e_tilde),
("rho_lab", rho_prime),
#("divD_lab_ldg", divD_prime_ldg),
#("divD_lab_ldg2", divD_prime_ldg2),
#("divD_lab_ldg3", divD_prime_ldg3),
("divD_lab_central", divD_prime_central),
("e_lab", e_prime),
("h_lab", h_prime),
],
)
method.add_to_vis(vis, visf, state)
visf.close()
return maxwell_op.assemble_fields(e=e_prime, h=h_prime, discr=discr)
def optimize_shape_bandwidth(method, state, analytic_rho, exponent):
discr = method.discretization
rec = method.depositor
adv_radius = method.mesh_data.advisable_particle_radius()
radii = [adv_radius*2**i
for i in numpy.linspace(-4, 2, 50)]
def set_radius(r):
method.depositor.set_shape_function(
state,
method.get_shape_function_class()
(r, method.mesh_data.dimensions, exponent,))
tried_radii = []
l1_errors = []
debug = "shape_bw" in method.debug
visualize = set(["shape_bw", "vis_files"]) <= method.debug
if visualize:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
import sys
if debug:
sys.stdout.write("optimizing shape bw (%d attempts): " % len(radii))
for step, radius in enumerate(radii):
if debug:
sys.stdout.write("%d." % step)
sys.stdout.flush()
try:
try:
method.set_ignore_core_warnings(True)
set_radius(radius)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
state.derived_quantity_cache.clear()
try:
try:
method.set_ignore_core_warnings(True)
rec_rho = method.deposit_rho(state)
except RuntimeError, re:
if "particle mass is zero" in str(re):
continue
else:
raise
finally:
method.set_ignore_core_warnings(False)
tried_radii.append(radius)
l1_errors.append(discr.integral(numpy.abs(rec_rho-analytic_rho)))
if visualize:
visf = vis.make_file("bwopt-%04d" % step)
method.add_to_vis(vis, visf, state, time=radius, step=step)
vis.add_data(visf, [
("rho", rec_rho),
#("j", method.deposit_j(state)),
("rho_analytic", analytic_rho),
],
expressions=[("rho_diff", "rho-rho_analytic")],
time=radius, step=step)
try:
rec.visualize_grid_quantities
except AttributeError:
pass
else:
rec.visualize_grid_quantities(visf, [
("rho_grid", rec.deposit_grid_rho(state)),
("j_grid", rec.deposit_grid_j(state, method.velocities(state))),
("rho_resid", rec.remap_residual(rec.deposit_grid_rho(state))),
])
visf.close()
if debug:
sys.stdout.write("\n")
sys.stdout.flush()
if visualize:
vis.close()
from pytools import argmin
min_idx = argmin(l1_errors)
min_rad = tried_radii[min_idx]
min_l1_error = l1_errors[min_idx]
rel_l1_error = abs(min_l1_error / discr.integral(analytic_rho))
if rel_l1_error > 0.1:
from warnings import warn
warn("Charge density is very poorly resolved (rel L1 error=%g)" % rel_l1_error)
def is_local_minimum(list, i):
if i == 0:
return False
elif i == len(list)-1:
return False
else:
return list[i] < list[i-1] and list[i] < list[i+1]
local_minima = [idx for idx in range(len(tried_radii))
if is_local_minimum(l1_errors, idx)]
chosen_idx = max(local_minima)
chosen_rad = tried_radii[chosen_idx]
if "shape_bw" in method.debug:
chosen_l1_error = l1_errors[chosen_idx]
print "radius: guessed optimum=%g, found optimum=%g, chosen=%g" % (
adv_radius, min_rad, chosen_rad)
print "radius: optimum l1 error=%g, chosen l1 error=%g" % (
min_l1_error, chosen_l1_error)
set_radius(chosen_rad)
state.derived_quantity_cache.clear()
if set(["interactive", "shape_bw"]) < method.debug:
from pylab import semilogx, show
semilogx(tried_radii, l1_errors)
show()
def inner_run(self):
t = 0
setup = self.setup
setup.hook_startup(self)
vis_order = setup.vis_order
if vis_order is None:
vis_order = setup.element_order
if vis_order != setup.element_order:
vis_discr = self.rcon.make_discretization(self.discr.mesh,
order=vis_order,
debug=setup.dg_debug)
from hedge.discretization import Projector
vis_proj = Projector(self.discr, vis_discr)
else:
vis_discr = self.discr
def vis_proj(f):
return f
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(vis_discr)
fields = self.fields
self.observer.set_fields_and_state(fields, self.state)
from hedge.tools import make_obj_array
from pyrticle.cloud import TimesteppablePicState
def visualize(observer):
sub_timer = self.vis_timer.start_sub_timer()
import os.path
visf = vis.make_file(
os.path.join(setup.output_path, setup.vis_pattern % step))
self.method.add_to_vis(vis,
visf,
observer.state,
time=t,
step=step)
vis.add_data(
visf, [(name, vis_proj(fld))
for name, fld in setup.hook_vis_quantities(observer)],
time=t,
step=step)
setup.hook_visualize(self, vis, visf, observer)
visf.close()
sub_timer.stop().submit()
from hedge.timestep.multirate_ab import TwoRateAdamsBashforthTimeStepper
if not isinstance(self.stepper, TwoRateAdamsBashforthTimeStepper):
def rhs(t, fields_and_state):
fields, ts_state = fields_and_state
state_f = lambda: ts_state.state
fields_f = lambda: fields
fields_rhs = (self.f_rhs_calculator(t, fields_f, state_f) +
self.p2f_rhs_calculator(t, fields_f, state_f))
state_rhs = (self.p_rhs_calculator(t, fields_f, state_f) +
self.f2p_rhs_calculator(t, fields_f, state_f))
return make_obj_array([fields_rhs, state_rhs])
step_args = (self.dt, rhs)
else:
def add_unwrap(rhs):
def unwrapping_rhs(t, fields, ts_state):
return rhs(t, fields, lambda: ts_state().state)
return unwrapping_rhs
step_args = ((
add_unwrap(self.f_rhs_calculator),
add_unwrap(self.p2f_rhs_calculator),
add_unwrap(self.f2p_rhs_calculator),
add_unwrap(self.p_rhs_calculator),
), )
y = make_obj_array(
[fields, TimesteppablePicState(self.method, self.state)])
del self.state
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(max_steps=self.nsteps,
logmgr=self.logmgr,
max_dt_getter=lambda t: self.dt)
for step, t, dt in step_it:
self.method.upkeep(y[1].state)
if step % setup.vis_interval == 0:
visualize(self.observer)
y = self.stepper(y, t, *step_args)
fields, ts_state = y
self.observer.set_fields_and_state(fields, ts_state.state)
setup.hook_after_step(self, self.observer)
finally:
vis.close()
self.discr.close()
self.logmgr.save()
setup.hook_when_done(self)
def prepare_with_pointwise_projection_and_basis_reduction(self):
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
min_s_values = []
max_s_values = []
cond_s_values = []
basis_len_vec = discr.volume_zeros()
el_condition_vec = discr.volume_zeros()
point_count_vec = discr.volume_zeros()
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
mode_id_to_index = dict(
(bid, i)
for i, bid in enumerate(ldis.generate_mode_identifiers()))
for el in eg.members:
basis = list(
zip(ldis.generate_mode_identifiers(),
ldis.basis_functions()))
eog, points = self.find_points_in_element(
el, self.el_tolerance)
while True:
scaled_vdm = self.scaled_vandermonde(
el, eog, points, [bf for bid, bf in basis])
max_bid_sum = max(sum(bid) for bid, bf in basis)
killable_basis_elements = [
(i, bid) for i, (bid, bf) in enumerate(basis)
if sum(bid) == max_bid_sum
]
try:
u, s, vt = svd = la.svd(scaled_vdm)
thresh = (numpy.finfo(float).eps *
max(scaled_vdm.shape) * s[0])
assert s[-1] == numpy.min(s)
assert s[0] == numpy.max(s)
# Imagine that--s can have negative entries.
# (AK: I encountered one negative zero.)
if len(basis) > len(points) or numpy.abs(
s[0] / s[-1]) > 10:
retry = True
# badly conditioned, kill a basis entry
vti = vt[-1]
from pytools import argmax2
kill_idx, kill_bid = argmax2(
((j, bid), abs(vti[j]))
for j, bid in killable_basis_elements)
assert kill_bid == basis[kill_idx][0]
basis.pop(kill_idx)
else:
retry = False
except la.LinAlgError:
# SVD likely didn't converge. Lacking an SVD, we don't have
# much guidance on what modes to kill. Any of the killable
# ones will do.
# Bang, you're dead.
basis.pop(killable_basis_elements[0][0])
retry = True
if not retry:
break
if len(basis) == 1:
raise RuntimeError(
"basis reduction has killed almost the entire basis on element %d"
% el.id)
if ldis.node_count() > len(basis):
print "element %d: #nodes=%d, killed modes=%d" % (
el.id,
ldis.node_count(),
ldis.node_count() - len(basis),
)
basis_len_vec[discr.find_el_range(el.id)] = len(basis)
el_condition_vec[discr.find_el_range(el.id)] = s[0] / s[-1]
point_count_vec[discr.find_el_range(el.id)] = len(points)
min_s_values.append(min(s))
max_s_values.append(max(s))
cond_s_values.append(max(s) / min(s))
self.make_pointwise_interpolation_matrix(
eog,
eg,
el,
ldis,
svd,
scaled_vdm,
basis_subset=[mode_id_to_index[bid] for bid, bf in basis])
backend.elements_on_grid.append(eog)
# visualize basis length for each element
if set(["depositor", "vis_files"]) < self.method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("rec-debug")
vis.add_data(visf, [
("basis_len", basis_len_vec),
("el_condition", el_condition_vec),
("point_count", point_count_vec),
])
visf.close()
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0] *
(len(backend.bricks) + 1))
# print some statistics
self.generate_point_statistics()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda", "mpi"])
if rcon.is_head_rank:
mesh = make_wingmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
wing = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=wing.gamma,
mu=wing.mu,
prandtl=wing.prandtl,
spec_gas_const=wing.spec_gas_const,
bc_inflow=wing,
bc_outflow=wing,
bc_noslip=wing,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code"
"cuda_no_metis",
],
default_scalar_type=numpy.float64,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = wing.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w",
rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.6 * op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("wing-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
from hedge.discretization import ones_on_boundary
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
t += dt
finally:
vis.close()
logmgr.save()
discr.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda"])
if rcon.is_head_rank:
mesh = make_boxmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
box = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=box.gamma,
mu=box.mu,
prandtl=box.prandtl,
spec_gas_const=box.spec_gas_const,
bc_inflow=box,
bc_outflow=box,
bc_noslip=box,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
#"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code",
"cuda_no_plan_el_local",
],
default_scalar_type=numpy.float32,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer # noqa
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = box.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w",
rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1",
"Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
logmgr.add_quantity(ChangeSinceLastStep())
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("box-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
# ("rhs_rho", discr.convert_volume(
# op.rho(rhs_fields), kind="numpy")),
# ("rhs_e", discr.convert_volume(
# op.e(rhs_fields), kind="numpy")),
# ("rhs_rho_u", discr.convert_volume(
# op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.save()
discr.close()
def initialize(self, method):
Depositor.initialize(self, method)
backend_class = getattr(
_internal,
"GridFindDepositor" + method.get_dimensionality_suffix())
backend = self.backend = backend_class(method.mesh_data)
discr = method.discretization
grid_node_num_to_nodes = {}
if self.brick_generator is None:
bbox_min, bbox_max = discr.mesh.bounding_box()
max_bbox_size = max(bbox_max - bbox_min)
self.brick_generator = SingleBrickGenerator(mesh_margin=1e-3 *
max_bbox_size,
overresolve=0.2)
from pyrticle._internal import Brick
for i, (stepwidths, origin,
dims) in enumerate(self.brick_generator(discr)):
backend.bricks.append(
Brick(i, backend.grid_node_count(), stepwidths, origin, dims))
from pyrticle._internal import BoxFloat
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
el_bbox = BoxFloat(*el.bounding_box(discr.mesh.points))
el_slice = discr.find_el_range(el.id)
for brk in backend.bricks:
if brk.bounding_box().intersect(el_bbox).is_empty():
continue
for node_num in range(el_slice.start, el_slice.stop):
try:
cell_number = brk.which_cell(discr.nodes[node_num])
except ValueError:
pass
else:
grid_node_num_to_nodes.setdefault(
brk.index(cell_number), []).append(node_num)
from pytools import flatten
unassigned_nodes = (set(xrange(len(discr))) -
set(flatten(grid_node_num_to_nodes.itervalues())))
if unassigned_nodes:
raise RuntimeError(
"dep_grid_find: unassigned mesh nodes found. "
"you should specify a mesh_margin when generating "
"bricks")
usecounts = numpy.zeros((backend.grid_node_count(), ))
for gnn in xrange(backend.grid_node_count()):
grid_nodes = grid_node_num_to_nodes.get(gnn, [])
usecounts[gnn] = len(grid_nodes)
backend.node_number_list_starts.append(
len(backend.node_number_lists))
backend.node_number_lists.extend(grid_nodes)
backend.node_number_list_starts.append(len(backend.node_number_lists))
if "depositor" in method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("grid-find-debug")
vis.add_data(visf, [])
self.visualize_grid_quantities(visf, [("usecounts", usecounts)])
visf.close()
if "interactive" in cloud.debug:
from matplotlib.pylab import hist, show
hist(usecounts, bins=20)
show()
def main():
import logging
logging.basicConfig(level=logging.INFO)
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
if True:
mesh = make_squaremesh()
else:
from hedge.mesh import make_rect_mesh
mesh = make_rect_mesh(
boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"],
max_area=0.1)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script(".")
for order in [3]:
from gas_dynamics_initials import UniformMachFlow
square = UniformMachFlow(gaussian_pulse_at=numpy.array([-2, 2]),
pulse_magnitude=0.003)
from hedge.models.gas_dynamics import (
GasDynamicsOperator,
GammaLawEOS)
op = GasDynamicsOperator(dimensions=2,
equation_of_state=GammaLawEOS(square.gamma), mu=square.mu,
prandtl=square.prandtl, spec_gas_const=square.spec_gas_const,
bc_inflow=square, bc_outflow=square, bc_noslip=square,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan",
"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"dump_op_code"
#"cuda_no_plan_el_local"
],
default_scalar_type=numpy.float64,
tune_for=op.op_template(),
quad_min_degrees={
"gasdyn_vol": 3*order,
"gasdyn_face": 3*order,
}
)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
from hedge.timestep.runge_kutta import (
LSRK4TimeStepper, ODE23TimeStepper, ODE45TimeStepper)
from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type,
#vector_primitive_factory=discr.get_vector_primitive_factory())
stepper = ODE23TimeStepper(dtype=discr.default_scalar_type,
rtol=1e-6,
vector_primitive_factory=discr.get_vector_primitive_factory())
# Dumka works kind of poorly
#stepper = Dumka3TimeStepper(dtype=discr.default_scalar_type,
#rtol=1e-7, pol_index=2,
#vector_primitive_factory=discr.get_vector_primitive_factory())
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, rtol=1e-7)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("cns-square-sp-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1", "Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
#logmgr.add_quantity(ChangeSinceLastStep())
add_simulation_quantities(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# filter setup ------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(discr,
ExponentialFilterResponseFunction(min_amplification=0.95, order=6))
# timestep loop -------------------------------------------------------
fields = square.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1000,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
model_stepper = LSRK4TimeStepper()
next_dt = op.estimate_timestep(discr,
stepper=model_stepper, t=0,
max_eigenvalue=max_eigval[0])
for step, t, dt in step_it:
#if (step % 10000 == 0): #and step < 950000) or (step % 500 == 0 and step > 950000):
#if False:
if step % 5 == 0:
visf = vis.make_file("square-%d-%06d" % (order, step))
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
if stepper.adaptive:
fields, t, taken_dt, next_dt = stepper(fields, t, dt, rhs)
else:
taken_dt = dt
fields = stepper(fields, t, dt, rhs)
dt = op.estimate_timestep(discr,
stepper=model_stepper, t=0,
max_eigenvalue=max_eigval[0])
#fields = mode_filter(fields)
finally:
vis.close()
logmgr.save()
discr.close()
def test_2d_gauss_theorem():
"""Verify Gauss's theorem explicitly on a mesh"""
from hedge.mesh.generator import make_disk_mesh
from math import sin, cos
from numpy import dot
mesh = make_disk_mesh()
order = 2
discr = discr_class(mesh,
order=order,
debug=discr_class.noninteractive_debug_flags())
ref_discr = discr_class(mesh, order=order)
from hedge.flux import make_normal, FluxScalarPlaceholder
normal = make_normal(discr.dimensions)
flux_f_ph = FluxScalarPlaceholder(0)
one_sided_x = flux_f_ph.int * normal[0]
one_sided_y = flux_f_ph.int * normal[1]
def f1(x, el):
return sin(3 * x[0]) + cos(3 * x[1])
def f2(x, el):
return sin(2 * x[0]) + cos(x[1])
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
f1_v = discr.interpolate_volume_function(f1)
f2_v = discr.interpolate_volume_function(f2)
from hedge.optemplate import BoundaryPair, Field, make_nabla, \
get_flux_operator
nabla = make_nabla(discr.dimensions)
divergence = nabla[0].apply(discr, f1_v) + nabla[1].apply(discr, f2_v)
int_div = discr.integral(divergence)
flux_optp = (
get_flux_operator(one_sided_x)(BoundaryPair(Field("f1"),
Field("fz"))) +
get_flux_operator(one_sided_y)(BoundaryPair(Field("f2"), Field("fz"))))
from hedge.mesh import TAG_ALL
bdry_val = discr.compile(flux_optp)(f1=f1_v,
f2=f2_v,
fz=discr.boundary_zeros(TAG_ALL))
ref_bdry_val = ref_discr.compile(flux_optp)(
f1=f1_v, f2=f2_v, fz=discr.boundary_zeros(TAG_ALL))
boundary_int = dot(bdry_val, ones)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
from hedge.tools import make_obj_array
from hedge.mesh import TAG_ALL
vis.add_data(visf, [
("bdry", bdry_val),
("ref_bdry", ref_bdry_val),
("div", divergence),
("f", make_obj_array([f1_v, f2_v])),
("n",
discr.volumize_boundary_field(discr.boundary_normals(TAG_ALL),
TAG_ALL)),
],
expressions=[("bdiff", "bdry-ref_bdry")])
#print abs(boundary_int-int_div)
assert abs(boundary_int - int_div) < 5e-15
def inner_run(self):
t = 0
setup = self.setup
setup.hook_startup(self)
vis_order = setup.vis_order
if vis_order is None:
vis_order = setup.element_order
if vis_order != setup.element_order:
vis_discr = self.rcon.make_discretization(self.discr.mesh,
order=vis_order, debug=setup.dg_debug)
from hedge.discretization import Projector
vis_proj = Projector(self.discr, vis_discr)
else:
vis_discr = self.discr
def vis_proj(f):
return f
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(vis_discr)
fields = self.fields
self.observer.set_fields_and_state(fields, self.state)
from hedge.tools import make_obj_array
from pyrticle.cloud import TimesteppablePicState
def visualize(observer):
sub_timer = self.vis_timer.start_sub_timer()
import os.path
visf = vis.make_file(os.path.join(
setup.output_path, setup.vis_pattern % step))
self.method.add_to_vis(vis, visf, observer.state, time=t, step=step)
vis.add_data(visf,
[(name, vis_proj(fld))
for name, fld in setup.hook_vis_quantities(observer)],
time=t, step=step)
setup.hook_visualize(self, vis, visf, observer)
visf.close()
sub_timer.stop().submit()
from hedge.timestep.multirate_ab import TwoRateAdamsBashforthTimeStepper
if not isinstance(self.stepper, TwoRateAdamsBashforthTimeStepper):
def rhs(t, fields_and_state):
fields, ts_state = fields_and_state
state_f = lambda: ts_state.state
fields_f = lambda: fields
fields_rhs = (
self.f_rhs_calculator(t, fields_f, state_f)
+ self.p2f_rhs_calculator(t, fields_f, state_f))
state_rhs = (
self.p_rhs_calculator(t, fields_f, state_f)
+ self.f2p_rhs_calculator(t, fields_f, state_f))
return make_obj_array([fields_rhs, state_rhs])
step_args = (self.dt, rhs)
else:
def add_unwrap(rhs):
def unwrapping_rhs(t, fields, ts_state):
return rhs(t, fields, lambda: ts_state().state)
return unwrapping_rhs
step_args = ((
add_unwrap(self.f_rhs_calculator),
add_unwrap(self.p2f_rhs_calculator),
add_unwrap(self.f2p_rhs_calculator),
add_unwrap(self.p_rhs_calculator),
),)
y = make_obj_array([
fields,
TimesteppablePicState(self.method, self.state)
])
del self.state
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
max_steps=self.nsteps,
logmgr=self.logmgr,
max_dt_getter=lambda t: self.dt)
for step, t, dt in step_it:
self.method.upkeep(y[1].state)
if step % setup.vis_interval == 0:
visualize(self.observer)
y = self.stepper(y, t, *step_args)
fields, ts_state = y
self.observer.set_fields_and_state(fields, ts_state.state)
setup.hook_after_step(self, self.observer)
finally:
vis.close()
self.discr.close()
self.logmgr.save()
setup.hook_when_done(self)
def run_setup(units, casename, setup, discr, pusher, visualize=False):
from hedge.timestep.runge_kutta import LSRK4TimeStepper
from hedge.visualization import SiloVisualizer
from hedge.models.em import MaxwellOperator
vis = SiloVisualizer(discr)
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
method = PicMethod(discr, units,
ShapeFunctionDepositor(),
pusher(),
3, 3, debug=set(["verbose_vis"]))
e, h = setup.fields(discr)
b = units.MU0 * h
init_positions = setup.positions(0)
init_velocities = setup.velocities(0)
nparticles = len(init_positions)
state = method.make_state()
method.add_particles(state,
zip(init_positions, init_velocities,
nparticles * [setup.charge],
nparticles * [units.EL_MASS],
),
nparticles)
final_time = setup.final_time()
nsteps = setup.nsteps()
dt = final_time/nsteps
# timestepping ------------------------------------------------------------
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(
epsilon=units.EPSILON0,
mu=units.MU0,
flux_type=1)
fields = max_op.assemble_eh(e, h)
from pyrticle.cloud import \
FieldToParticleRhsCalculator, \
ParticleRhsCalculator
p_rhs_calculator = ParticleRhsCalculator(method, max_op)
f2p_rhs_calculator = FieldToParticleRhsCalculator(method, max_op)
def rhs(t, ts_state):
return (p_rhs_calculator(t, lambda: fields, lambda: ts_state.state)
+ f2p_rhs_calculator(t, lambda: fields, lambda: ts_state.state))
stepper = LSRK4TimeStepper()
t = 0
bbox = discr.mesh.bounding_box()
z_period = bbox[1][2] - bbox[0][2]
def check_result():
from hedge.tools import cross
deriv_dt = 1e-12
dim = discr.dimensions
true_x = setup.positions(t)
true_v = setup.velocities(t)
true_f = [(p2-p1)/(2*deriv_dt)
for p1, p2 in zip(setup.momenta(t-deriv_dt), setup.momenta(t+deriv_dt))]
state = ts_state.state
from pyrticle.tools import NumberShiftableVector
vis_info = state.vis_listener.particle_vis_map
sim_x = state.positions
sim_v = method.velocities(state)
sim_f = NumberShiftableVector.unwrap(
vis_info["mag_force"] + vis_info["el_force"])
sim_el_f = NumberShiftableVector.unwrap(vis_info["el_force"])
sim_mag_f = NumberShiftableVector.unwrap(vis_info["mag_force"])
local_e = setup.e()
local_b = units.MU0 * setup.h()
x_err = 0
v_err = 0
f_err = 0
for i in range(len(state)):
#real_f = numpy.array(cross(sim_v, setup.charge*local_b)) + setup.charge*local_e
my_true_x = true_x[i]
my_true_x[2] = my_true_x[2] % z_period
if False and i == 0:
#print "particle %d" % i
print "pos:", la.norm(true_x[i]-sim_x[i])/la.norm(true_x[i])
#print "vel:", la.norm(true_v[i]-sim_v[i])/la.norm(true_v[i])
#print "force:", la.norm(true_f[i]-sim_f[i])/la.norm(true_f[i])
print "pos:", true_x[i], sim_x[i]
#print "vel:", true_v[i], sim_v[i]
#print "force:", true_f[i], sim_f[i]
#print "forces%d:..." % i, sim_el_f[i], sim_mag_f[i]
#print "acc%d:" % i, la.norm(a-sim_a)
#u = numpy.vstack((v, sim_v, f, sim_f, real_f))
#print "acc%d:\n%s" % (i, u)
#raw_input()
def rel_err(sim, true):
return la.norm(true-sim)/la.norm(true)
x_err = max(x_err, rel_err(sim_x[i], my_true_x))
v_err = max(v_err, rel_err(sim_v[i], true_v[i]))
f_err = max(f_err, rel_err(sim_f[i], true_f[i]))
return x_err, v_err, f_err
# make sure verbose-vis fields are filled
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
del state
rhs(t, ts_state)
errors = (0, 0, 0)
for step in xrange(nsteps):
if step % int(setup.nsteps()/300) == 0:
errors = tuple(
max(old_err, new_err)
for old_err, new_err in zip(errors, check_result()))
if visualize:
visf = vis.make_file("%s-%04d" % (casename, step))
method.add_to_vis(vis, visf, ts_state.state, time=t, step=step)
if True:
vis.add_data(visf, [ ("e", e), ("h", h), ],
time=t, step=step)
else:
vis.add_data(visf, [], time=t, step=step)
visf.close()
method.upkeep(ts_state.state)
ts_state = stepper(ts_state, t, dt, rhs)
t += dt
assert errors[0] < 2e-12, casename+"-pos"
assert errors[1] < 2e-13, casename+"-vel"
assert errors[2] < 2e-4, casename+"-acc"
vis.close()
def check_time_harmonic_solution(discr, mode, c_sol):
from hedge.discretization import bind_nabla, bind_mass_matrix
from hedge.visualization import SiloVisualizer
from hedge.silo import SiloFile
from hedge.tools import dot, cross
from hedge.silo import DB_VARTYPE_VECTOR
def curl(field):
return cross(nabla, field)
vis = SiloVisualizer(discr)
nabla = bind_nabla(discr)
mass = bind_mass_matrix(discr)
def rel_l2_error(err, base):
def l2_norm(field):
return sqrt(dot(field, mass * field))
base_l2 = l2_norm(base)
err_l2 = l2_norm(err)
if base_l2 == 0:
if err_l2 == 0:
return 0.
else:
return float("inf")
else:
return err_l2 / base_l2
dt = 0.1
for step in range(10):
t = step * dt
mode.set_time(t)
fields = discr.interpolate_volume_function(c_sol)
er = fields[0:3]
hr = fields[3:6]
ei = fields[6:9]
hi = fields[9:12]
silo = SiloFile("em-complex-%04d.silo" % step)
vis.add_to_silo(silo,
vectors=[
("curl_er", curl(er)),
("om_hi", -mode.mu * mode.omega * hi),
("curl_hr", curl(hr)),
("om_ei", mode.epsilon * mode.omega * hi),
],
expressions=[
("diff_er", "curl_er-om_hi", DB_VARTYPE_VECTOR),
("diff_hr", "curl_hr-om_ei", DB_VARTYPE_VECTOR),
],
write_coarse_mesh=True,
time=t,
step=step)
er_res = curl(er) + mode.mu * mode.omega * hi
ei_res = curl(ei) - mode.mu * mode.omega * hr
hr_res = curl(hr) - mode.epsilon * mode.omega * ei
hi_res = curl(hi) + mode.epsilon * mode.omega * er
print "time=%f, rel l2 residual in Re[E]=%g\tIm[E]=%g\tRe[H]=%g\tIm[H]=%g" % (
t,
rel_l2_error(er_res, er),
rel_l2_error(ei_res, ei),
rel_l2_error(hr_res, hr),
rel_l2_error(hi_res, hi),
)
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda"])
if rcon.is_head_rank:
mesh = make_boxmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
box = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=box.gamma, mu=box.mu,
prandtl=box.prandtl, spec_gas_const=box.spec_gas_const,
bc_inflow=box, bc_outflow=box, bc_noslip=box,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=[
#"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code",
"cuda_no_plan_el_local",
],
default_scalar_type=numpy.float32,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer # noqa
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = box.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1", "Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
logmgr.add_quantity(ChangeSinceLastStep())
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("box-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
vis.add_data(visf,
[
("rho", discr.convert_volume(
op.rho(fields), kind="numpy")),
("e", discr.convert_volume(
op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(
op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(
op.u(fields), kind="numpy")),
# ("rhs_rho", discr.convert_volume(
# op.rho(rhs_fields), kind="numpy")),
# ("rhs_e", discr.convert_volume(
# op.e(rhs_fields), kind="numpy")),
# ("rhs_rho_u", discr.convert_volume(
# op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.save()
discr.close()
def initialize(self, method):
Depositor.initialize(self, method)
backend_class = getattr(_internal, "GridFindDepositor"
+ method.get_dimensionality_suffix())
backend = self.backend = backend_class(method.mesh_data)
discr = method.discretization
grid_node_num_to_nodes = {}
if self.brick_generator is None:
bbox_min, bbox_max = discr.mesh.bounding_box()
max_bbox_size = max(bbox_max-bbox_min)
self.brick_generator = SingleBrickGenerator(
mesh_margin=1e-3*max_bbox_size,
overresolve=0.2)
from pyrticle._internal import Brick
for i, (stepwidths, origin, dims) in enumerate(
self.brick_generator(discr)):
backend.bricks.append(
Brick(i, backend.grid_node_count(), stepwidths, origin, dims))
from pyrticle._internal import BoxFloat
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
el_bbox = BoxFloat(*el.bounding_box(discr.mesh.points))
el_slice = discr.find_el_range(el.id)
for brk in backend.bricks:
if brk.bounding_box().intersect(el_bbox).is_empty():
continue
for node_num in range(el_slice.start, el_slice.stop):
try:
cell_number = brk.which_cell(
discr.nodes[node_num])
except ValueError:
pass
else:
grid_node_num_to_nodes.setdefault(
brk.index(cell_number), []).append(node_num)
from pytools import flatten
unassigned_nodes = (set(xrange(len(discr)))
- set(flatten(grid_node_num_to_nodes.itervalues())))
if unassigned_nodes:
raise RuntimeError("dep_grid_find: unassigned mesh nodes found. "
"you should specify a mesh_margin when generating "
"bricks")
usecounts = numpy.zeros(
(backend.grid_node_count(),))
for gnn in xrange(backend.grid_node_count()):
grid_nodes = grid_node_num_to_nodes.get(gnn, [])
usecounts[gnn] = len(grid_nodes)
backend.node_number_list_starts.append(len(backend.node_number_lists))
backend.node_number_lists.extend(grid_nodes)
backend.node_number_list_starts.append(len(backend.node_number_lists))
if "depositor" in method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("grid-find-debug")
vis.add_data(visf, [])
self.visualize_grid_quantities(visf, [
("usecounts", usecounts)
])
visf.close()
if "interactive" in cloud.debug:
from matplotlib.pylab import hist, show
hist(usecounts, bins=20)
show()
def compute_initial_condition(rcon,
discr,
method,
state,
maxwell_op,
potential_bc,
force_zero=False):
from hedge.models.poisson import PoissonOperator
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import ConstantGivenFunction, GivenVolumeInterpolant
def rel_l2_error(field, true):
from hedge.tools import relative_error
return relative_error(discr.norm(field - true), discr.norm(true))
mean_beta = method.mean_beta(state)
gamma = method.units.gamma_from_beta(mean_beta)
# see doc/notes.tm for derivation of IC
def make_scaling_matrix(beta_scale, other_scale):
if la.norm(mean_beta) < 1e-10:
return other_scale * numpy.eye(discr.dimensions)
else:
beta_unit = mean_beta / la.norm(mean_beta)
return (
other_scale * numpy.identity(discr.dimensions) +
(beta_scale - other_scale) * numpy.outer(beta_unit, beta_unit))
poisson_op = PoissonOperator(discr.dimensions,
diffusion_tensor=make_scaling_matrix(
1 / gamma**2, 1),
dirichlet_tag=TAG_ALL,
neumann_tag=TAG_NONE,
dirichlet_bc=potential_bc)
rho_prime = method.deposit_rho(state)
rho_tilde = rho_prime / gamma
bound_poisson = poisson_op.bind(discr)
if force_zero:
phi_tilde = discr.volume_zeros()
else:
from hedge.iterative import parallel_cg
phi_tilde = -parallel_cg(
rcon,
-bound_poisson,
bound_poisson.prepare_rhs(rho_tilde / maxwell_op.epsilon),
debug=40 if "poisson" in method.debug else False,
tol=1e-10)
from hedge.tools import ptwise_dot
from hedge.models.nd_calculus import GradientOperator
e_tilde = ptwise_dot(
2, 1, make_scaling_matrix(1 / gamma, 1),
GradientOperator(discr.dimensions).bind(discr)(phi_tilde))
e_prime = ptwise_dot(2, 1, make_scaling_matrix(1, gamma), e_tilde)
from pyrticle.tools import make_cross_product
v_e_to_h_cross = make_cross_product(method, maxwell_op, "v", "e", "h")
h_prime = (1 / maxwell_op.mu) * gamma / maxwell_op.c * v_e_to_h_cross(
mean_beta, e_tilde)
if "ic" in method.debug:
deposited_charge = discr.integral(rho_prime)
real_charge = numpy.sum(state.charges)
print "charge: supposed=%g deposited=%g error=%g %%" % (
real_charge, deposited_charge,
100 * abs(deposited_charge - real_charge) / abs(real_charge))
from hedge.models.nd_calculus import DivergenceOperator
bound_div_op = DivergenceOperator(discr.dimensions).bind(discr)
d_tilde = maxwell_op.epsilon * e_tilde
d_prime = maxwell_op.epsilon * e_prime
#divD_prime_ldg = bound_poisson.div(d_prime)
#divD_prime_ldg2 = bound_poisson.div(d_prime, maxwell_op.epsilon*gamma*phi_tilde)
from hedge.optemplate import InverseMassOperator
divD_prime_ldg3 = maxwell_op.epsilon*\
(InverseMassOperator().apply(discr, bound_poisson.op(gamma*phi_tilde)))
divD_prime_central = bound_div_op(d_prime)
print "l2 div D_prime error central: %g" % \
rel_l2_error(divD_prime_central, rho_prime)
#print "l2 div D_prime error ldg: %g" % \
#rel_l2_error(divD_prime_ldg, rho_prime)
#print "l2 div D_prime error ldg with phi: %g" % \
#rel_l2_error(divD_prime_ldg2, rho_prime)
print "l2 div D_prime error ldg with phi 3: %g" % \
rel_l2_error(divD_prime_ldg3, rho_prime)
if "vis_files" in method.debug:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("ic")
vis.add_data(
visf,
[
("phi_moving", phi_tilde),
("rho_moving", rho_tilde),
("e_moving", e_tilde),
("rho_lab", rho_prime),
#("divD_lab_ldg", divD_prime_ldg),
#("divD_lab_ldg2", divD_prime_ldg2),
#("divD_lab_ldg3", divD_prime_ldg3),
("divD_lab_central", divD_prime_central),
("e_lab", e_prime),
("h_lab", h_prime),
],
)
method.add_to_vis(vis, visf, state)
visf.close()
return maxwell_op.assemble_fields(e=e_prime, h=h_prime, discr=discr)
def check_time_harmonic_solution(discr, mode, c_sol):
from hedge.discretization import bind_nabla, bind_mass_matrix
from hedge.visualization import SiloVisualizer
from hedge.silo import SiloFile
from hedge.tools import dot, cross
from hedge.silo import DB_VARTYPE_VECTOR
def curl(field):
return cross(nabla, field)
vis = SiloVisualizer(discr)
nabla = bind_nabla(discr)
mass = bind_mass_matrix(discr)
def rel_l2_error(err, base):
def l2_norm(field):
return sqrt(dot(field, mass*field))
base_l2 = l2_norm(base)
err_l2 = l2_norm(err)
if base_l2 == 0:
if err_l2 == 0:
return 0.
else:
return float("inf")
else:
return err_l2/base_l2
dt = 0.1
for step in range(10):
t = step*dt
mode.set_time(t)
fields = discr.interpolate_volume_function(c_sol)
er = fields[0:3]
hr = fields[3:6]
ei = fields[6:9]
hi = fields[9:12]
silo = SiloFile("em-complex-%04d.silo" % step)
vis.add_to_silo(silo,
vectors=[
("curl_er", curl(er)),
("om_hi", -mode.mu*mode.omega*hi),
("curl_hr", curl(hr)),
("om_ei", mode.epsilon*mode.omega*hi),
],
expressions=[
("diff_er", "curl_er-om_hi", DB_VARTYPE_VECTOR),
("diff_hr", "curl_hr-om_ei", DB_VARTYPE_VECTOR),
],
write_coarse_mesh=True,
time=t, step=step
)
er_res = curl(er) + mode.mu *mode.omega*hi
ei_res = curl(ei) - mode.mu *mode.omega*hr
hr_res = curl(hr) - mode.epsilon*mode.omega*ei
hi_res = curl(hi) + mode.epsilon*mode.omega*er
print "time=%f, rel l2 residual in Re[E]=%g\tIm[E]=%g\tRe[H]=%g\tIm[H]=%g" % (
t,
rel_l2_error(er_res, er),
rel_l2_error(ei_res, ei),
rel_l2_error(hr_res, hr),
rel_l2_error(hi_res, hi),
)
def run_setup(units, casename, setup, discr, pusher, visualize=False):
from hedge.timestep.runge_kutta import LSRK4TimeStepper
from hedge.visualization import SiloVisualizer
from hedge.models.em import MaxwellOperator
vis = SiloVisualizer(discr)
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
method = PicMethod(discr,
units,
ShapeFunctionDepositor(),
pusher(),
3,
3,
debug=set(["verbose_vis"]))
e, h = setup.fields(discr)
b = units.MU0 * h
init_positions = setup.positions(0)
init_velocities = setup.velocities(0)
nparticles = len(init_positions)
state = method.make_state()
method.add_particles(
state,
zip(
init_positions,
init_velocities,
nparticles * [setup.charge],
nparticles * [units.EL_MASS],
), nparticles)
final_time = setup.final_time()
nsteps = setup.nsteps()
dt = final_time / nsteps
# timestepping ------------------------------------------------------------
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(epsilon=units.EPSILON0, mu=units.MU0, flux_type=1)
fields = max_op.assemble_eh(e, h)
from pyrticle.cloud import \
FieldToParticleRhsCalculator, \
ParticleRhsCalculator
p_rhs_calculator = ParticleRhsCalculator(method, max_op)
f2p_rhs_calculator = FieldToParticleRhsCalculator(method, max_op)
def rhs(t, ts_state):
return (p_rhs_calculator(t, lambda: fields, lambda: ts_state.state) +
f2p_rhs_calculator(t, lambda: fields, lambda: ts_state.state))
stepper = LSRK4TimeStepper()
t = 0
bbox = discr.mesh.bounding_box()
z_period = bbox[1][2] - bbox[0][2]
def check_result():
from hedge.tools import cross
deriv_dt = 1e-12
dim = discr.dimensions
true_x = setup.positions(t)
true_v = setup.velocities(t)
true_f = [(p2 - p1) / (2 * deriv_dt) for p1, p2 in zip(
setup.momenta(t - deriv_dt), setup.momenta(t + deriv_dt))]
state = ts_state.state
from pyrticle.tools import NumberShiftableVector
vis_info = state.vis_listener.particle_vis_map
sim_x = state.positions
sim_v = method.velocities(state)
sim_f = NumberShiftableVector.unwrap(vis_info["mag_force"] +
vis_info["el_force"])
sim_el_f = NumberShiftableVector.unwrap(vis_info["el_force"])
sim_mag_f = NumberShiftableVector.unwrap(vis_info["mag_force"])
local_e = setup.e()
local_b = units.MU0 * setup.h()
x_err = 0
v_err = 0
f_err = 0
for i in range(len(state)):
#real_f = numpy.array(cross(sim_v, setup.charge*local_b)) + setup.charge*local_e
my_true_x = true_x[i]
my_true_x[2] = my_true_x[2] % z_period
if False and i == 0:
#print "particle %d" % i
print "pos:", la.norm(true_x[i] - sim_x[i]) / la.norm(
true_x[i])
#print "vel:", la.norm(true_v[i]-sim_v[i])/la.norm(true_v[i])
#print "force:", la.norm(true_f[i]-sim_f[i])/la.norm(true_f[i])
print "pos:", true_x[i], sim_x[i]
#print "vel:", true_v[i], sim_v[i]
#print "force:", true_f[i], sim_f[i]
#print "forces%d:..." % i, sim_el_f[i], sim_mag_f[i]
#print "acc%d:" % i, la.norm(a-sim_a)
#u = numpy.vstack((v, sim_v, f, sim_f, real_f))
#print "acc%d:\n%s" % (i, u)
#raw_input()
def rel_err(sim, true):
return la.norm(true - sim) / la.norm(true)
x_err = max(x_err, rel_err(sim_x[i], my_true_x))
v_err = max(v_err, rel_err(sim_v[i], true_v[i]))
f_err = max(f_err, rel_err(sim_f[i], true_f[i]))
return x_err, v_err, f_err
# make sure verbose-vis fields are filled
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
del state
rhs(t, ts_state)
errors = (0, 0, 0)
for step in xrange(nsteps):
if step % int(setup.nsteps() / 300) == 0:
errors = tuple(
max(old_err, new_err)
for old_err, new_err in zip(errors, check_result()))
if visualize:
visf = vis.make_file("%s-%04d" % (casename, step))
method.add_to_vis(vis, visf, ts_state.state, time=t, step=step)
if True:
vis.add_data(visf, [
("e", e),
("h", h),
],
time=t,
step=step)
else:
vis.add_data(visf, [], time=t, step=step)
visf.close()
method.upkeep(ts_state.state)
ts_state = stepper(ts_state, t, dt, rhs)
t += dt
assert errors[0] < 2e-12, casename + "-pos"
assert errors[1] < 2e-13, casename + "-vel"
assert errors[2] < 2e-4, casename + "-acc"
vis.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
def boundary_tagger(vertices, el, face_nr, all_v):
return ["inflow"]
if rcon.is_head_rank:
from hedge.mesh import make_rect_mesh, \
make_centered_regular_rect_mesh
#mesh = make_rect_mesh((0,0), (10,1), max_area=0.01)
refine = 1
mesh = make_centered_regular_rect_mesh((0,0), (10,1), n=(20,4),
#periodicity=(True, False),
post_refine_factor=refine,
boundary_tagger=boundary_tagger)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
shearflow = SteadyShearFlow()
fields = shearflow.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = shearflow.properties()
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=2, gamma=gamma, mu=mu,
prandtl=prandtl, spec_gas_const=spec_gas_const,
bc_inflow=shearflow, bc_outflow=shearflow, bc_noslip=shearflow,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
# needed to get first estimate of maximum eigenvalue
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-cpu-%d-%d.dat" % (order, refine),
"w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.3,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 10 == 0:
#if False:
visf = vis.make_file("shearflow-%d-%04d" % (order, step))
#true_fields = shearflow.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = shearflow.volume_interpolant(t, discr)
l2_error = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
finally:
vis.close()
logmgr.save()
discr.close()
def prepare_with_pointwise_projection_and_enlargement(self):
tolerance_bound = 1.5
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
cond_claims = 0
min_s_values = []
max_s_values = []
cond_s_values = []
from hedge.discretization import Projector, Discretization
fine_discr = Discretization(discr.mesh, order=8)
proj = Projector(discr, fine_discr)
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(fine_discr)
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
# If the structured Vandermonde matrix is singular,
# enlarge the element tolerance
my_tolerance = self.el_tolerance
orig_point_count = None
while True:
eog, points = self.find_points_in_element(el, my_tolerance)
if orig_point_count is None:
orig_point_count = len(points)
scaled_vdm = self.scaled_vandermonde(
el, eog, points, ldis.basis_functions())
bad_vdm = len(points) < ldis.node_count()
if not bad_vdm:
try:
u, s, vt = svd = la.svd(scaled_vdm)
thresh = (numpy.finfo(float).eps *
max(scaled_vdm.shape) * s[0])
zero_indices = [
i for i, si in enumerate(s) if abs(si) < thresh
]
bad_vdm = bool(zero_indices)
except la.LinAlgError:
bad_vdm = True
if not bad_vdm:
break
my_tolerance += 0.03
if my_tolerance >= tolerance_bound:
from warnings import warn
warn("rec_grid: could not regularize structured "
"vandermonde matrix for el #%d by enlargement" %
el.id)
break
#from pytools import average
#print average(eog.weight_factors), min(s)
#raw_input()
if my_tolerance > self.el_tolerance:
print "element %d: #nodes=%d, orig #sgridpt=%d, extra tol=%g, #extra points=%d" % (
el.id, ldis.node_count(),
orig_point_count, my_tolerance - self.el_tolerance,
len(points) - orig_point_count)
cond_claims += len(points) - orig_point_count
min_s_values.append(min(s))
max_s_values.append(max(s))
cond_s_values.append(max(s) / min(s))
if max(s) / min(s) > 1e2:
for i in range(len(s)):
if s[0] / s[i] > 1e2:
zeroed_mode = vt[i]
zeroed_mode_nodal = numpy.dot(
ldis.vandermonde(), zeroed_mode)
print el.id, i, s[0] / s[i]
fromvec = discr.volume_zeros()
fromvec[discr.find_el_range(
el.id)] = zeroed_mode_nodal
gn = list(eog.grid_nodes)
assert len(gn) == len(u[i])
tovec = numpy.zeros(
(backend.grid_node_count_with_extra(), ),
dtype=float)
tovec[gn] = s[i] * u[i]
usevec = numpy.zeros(
(backend.grid_node_count_with_extra(), ),
dtype=float)
usevec[gn] = 1
visf = vis.make_file("nulled-%04d%02d" %
(el.id, i))
vis.add_data(visf, [("meshmode", proj(fromvec))],
expressions=[
("absmesh", "abs(meshmode)"),
("absgrid", "abs(gridmode)"),
])
self.visualize_grid_quantities(
visf,
[
("gridmode", tovec),
("usevec", usevec),
],
)
visf.close()
#print s
#raw_input()
self.make_pointwise_interpolation_matrix(
eog, eg, el, ldis, svd, scaled_vdm)
backend.elements_on_grid.append(eog)
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0] *
(len(backend.bricks) + 1))
# print some statistics
self.generate_point_statistics(cond_claims)
def test_2d_gauss_theorem():
"""Verify Gauss's theorem explicitly on a mesh"""
from hedge.mesh.generator import make_disk_mesh
from math import sin, cos, sqrt, exp, pi
from numpy import dot
mesh = make_disk_mesh()
order = 2
discr = discr_class(mesh, order=order, debug=discr_class.noninteractive_debug_flags())
ref_discr = discr_class(mesh, order=order)
from hedge.flux import make_normal, FluxScalarPlaceholder
normal = make_normal(discr.dimensions)
flux_f_ph = FluxScalarPlaceholder(0)
one_sided_x = flux_f_ph.int * normal[0]
one_sided_y = flux_f_ph.int * normal[1]
def f1(x, el):
return sin(3 * x[0]) + cos(3 * x[1])
def f2(x, el):
return sin(2 * x[0]) + cos(x[1])
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
f1_v = discr.interpolate_volume_function(f1)
f2_v = discr.interpolate_volume_function(f2)
from hedge.optemplate import BoundaryPair, Field, make_nabla, get_flux_operator
nabla = make_nabla(discr.dimensions)
diff_optp = nabla[0] * Field("f1") + nabla[1] * Field("f2")
divergence = nabla[0].apply(discr, f1_v) + nabla[1].apply(discr, f2_v)
int_div = discr.integral(divergence)
flux_optp = get_flux_operator(one_sided_x)(BoundaryPair(Field("f1"), Field("fz"))) + get_flux_operator(one_sided_y)(
BoundaryPair(Field("f2"), Field("fz"))
)
from hedge.mesh import TAG_ALL
bdry_val = discr.compile(flux_optp)(f1=f1_v, f2=f2_v, fz=discr.boundary_zeros(TAG_ALL))
ref_bdry_val = ref_discr.compile(flux_optp)(f1=f1_v, f2=f2_v, fz=discr.boundary_zeros(TAG_ALL))
boundary_int = dot(bdry_val, ones)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
from hedge.tools import make_obj_array
from hedge.mesh import TAG_ALL
vis.add_data(
visf,
[
("bdry", bdry_val),
("ref_bdry", ref_bdry_val),
("div", divergence),
("f", make_obj_array([f1_v, f2_v])),
("n", discr.volumize_boundary_field(discr.boundary_normals(TAG_ALL), TAG_ALL)),
],
expressions=[("bdiff", "bdry-ref_bdry")],
)
# print abs(boundary_int-int_div)
assert abs(boundary_int - int_div) < 5e-15
def main(write_output=True):
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
gamma = 1.4
# at A=1 we have case of isentropic vortex, source terms
# arise for other values
densityA = 2.0
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 1
mesh = make_centered_regular_rect_mesh((0,-5), (10,5), n=(9,9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4,5]:
discr = rcon.make_discretization(mesh_data, order=order,
debug=[#"cuda_no_plan",
#"print_op_code"
],
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
vis = SiloVisualizer(discr, rcon)
vortex = Vortex(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
fields = vortex.volume_interpolant(0, discr)
sources=SourceTerms(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
from hedge.models.gas_dynamics import (
GasDynamicsOperator, GammaLawEOS)
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(dimensions=2,
mu=0.0, prandtl=0.72, spec_gas_const=287.1,
equation_of_state=GammaLawEOS(vortex.gamma),
bc_inflow=vortex, bc_outflow=vortex, bc_noslip=vortex,
inflow_tag=TAG_ALL, source=sources)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter setup -------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, gamma, 2, op)
# time stepper --------------------------------------------------------
from hedge.timestep import SSPRK3TimeStepper, RK4TimeStepper
#stepper = SSPRK3TimeStepper(limiter=limiter)
#stepper = SSPRK3TimeStepper()
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
t = 0
#fields = limiter(fields)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=.1,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.4*op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 1 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
true_fields = vortex.volume_interpolant(t, discr)
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = vortex.volume_interpolant(t, discr)
l2_error = discr.norm(fields-true_fields)
l2_error_rho = discr.norm(op.rho(fields)-op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields)-op.e(true_fields))
l2_error_rhou = discr.norm(op.rho_u(fields)-op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error_rho)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main():
import logging
logging.basicConfig(level=logging.INFO)
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
if True:
mesh = make_squaremesh()
else:
from hedge.mesh import make_rect_mesh
mesh = make_rect_mesh(
boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"],
max_area=0.1)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script(".")
for order in [3]:
from gas_dynamics_initials import UniformMachFlow
square = UniformMachFlow(gaussian_pulse_at=numpy.array([-2, 2]),
pulse_magnitude=0.003)
from hedge.models.gas_dynamics import (GasDynamicsOperator,
GammaLawEOS)
op = GasDynamicsOperator(dimensions=2,
equation_of_state=GammaLawEOS(square.gamma),
mu=square.mu,
prandtl=square.prandtl,
spec_gas_const=square.spec_gas_const,
bc_inflow=square,
bc_outflow=square,
bc_noslip=square,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
"cuda_no_plan",
"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"dump_op_code"
#"cuda_no_plan_el_local"
],
default_scalar_type=numpy.float64,
tune_for=op.op_template(),
quad_min_degrees={
"gasdyn_vol": 3 * order,
"gasdyn_face": 3 * order,
})
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
from hedge.timestep.runge_kutta import (LSRK4TimeStepper,
ODE23TimeStepper,
ODE45TimeStepper)
from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type,
#vector_primitive_factory=discr.get_vector_primitive_factory())
stepper = ODE23TimeStepper(
dtype=discr.default_scalar_type,
rtol=1e-6,
vector_primitive_factory=discr.get_vector_primitive_factory())
# Dumka works kind of poorly
#stepper = Dumka3TimeStepper(dtype=discr.default_scalar_type,
#rtol=1e-7, pol_index=2,
#vector_primitive_factory=discr.get_vector_primitive_factory())
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, rtol=1e-7)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("cns-square-sp-%d.dat" % order, "w",
rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1",
"Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
#logmgr.add_quantity(ChangeSinceLastStep())
add_simulation_quantities(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# filter setup ------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(
discr,
ExponentialFilterResponseFunction(min_amplification=0.95, order=6))
# timestep loop -------------------------------------------------------
fields = square.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1000,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
model_stepper = LSRK4TimeStepper()
next_dt = op.estimate_timestep(discr,
stepper=model_stepper,
t=0,
max_eigenvalue=max_eigval[0])
for step, t, dt in step_it:
#if (step % 10000 == 0): #and step < 950000) or (step % 500 == 0 and step > 950000):
#if False:
if step % 5 == 0:
visf = vis.make_file("square-%d-%06d" % (order, step))
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf, [
("rho",
discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields),
kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields),
kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
if stepper.adaptive:
fields, t, taken_dt, next_dt = stepper(fields, t, dt, rhs)
else:
taken_dt = dt
fields = stepper(fields, t, dt, rhs)
dt = op.estimate_timestep(discr,
stepper=model_stepper,
t=0,
max_eigenvalue=max_eigval[0])
#fields = mode_filter(fields)
finally:
vis.close()
logmgr.save()
discr.close()