def my_box_mesh(boundary_tagger):
from hedge.mesh.generator import make_rect_mesh
from math import pi
return make_rect_mesh(
b=(2*pi, 3), max_area=0.4,
#periodicity=(True, False),
# meshpy doesn't do periodic at the moment (5/2014)
periodicity=(False, False),
subdivisions=(5, 10),
boundary_tagger=boundary_tagger,
)
def my_box_mesh(boundary_tagger):
from hedge.mesh.generator import make_rect_mesh
from math import pi
return make_rect_mesh(
b=(2 * pi, 3),
max_area=0.4,
#periodicity=(True, False),
# meshpy doesn't do periodic at the moment (5/2014)
periodicity=(False, False),
subdivisions=(5, 10),
boundary_tagger=boundary_tagger,
)
def main(write_output=True):
from math import sin, exp, sqrt # noqa
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(
-0.1,
discr.dimensions,
source_f=sym.CFunction("sin")(
source_omega * sym.ScalarParameter("t")) * sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(10 / dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step * dt
if step % 10 == 0 and write_output:
print step, t, discr.norm(fields[0])
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
vis.close()
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = np.array([0.7, 0.4])
source_width = 1 / 16
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import VariableVelocityStrongWaveOperator
op = VariableVelocityStrongWaveOperator(
c=sym.If(sym.Comparison(np.dot(sym_x, sym_x), "<", 0.4**2), 1, 0.5),
dimensions=discr.dimensions,
source=sym.CFunction("sin")(source_omega * sym.ScalarParameter("t")) *
sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg)
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
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)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep.stability import \
approximate_rk4_relative_imag_stability_region
max_dt = (1 / discr.compile(op.max_eigenvalue_expr())() *
discr.dt_non_geometric_factor() *
discr.dt_geometric_factor() *
approximate_rk4_relative_imag_stability_region(stepper))
if flux_type_arg == "central":
max_dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3,
logmgr=logmgr,
max_dt_getter=lambda t: max_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
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 main():
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import to_obj_array
if rcon.is_head_rank:
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh((-5, -5), (5, 5), max_area=0.01)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [1]:
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "Sod2D-%d" % order)
#vis = SiloVisualizer(discr, rcon)
sod_field = Sod(gamma=1.4)
fields = sod_field.volume_interpolant(0, discr)
from hedge.models.gas_dynamics import GasDynamicsOperator
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(dimensions=2,
gamma=sod_field.gamma,
mu=0.0,
prandtl=sod_field.prandtl,
bc_inflow=sod_field,
bc_outflow=sod_field,
bc_noslip=sod_field,
inflow_tag=TAG_ALL,
source=None)
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, sod_field.gamma, 2, op)
# integrator setup---------------------------------------------------------
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
logmgr = LogManager("euler-%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"])
# filter setup-------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(
discr,
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1.0,
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 % 5 == 0:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
#true_fields = vortex.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", 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", op.rho(rhs_fields)),
#("rhs_e", op.e(rhs_fields)),
#("rhs_rho_u", op.rho_u(rhs_fields)),
],
#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)
# fields = limiter(fields)
# fields = mode_filter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
finally:
vis.close()
logmgr.close()
discr.close()
# not solution, just to check against when making code changes
true_fields = sod_field.volume_interpolant(t, discr)
print discr.norm(fields - true_fields)
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import to_obj_array
if rcon.is_head_rank:
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh((-5, -5), (5, 5), max_area=0.01)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [1]:
discr = rcon.make_discretization(mesh_data, order=order, default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "Sod2D-%d" % order)
# vis = SiloVisualizer(discr, rcon)
sod_field = Sod(gamma=1.4)
fields = sod_field.volume_interpolant(0, discr)
from hedge.models.gas_dynamics import GasDynamicsOperator
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(
dimensions=2,
gamma=sod_field.gamma,
mu=0.0,
prandtl=sod_field.prandtl,
bc_inflow=sod_field,
bc_outflow=sod_field,
bc_noslip=sod_field,
inflow_tag=TAG_ALL,
source=None,
)
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, sod_field.gamma, 2, op)
# integrator setup---------------------------------------------------------
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
logmgr = LogManager("euler-%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"])
# filter setup-------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(discr, ExponentialFilterResponseFunction(min_amplification=0.9, order=4))
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1.0,
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 % 5 == 0:
# if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
# true_fields = vortex.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", 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", op.rho(rhs_fields)),
# ("rhs_e", op.e(rhs_fields)),
# ("rhs_rho_u", op.rho_u(rhs_fields)),
],
# 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)
# fields = limiter(fields)
# fields = mode_filter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
finally:
vis.close()
logmgr.close()
discr.close()
# not solution, just to check against when making code changes
true_fields = sod_field.volume_interpolant(t, discr)
print discr.norm(fields - true_fields)
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind",
dtype=np.float64,
debug=[]):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype)
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE # noqa
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
op = StrongWaveOperator(
-1,
dim,
source_f=sym.CFunction("sin")(
source_omega * sym.ScalarParameter("t")) * sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg)
discr = rcon.make_discretization(mesh_data,
order=4,
debug=debug,
default_scalar_type=dtype,
tune_for=op.op_template())
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
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)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(fields[0], kind="numpy")),
("v", discr.convert_volume(fields[1:], kind="numpy")),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, dtype=np.float32):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
h_fac = 1
mesh = make_rect_mesh(a=(0, 0),
b=(1, 1),
max_area=h_fac**2 * 1e-4,
periodicity=(True, True),
subdivisions=(int(70 / h_fac), int(70 / h_fac)))
from hedge.models.gas_dynamics.lbm import \
D2Q9LBMMethod, LatticeBoltzmannOperator
op = LatticeBoltzmannOperator(D2Q9LBMMethod(), lbm_delta_t=0.001, nu=1e-4)
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data,
order=3,
default_scalar_type=dtype,
debug=["cuda_no_plan"])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(
dtype=dtype,
#vector_primitive_factory=discr.get_vector_primitive_factory()
)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.data import CompiledExpressionData
def ic_expr(t, x, fields):
from hedge.optemplate import CFunction
from pymbolic.primitives import IfPositive
from pytools.obj_array import make_obj_array
tanh = CFunction("tanh")
sin = CFunction("sin")
rho = 1
u0 = 0.05
w = 0.05
delta = 0.05
from hedge.optemplate.primitives import make_common_subexpression as cse
u = cse(
make_obj_array([
IfPositive(x[1] - 1 / 2, u0 * tanh(4 * (3 / 4 - x[1]) / w),
u0 * tanh(4 * (x[1] - 1 / 4) / w)),
u0 * delta * sin(2 * np.pi * (x[0] + 1 / 4))
]), "u")
return make_obj_array([
op.method.f_equilibrium(rho, alpha, u)
for alpha in range(len(op.method))
])
# timestep loop -----------------------------------------------------------
stream_rhs = op.bind_rhs(discr)
collision_update = op.bind(discr, op.collision_update)
get_rho = op.bind(discr, op.rho)
get_rho_u = op.bind(discr, op.rho_u)
f_bar = CompiledExpressionData(ic_expr).volume_interpolant(0, discr)
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))\
.bind(discr)
final_time = 1000
try:
lbm_dt = op.lbm_delta_t
dg_dt = op.estimate_timestep(discr, stepper=stepper)
print dg_dt
dg_steps_per_lbm_step = int(np.ceil(lbm_dt / dg_dt))
dg_dt = lbm_dt / dg_steps_per_lbm_step
lbm_steps = int(final_time // op.lbm_delta_t)
for step in xrange(lbm_steps):
t = step * lbm_dt
if step % 100 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
rho = get_rho(f_bar)
rho_u = get_rho_u(f_bar)
vis.add_data(
visf,
[("fbar%d" % i, discr.convert_volume(f_bar_i, "numpy"))
for i, f_bar_i in enumerate(f_bar)] + [
("rho", discr.convert_volume(rho, "numpy")),
("rho_u", discr.convert_volume(rho_u, "numpy")),
],
time=t,
step=step)
visf.close()
print "step=%d, t=%f" % (step, t)
f_bar = collision_update(f_bar)
for substep in range(dg_steps_per_lbm_step):
f_bar = stepper(f_bar, t + substep * dg_dt, dg_dt, stream_rhs)
#f_bar = mode_filter(f_bar)
finally:
if write_output:
vis.close()
discr.close()
def main(write_output=True, \
dir_tag=TAG_NONE, \
neu_tag=TAG_NONE,\
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1,-1),b=(1,1),max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError, "bad number of dimensions"
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
def source_u(x, el):
x = x - numpy.array([0.7, 0.4])
return exp(-numpy.dot(x, x)*256)
def c_speed(x, el):
if la.norm(x) < 0.4:
return 1
else:
return 0.5
from hedge.models.wave import VariableVelocityStrongWaveOperator
from hedge.data import \
TimeIntervalGivenFunction, \
make_tdep_given
from hedge.mesh import TAG_ALL, TAG_NONE
op = VariableVelocityStrongWaveOperator(
make_tdep_given(c_speed),
discr.dimensions,
source=TimeIntervalGivenFunction(
make_tdep_given(source_u),
0, 0.1),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
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)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import Integral, LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
if flux_type_arg == "central":
dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3, logmgr=logmgr,
max_dt_getter=lambda t: dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", fields[0]),
("v", fields[1:]),
("c", op.c.volume_interpolant(0, discr)),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True):
from math import sin, exp, sqrt
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5,-0.5),b=(0.5,0.5),max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
def source_u(x, el):
x = x - numpy.array([0.1,0.22])
return exp(-numpy.dot(x, x)*128)
from hedge.data import \
make_tdep_given, \
TimeHarmonicGivenFunction, \
TimeIntervalGivenFunction
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(-1, discr.dimensions,
source_f=TimeIntervalGivenFunction(
TimeHarmonicGivenFunction(
make_tdep_given(source_u), omega=10),
0, 1),
dirichlet_tag=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(1/dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step*dt
if step % 50 == 0 and write_output:
print step, t, discr.norm(fields[0])
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[ ("u", fields[0]), ("v", fields[1:]), ],
time=t, step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
vis.close()
def main(write_output=True,
dir_tag=TAG_NONE, neu_tag=TAG_NONE, rad_tag=TAG_ALL,
flux_type_arg="upwind", dtype=np.float64, debug=[]):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype)
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE # noqa
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
op = StrongWaveOperator(-1, dim,
source_f=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
discr = rcon.make_discretization(mesh_data, order=4, debug=debug,
default_scalar_type=dtype,
tune_for=op.op_template())
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
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)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", discr.convert_volume(fields[0], kind="numpy")),
("v", discr.convert_volume(fields[1:], kind="numpy")),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, flux_type_arg="upwind",
#case = CenteredStationaryTestCase(),
#case = OffCenterStationaryTestCase(),
#case = OffCenterMigratingTestCase(),
case = ExactTestCase(),
):
from hedge.backends import guess_run_context
rcon = guess_run_context()
order = 3
if rcon.is_head_rank:
if True:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(case.a, case.b, 20, periodic=True)
else:
from hedge.mesh.generator import make_rect_mesh
print (pi*2)/(11*5*2)
mesh = make_rect_mesh((-pi, -1), (pi, 1),
periodicity=(True, True),
subdivisions=(11,5),
max_area=(pi*2)/(11*5*2)
)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=order,
quad_min_degrees={"quad": 3*order})
if write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
# operator setup ----------------------------------------------------------
from hedge.second_order import IPDGSecondDerivative
from hedge.models.burgers import BurgersOperator
op = BurgersOperator(mesh.dimensions,
viscosity_scheme=IPDGSecondDerivative())
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# exact solution ----------------------------------------------------------
import pymbolic
var = pymbolic.var
u = discr.interpolate_volume_function(lambda x, el: case.u0(x[0]))
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "burgers.dat"
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)
from hedge.log import LpNorm
u_getter = lambda: u
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l1_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
from hedge.timestep.runge_kutta import ODE45TimeStepper, LSRK4TimeStepper
stepper = ODE45TimeStepper()
stepper.add_instrumentation(logmgr)
try:
from hedge.timestep import times_and_steps
# for visc=0.01
#stab_fac = 0.1 # RK4
#stab_fac = 1.6 # dumka3(3), central
#stab_fac = 3 # dumka3(4), central
#stab_fac = 0.01 # RK4
stab_fac = 0.2 # dumka3(3), central
#stab_fac = 3 # dumka3(4), central
dt = stab_fac*op.estimate_timestep(discr,
stepper=LSRK4TimeStepper(), t=0, fields=u)
step_it = times_and_steps(
final_time=case.final_time, logmgr=logmgr, max_dt_getter=lambda t: dt)
from hedge.optemplate import InverseVandermondeOperator
inv_vdm = InverseVandermondeOperator().bind(discr)
for step, t, dt in step_it:
if step % 3 == 0 and write_output:
if hasattr(case, "u_exact"):
extra_fields = [
("u_exact",
discr.interpolate_volume_function(
lambda x, el: case.u_exact(x[0], t)))]
else:
extra_fields = []
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", u),
] + extra_fields,
time=t,
step=step)
visf.close()
u = stepper(u, t, dt, rhs)
if isinstance(case, ExactTestCase):
assert discr.norm(u, 1) < 50
finally:
if write_output:
vis.close()
logmgr.save()
def main(write_output=True,
flux_type_arg="central",
use_quadrature=True,
final_time=20):
from math import sin, cos, pi, sqrt
from hedge.backends import guess_run_context
rcon = guess_run_context()
# mesh setup --------------------------------------------------------------
if rcon.is_head_rank:
#from hedge.mesh.generator import make_disk_mesh
#mesh = make_disk_mesh()
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.008)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
# space-time-dependent-velocity-field -------------------------------------
# simple vortex
class TimeDependentVField:
""" `TimeDependentVField` is a callable expecting `(x, t)` representing space and time
`x` is of the length of the spatial dimension and `t` is the time."""
shape = (2, )
def __call__(self, pt, el, t):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y * fac, x * fac]) * cos(pi * t)
class VField:
""" `VField` is a callable expecting `(x)` representing space
`x` is of the length of the spatial dimension."""
shape = (2, )
def __call__(self, pt, el):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y * fac, x * fac])
# space-time-dependent State BC (optional)-----------------------------------
class TimeDependentBc_u:
""" space and time dependent BC for state u"""
def __call__(self, pt, el, t):
x, y = pt
if t <= 0.5:
if x > 0:
return 1
else:
return 0
else:
return 0
class Bc_u:
""" Only space dependent BC for state u"""
def __call__(seld, pt, el):
x, y = pt
if x > 0:
return 1
else:
return 0
# operator setup ----------------------------------------------------------
# In the operator setup it is possible to switch between a only space
# dependent velocity field `VField` or a time and space dependent
# `TimeDependentVField`.
# For `TimeDependentVField`: advec_v=TimeDependentGivenFunction(VField())
# For `VField`: advec_v=TimeConstantGivenFunction(GivenFunction(VField()))
# Same for the Bc_u Function! If you don't define Bc_u then the BC for u = 0.
from hedge.data import \
ConstantGivenFunction, \
TimeConstantGivenFunction, \
TimeDependentGivenFunction, \
GivenFunction
from hedge.models.advection import VariableCoefficientAdvectionOperator
op = VariableCoefficientAdvectionOperator(
mesh.dimensions,
#advec_v=TimeDependentGivenFunction(
# TimeDependentVField()),
advec_v=TimeConstantGivenFunction(GivenFunction(VField())),
#bc_u_f=TimeDependentGivenFunction(
# TimeDependentBc_u()),
bc_u_f=TimeConstantGivenFunction(GivenFunction(Bc_u())),
flux_type=flux_type_arg)
# discretization setup ----------------------------------------------------
order = 5
if use_quadrature:
quad_min_degrees = {"quad": 3 * order}
else:
quad_min_degrees = {}
discr = rcon.make_discretization(
mesh_data,
order=order,
default_scalar_type=numpy.float64,
debug=["cuda_no_plan"],
quad_min_degrees=quad_min_degrees,
tune_for=op.op_template(),
)
vis_discr = discr
# visualization setup -----------------------------------------------------
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(vis_discr, rcon, "fld")
# initial condition -------------------------------------------------------
if True:
def initial(pt, el):
# Gauss pulse
from math import exp
x = (pt - numpy.array([0.3, 0.5])) * 8
return exp(-numpy.dot(x, x))
else:
def initial(pt, el):
# Rectangle
x, y = pt
if abs(x) < 0.5 and abs(y) < 0.2:
return 2
else:
return 1
u = discr.interpolate_volume_function(initial)
# timestep setup ----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(
vector_primitive_factory=discr.get_vector_primitive_factory())
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# filter setup-------------------------------------------------------------
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9,order=4))\
.bind(discr)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "space-dep.dat"
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)
from hedge.log import Integral, LpNorm
u_getter = lambda: u
logmgr.add_quantity(Integral(u_getter, discr, name="int_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# Initialize v for data output:
v = op.advec_v.volume_interpolant(0, discr)
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[("u", discr.convert_volume(u, kind="numpy")),
("v", discr.convert_volume(v, kind="numpy"))],
time=t,
step=step)
visf.close()
u = stepper(u, t, dt, rhs)
# We're feeding in a discontinuity through the BCs.
# Quadrature does not help with shock capturing--
# therefore we do need to filter here, regardless
# of whether quadrature is enabled.
u = mode_filter(u)
assert discr.norm(u) < 10
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def test_cuda_volume_quadrature():
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1,-1),b=(1,1),max_area=0.08)
from hedge.backends import guess_run_context
cpu_rcon = guess_run_context(['jit'])
gpu_rcon = guess_run_context(['cuda'])
order = 4
quad_min_degrees = {"quad": 3*order}
cpu_discr, gpu_discr = [
rcon.make_discretization(mesh, order=order,
default_scalar_type=numpy.float64,
debug=["cuda_no_plan", "cuda_no_microblock", ],
quad_min_degrees=quad_min_degrees
)
for rcon in [cpu_rcon, gpu_rcon]]
from math import sin, cos
def f(x, el):
return sin(x[0])*cos(x[1])
cpu_field, gpu_field = [
discr.interpolate_volume_function(f)
for discr in [cpu_discr, gpu_discr]]
def make_optemplate():
from hedge.optemplate.operators import QuadratureGridUpsampler
from hedge.optemplate import Field, make_stiffness_t
u = Field("u")
qu = QuadratureGridUpsampler("quad")(u)
return make_stiffness_t(2)[0](Field("intercept")(qu))
saved_vectors = []
def intercept(x):
saved_vectors.append(x)
return x
for discr in [cpu_discr, gpu_discr]:
discr.add_function("intercept", intercept)
opt = make_optemplate()
cpu_bound, gpu_bound = [discr.compile(make_optemplate())
for discr in [cpu_discr, gpu_discr]]
cpu_result = cpu_bound(u=cpu_field)
gpu_result = gpu_bound(u=gpu_field)
cpu_ivec, gpu_ivec = saved_vectors
gpu_ivec_on_host = gpu_ivec.get()[gpu_discr._gpu_volume_embedding("quad")]
ierr = cpu_ivec-gpu_ivec_on_host
assert la.norm(ierr) < 5e-15
gpu_result_on_host = gpu_discr.convert_volume(gpu_result, kind="numpy")
err = cpu_result-gpu_result_on_host
assert la.norm(err) < 2e-14
cpu_discr.close()
gpu_discr.close()
def main(write_output=True, flux_type_arg="central", use_quadrature=True,
final_time=20):
from math import sin, cos, pi, sqrt
from hedge.backends import guess_run_context
rcon = guess_run_context()
# mesh setup --------------------------------------------------------------
if rcon.is_head_rank:
#from hedge.mesh.generator import make_disk_mesh
#mesh = make_disk_mesh()
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1,-1),b=(1,1),max_area=0.008)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
# space-time-dependent-velocity-field -------------------------------------
# simple vortex
class TimeDependentVField:
""" `TimeDependentVField` is a callable expecting `(x, t)` representing space and time
`x` is of the length of the spatial dimension and `t` is the time."""
shape = (2,)
def __call__(self, pt, el, t):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y*fac, x*fac]) * cos(pi*t)
class VField:
""" `VField` is a callable expecting `(x)` representing space
`x` is of the length of the spatial dimension."""
shape = (2,)
def __call__(self, pt, el):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y*fac, x*fac])
# space-time-dependent State BC (optional)-----------------------------------
class TimeDependentBc_u:
""" space and time dependent BC for state u"""
def __call__(self, pt, el, t):
x, y = pt
if t <= 0.5:
if x > 0:
return 1
else:
return 0
else:
return 0
class Bc_u:
""" Only space dependent BC for state u"""
def __call__(seld, pt, el):
x, y = pt
if x > 0:
return 1
else:
return 0
# operator setup ----------------------------------------------------------
# In the operator setup it is possible to switch between a only space
# dependent velocity field `VField` or a time and space dependent
# `TimeDependentVField`.
# For `TimeDependentVField`: advec_v=TimeDependentGivenFunction(VField())
# For `VField`: advec_v=TimeConstantGivenFunction(GivenFunction(VField()))
# Same for the Bc_u Function! If you don't define Bc_u then the BC for u = 0.
from hedge.data import \
ConstantGivenFunction, \
TimeConstantGivenFunction, \
TimeDependentGivenFunction, \
GivenFunction
from hedge.models.advection import VariableCoefficientAdvectionOperator
op = VariableCoefficientAdvectionOperator(mesh.dimensions,
#advec_v=TimeDependentGivenFunction(
# TimeDependentVField()),
advec_v=TimeConstantGivenFunction(
GivenFunction(VField())),
#bc_u_f=TimeDependentGivenFunction(
# TimeDependentBc_u()),
bc_u_f=TimeConstantGivenFunction(
GivenFunction(Bc_u())),
flux_type=flux_type_arg)
# discretization setup ----------------------------------------------------
order = 5
if use_quadrature:
quad_min_degrees = {"quad": 3*order}
else:
quad_min_degrees = {}
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64,
debug=["cuda_no_plan"],
quad_min_degrees=quad_min_degrees,
tune_for=op.op_template(),
)
vis_discr = discr
# visualization setup -----------------------------------------------------
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(vis_discr, rcon, "fld")
# initial condition -------------------------------------------------------
if True:
def initial(pt, el):
# Gauss pulse
from math import exp
x = (pt-numpy.array([0.3, 0.5]))*8
return exp(-numpy.dot(x, x))
else:
def initial(pt, el):
# Rectangle
x, y = pt
if abs(x) < 0.5 and abs(y) < 0.2:
return 2
else:
return 1
u = discr.interpolate_volume_function(initial)
# timestep setup ----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(
vector_primitive_factory=discr.get_vector_primitive_factory())
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# filter setup-------------------------------------------------------------
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9,order=4))\
.bind(discr)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "space-dep.dat"
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)
from hedge.log import Integral, LpNorm
u_getter = lambda: u
logmgr.add_quantity(Integral(u_getter, discr, name="int_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# Initialize v for data output:
v = op.advec_v.volume_interpolant(0, discr)
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
("v", discr.convert_volume(v, kind="numpy"))
], time=t, step=step)
visf.close()
u = stepper(u, t, dt, rhs)
# We're feeding in a discontinuity through the BCs.
# Quadrature does not help with shock capturing--
# therefore we do need to filter here, regardless
# of whether quadrature is enabled.
u = mode_filter(u)
assert discr.norm(u) < 10
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
#case = OffCenterMigratingTestCase(),
case=ExactTestCase(),
):
from hedge.backends import guess_run_context
rcon = guess_run_context()
order = 3
if rcon.is_head_rank:
if True:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(case.a, case.b, 20, periodic=True)
else:
from hedge.mesh.generator import make_rect_mesh
print(pi * 2) / (11 * 5 * 2)
mesh = make_rect_mesh((-pi, -1), (pi, 1),
periodicity=(True, True),
subdivisions=(11, 5),
max_area=(pi * 2) / (11 * 5 * 2))
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data,
order=order,
quad_min_degrees={"quad": 3 * order})
if write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = np.array([0.7, 0.4])
source_width = 1/16
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import VariableVelocityStrongWaveOperator
op = VariableVelocityStrongWaveOperator(
c=sym.If(sym.Comparison(
np.dot(sym_x, sym_x), "<", 0.4**2),
1, 0.5),
dimensions=discr.dimensions,
source=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
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)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep.stability import \
approximate_rk4_relative_imag_stability_region
max_dt = (
1/discr.compile(op.max_eigenvalue_expr())()
* discr.dt_non_geometric_factor()
* discr.dt_geometric_factor()
* approximate_rk4_relative_imag_stability_region(stepper))
if flux_type_arg == "central":
max_dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3, logmgr=logmgr,
max_dt_getter=lambda t: max_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True):
from math import sin, exp, sqrt # noqa
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(-0.1, discr.dimensions,
source_f=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(10/dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step*dt
if step % 10 == 0 and write_output:
print step, t, discr.norm(fields[0])
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[("u", fields[0]), ("v", fields[1:]), ],
time=t, step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
vis.close()
def main(write_output=True, dtype=np.float32):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
h_fac = 1
mesh = make_rect_mesh(a=(0,0),b=(1,1), max_area=h_fac**2*1e-4,
periodicity=(True,True),
subdivisions=(int(70/h_fac), int(70/h_fac)))
from hedge.models.gas_dynamics.lbm import \
D2Q9LBMMethod, LatticeBoltzmannOperator
op = LatticeBoltzmannOperator(
D2Q9LBMMethod(), lbm_delta_t=0.001, nu=1e-4)
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=3,
default_scalar_type=dtype,
debug=["cuda_no_plan"])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype,
#vector_primitive_factory=discr.get_vector_primitive_factory()
)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.data import CompiledExpressionData
def ic_expr(t, x, fields):
from hedge.optemplate import CFunction
from pymbolic.primitives import IfPositive
from pytools.obj_array import make_obj_array
tanh = CFunction("tanh")
sin = CFunction("sin")
rho = 1
u0 = 0.05
w = 0.05
delta = 0.05
from hedge.optemplate.primitives import make_common_subexpression as cse
u = cse(make_obj_array([
IfPositive(x[1]-1/2,
u0*tanh(4*(3/4-x[1])/w),
u0*tanh(4*(x[1]-1/4)/w)),
u0*delta*sin(2*np.pi*(x[0]+1/4))]),
"u")
return make_obj_array([
op.method.f_equilibrium(rho, alpha, u)
for alpha in range(len(op.method))
])
# timestep loop -----------------------------------------------------------
stream_rhs = op.bind_rhs(discr)
collision_update = op.bind(discr, op.collision_update)
get_rho = op.bind(discr, op.rho)
get_rho_u = op.bind(discr, op.rho_u)
f_bar = CompiledExpressionData(ic_expr).volume_interpolant(0, discr)
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))\
.bind(discr)
final_time = 1000
try:
lbm_dt = op.lbm_delta_t
dg_dt = op.estimate_timestep(discr, stepper=stepper)
print dg_dt
dg_steps_per_lbm_step = int(np.ceil(lbm_dt / dg_dt))
dg_dt = lbm_dt / dg_steps_per_lbm_step
lbm_steps = int(final_time // op.lbm_delta_t)
for step in xrange(lbm_steps):
t = step*lbm_dt
if step % 100 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
rho = get_rho(f_bar)
rho_u = get_rho_u(f_bar)
vis.add_data(visf,
[ ("fbar%d" %i,
discr.convert_volume(f_bar_i, "numpy")) for i, f_bar_i in enumerate(f_bar)]+
[
("rho", discr.convert_volume(rho, "numpy")),
("rho_u", discr.convert_volume(rho_u, "numpy")),
],
time=t,
step=step)
visf.close()
print "step=%d, t=%f" % (step, t)
f_bar = collision_update(f_bar)
for substep in range(dg_steps_per_lbm_step):
f_bar = stepper(f_bar, t + substep*dg_dt, dg_dt, stream_rhs)
#f_bar = mode_filter(f_bar)
finally:
if write_output:
vis.close()
discr.close()
def test_cuda_volume_quadrature():
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.08)
from hedge.backends import guess_run_context
cpu_rcon = guess_run_context(['jit'])
gpu_rcon = guess_run_context(['cuda'])
order = 4
quad_min_degrees = {"quad": 3 * order}
cpu_discr, gpu_discr = [
rcon.make_discretization(mesh,
order=order,
default_scalar_type=numpy.float64,
debug=[
"cuda_no_plan",
"cuda_no_microblock",
],
quad_min_degrees=quad_min_degrees)
for rcon in [cpu_rcon, gpu_rcon]
]
from math import sin, cos
def f(x, el):
return sin(x[0]) * cos(x[1])
cpu_field, gpu_field = [
discr.interpolate_volume_function(f)
for discr in [cpu_discr, gpu_discr]
]
def make_optemplate():
from hedge.optemplate.operators import QuadratureGridUpsampler
from hedge.optemplate import Field, make_stiffness_t
u = Field("u")
qu = QuadratureGridUpsampler("quad")(u)
return make_stiffness_t(2)[0](Field("intercept")(qu))
saved_vectors = []
def intercept(x):
saved_vectors.append(x)
return x
for discr in [cpu_discr, gpu_discr]:
discr.add_function("intercept", intercept)
opt = make_optemplate()
cpu_bound, gpu_bound = [
discr.compile(make_optemplate())
for discr in [cpu_discr, gpu_discr]
]
cpu_result = cpu_bound(u=cpu_field)
gpu_result = gpu_bound(u=gpu_field)
cpu_ivec, gpu_ivec = saved_vectors
gpu_ivec_on_host = gpu_ivec.get()[gpu_discr._gpu_volume_embedding(
"quad")]
ierr = cpu_ivec - gpu_ivec_on_host
assert la.norm(ierr) < 5e-15
gpu_result_on_host = gpu_discr.convert_volume(gpu_result, kind="numpy")
err = cpu_result - gpu_result_on_host
assert la.norm(err) < 2e-14
cpu_discr.close()
gpu_discr.close()