def test_symbolic_evaluation(actx_factory):
"""
Evaluate a symbolic expression by plugging in numbers and
:class:`~meshmode.dof_array.DOFArray`s and compare the result to the equivalent
quantity computed explicitly.
"""
actx = actx_factory()
mesh = generate_regular_rect_mesh(
a=(-np.pi/2,)*2,
b=(np.pi/2,)*2,
nelements_per_axis=(4,)*2)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=2)
nodes = thaw(actx, discr.nodes())
sym_coords = pmbl.make_sym_vector("x", 2)
sym_f = (
pmbl.var("exp")(-pmbl.var("t"))
* pmbl.var("cos")(sym_coords[0])
* pmbl.var("sin")(sym_coords[1]))
t = 0.5
f = sym.EvaluationMapper({"t": t, "x": nodes})(sym_f)
expected_f = np.exp(-t) * actx.np.cos(nodes[0]) * actx.np.sin(nodes[1])
assert actx.to_numpy(discr.norm(f - expected_f)/discr.norm(expected_f)) < 1e-12
def test_wave_stability(actx_factory,
problem,
timestep_scale,
order,
visualize=False):
"""Checks stability of the wave operator for a given problem setup.
Adjust *timestep_scale* to get timestep close to stability limit.
"""
actx = actx_factory()
p = problem
sym_u, sym_v, sym_f, sym_rhs = sym_wave(p.dim, p.sym_phi)
mesh = p.mesh_factory(8)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"c": p.c, "x": nodes, "t": t})(expr)
def get_rhs(t, w):
result = wave_operator(discr, c=p.c, w=w)
result[0] += sym_eval(sym_f, t)
return result
t = 0.
u = sym_eval(sym_u, t)
v = sym_eval(sym_v, t)
fields = flat_obj_array(u, v)
from mirgecom.integrators import rk4_step
dt = timestep_scale / order**2
for istep in range(10):
fields = rk4_step(fields, t, dt, get_rhs)
t += dt
expected_u = sym_eval(sym_u, 10 * dt)
expected_v = sym_eval(sym_v, 10 * dt)
expected_fields = flat_obj_array(expected_u, expected_v)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order)
vis.write_vtk_file("wave_stability.vtu", [
("u", fields[0]),
("v", fields[1:]),
("u_expected", expected_fields[0]),
("v_expected", expected_fields[1:]),
])
err = discr.norm(fields - expected_fields, np.inf)
max_err = discr.norm(expected_fields, np.inf)
assert err < max_err
def test_pulse(ctx_factory, dim):
"""
Test of Gaussian pulse generator.
If it looks, walks, and quacks like a Gaussian, then ...
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nel_1d = 10
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 1
print(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
print(f"DIM = {dim}, {len(nodes)}")
print(f"Nodes={nodes}")
tol = 1e-15
from mirgecom.initializers import make_pulse
amp = 1.0
w = .1
rms2 = w * w
r0 = np.zeros(dim)
r2 = np.dot(nodes, nodes) / rms2
pulse = make_pulse(amp=amp, r0=r0, w=w, r=nodes)
print(f"Pulse = {pulse}")
# does it return the expected exponential?
pulse_check = actx.np.exp(-.5 * r2)
print(f"exact: {pulse_check}")
pulse_resid = pulse - pulse_check
print(f"pulse residual: {pulse_resid}")
assert (discr.norm(pulse_resid, np.inf) < tol)
# proper scaling with amplitude?
amp = 2.0
pulse = 0
pulse = make_pulse(amp=amp, r0=r0, w=w, r=nodes)
pulse_resid = pulse - (pulse_check + pulse_check)
assert (discr.norm(pulse_resid, np.inf) < tol)
# proper scaling with r?
amp = 1.0
rcheck = np.sqrt(2.0) * nodes
pulse = make_pulse(amp=amp, r0=r0, w=w, r=rcheck)
assert (discr.norm(pulse - (pulse_check * pulse_check), np.inf) < tol)
# proper scaling with w?
w = w / np.sqrt(2.0)
pulse = make_pulse(amp=amp, r0=r0, w=w, r=nodes)
assert (discr.norm(pulse - (pulse_check * pulse_check), np.inf) < tol)
def test_inviscid_flux_components(actx_factory, dim):
"""Test uniform pressure case.
Checks that the Euler-internal inviscid flux routine
:func:`mirgecom.inviscid.inviscid_flux` returns exactly the expected result
with a constant pressure and no flow.
Expected inviscid flux is:
F(q) = <rhoV, (E+p)V, rho(V.x.V) + pI>
Checks that only diagonal terms of the momentum flux:
[ rho(V.x.V) + pI ] are non-zero and return the correctly calculated p.
"""
actx = actx_factory()
eos = IdealSingleGas()
p0 = 1.0
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
eos = IdealSingleGas()
logger.info(f"Number of {dim}d elems: {mesh.nelements}")
# === this next block tests 1,2,3 dimensions,
# with single and multiple nodes/states. The
# purpose of this block is to ensure that when
# all components of V = 0, the flux recovers
# the expected values (and p0 within tolerance)
# === with V = 0, fixed P = p0
tolerance = 1e-15
nodes = thaw(actx, discr.nodes())
mass = discr.zeros(actx) + np.dot(nodes, nodes) + 1.0
mom = make_obj_array([discr.zeros(actx) for _ in range(dim)])
p_exact = discr.zeros(actx) + p0
energy = p_exact / 0.4 + 0.5 * np.dot(mom, mom) / mass
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
p = eos.pressure(cv)
flux = inviscid_flux(discr, eos, cv)
assert discr.norm(p - p_exact, np.inf) < tolerance
logger.info(f"{dim}d flux = {flux}")
# for velocity zero, these components should be == zero
assert discr.norm(flux.mass, 2) == 0.0
assert discr.norm(flux.energy, 2) == 0.0
# The momentum diagonal should be p
# Off-diagonal should be identically 0
assert discr.norm(flux.momentum - p0 * np.identity(dim),
np.inf) < tolerance
def test_wave_accuracy(actx_factory, problem, order, visualize=False):
"""Checks accuracy of the wave operator for a given problem setup.
"""
actx = actx_factory()
p = problem
sym_u, sym_v, sym_f, sym_rhs = sym_wave(p.dim, p.sym_phi)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in [8, 10, 12] if p.dim == 3 else [8, 12, 16]:
mesh = p.mesh_factory(n)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"c": p.c, "x": nodes, "t": t})(expr)
t_check = 1.23456789
u = sym_eval(sym_u, t_check)
v = sym_eval(sym_v, t_check)
fields = flat_obj_array(u, v)
rhs = wave_operator(discr, c=p.c, w=fields)
rhs[0] = rhs[0] + sym_eval(sym_f, t_check)
expected_rhs = sym_eval(sym_rhs, t_check)
rel_linf_err = actx.to_numpy(
discr.norm(rhs - expected_rhs, np.inf) /
discr.norm(expected_rhs, np.inf))
eoc_rec.add_data_point(1. / n, rel_linf_err)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order)
vis.write_vtk_file(
"wave_accuracy_{order}_{n}.vtu".format(order=order, n=n), [
("u", fields[0]),
("v", fields[1:]),
("rhs_u_actual", rhs[0]),
("rhs_v_actual", rhs[1:]),
("rhs_u_expected", expected_rhs[0]),
("rhs_v_expected", expected_rhs[1:]),
])
print("Approximation error:")
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
def test_idealsingle_lump(ctx_factory):
"""Test EOS with mass lump.
Tests that the IdealSingleGas EOS returns
the correct (uniform) pressure for the Lump
solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
n=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
center = np.zeros(shape=(dim, ))
velocity = np.zeros(shape=(dim, ))
center[0] = 5
velocity[0] = 1
lump = Lump(center=center, velocity=velocity)
eos = IdealSingleGas()
lump_soln = lump(0, nodes)
cv = split_conserved(dim, lump_soln)
p = eos.pressure(cv)
exp_p = 1.0
errmax = discr.norm(p - exp_p, np.inf)
exp_ke = 0.5 * cv.mass
ke = eos.kinetic_energy(cv)
kerr = discr.norm(ke - exp_ke, np.inf)
te = eos.total_energy(cv, p)
terr = discr.norm(te - cv.energy, np.inf)
logger.info(f"lump_soln = {lump_soln}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
assert kerr < 1e-15
assert terr < 1e-15
def test_species_mass_gradient(actx_factory, dim):
"""Test gradY structure and values against exact."""
actx = actx_factory()
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(1.0, ) * dim,
b=(2.0, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 1
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
ones = zeros + 1
nspecies = 2 * dim
mass = 2 * ones # make mass != 1
energy = zeros + 2.5
velocity = make_obj_array([ones for _ in range(dim)])
mom = mass * velocity
# assemble y so that each one has simple, but unique grad components
y = make_obj_array([ones for _ in range(nspecies)])
for idim in range(dim):
ispec = 2 * idim
y[ispec] = ispec * (idim * dim + 1) * sum([(iidim + 1) * nodes[iidim]
for iidim in range(dim)])
y[ispec + 1] = -y[ispec]
species_mass = mass * y
cv = make_conserved(dim,
mass=mass,
energy=energy,
momentum=mom,
species_mass=species_mass)
from grudge.op import local_grad
grad_cv = make_conserved(dim, q=local_grad(discr, cv.join()))
from mirgecom.fluid import species_mass_fraction_gradient
grad_y = species_mass_fraction_gradient(discr, cv, grad_cv)
assert grad_y.shape == (nspecies, dim)
from meshmode.dof_array import DOFArray
assert type(grad_y[0, 0]) == DOFArray
tol = 1e-11
for idim in range(dim):
ispec = 2 * idim
exact_grad = np.array([(ispec * (idim * dim + 1)) * (iidim + 1)
for iidim in range(dim)])
assert discr.norm(grad_y[ispec] - exact_grad, np.inf) < tol
assert discr.norm(grad_y[ispec + 1] + exact_grad, np.inf) < tol
def test_idealsingle_vortex(ctx_factory):
r"""Test EOS with isentropic vortex.
Tests that the IdealSingleGas EOS returns
the correct pressure (p) for the Vortex2D solution
field (i.e. $p = \rho^{\gamma}$).
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
n=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
eos = IdealSingleGas()
# Init soln with Vortex
vortex = Vortex2D()
vortex_soln = vortex(0, nodes)
cv = split_conserved(dim, vortex_soln)
gamma = eos.gamma()
p = eos.pressure(cv)
exp_p = cv.mass**gamma
errmax = discr.norm(p - exp_p, np.inf)
exp_ke = 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass
ke = eos.kinetic_energy(cv)
kerr = discr.norm(ke - exp_ke, np.inf)
te = eos.total_energy(cv, p)
terr = discr.norm(te - cv.energy, np.inf)
logger.info(f"vortex_soln = {vortex_soln}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
assert kerr < 1e-15
assert terr < 1e-15
def test_inviscid_mom_flux_components(actx_factory, dim, livedim):
r"""Test components of the momentum flux with constant pressure, V != 0.
Checks that the flux terms are returned in the proper order by running
only 1 non-zero velocity component at-a-time.
"""
actx = actx_factory()
eos = IdealSingleGas()
p0 = 1.0
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(-0.5,) * dim, b=(0.5,) * dim, nelements_per_axis=(nel_1d,) * dim
)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
tolerance = 1e-15
for livedim in range(dim):
mass = discr.zeros(actx) + 1.0 + np.dot(nodes, nodes)
mom = make_obj_array([discr.zeros(actx) for _ in range(dim)])
mom[livedim] = mass
p_exact = discr.zeros(actx) + p0
energy = (
p_exact / (eos.gamma() - 1.0)
+ 0.5 * np.dot(mom, mom) / mass
)
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
p = eos.pressure(cv)
assert discr.norm(p - p_exact, np.inf) < tolerance
flux = inviscid_flux(discr, eos, cv)
logger.info(f"{dim}d flux = {flux}")
vel_exact = mom / mass
# first two components should be nonzero in livedim only
assert discr.norm(flux.mass - mom, np.inf) == 0
eflux_exact = (energy + p_exact)*vel_exact
assert discr.norm(flux.energy - eflux_exact, np.inf) == 0
logger.info("Testing momentum")
xpmomflux = mass*np.outer(vel_exact, vel_exact) + p_exact*np.identity(dim)
assert discr.norm(flux.momentum - xpmomflux, np.inf) < tolerance
def test_vortex_init(ctx_factory):
"""
Simple test to check that Vortex2D initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
vortex = Vortex2D()
cv = vortex(nodes)
gamma = 1.4
p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass)
exp_p = cv.mass**gamma
errmax = discr.norm(p - exp_p, np.inf)
logger.info(f"vortex_soln = {cv}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
def test_velocity_gradient_structure(actx_factory):
"""Test gradv data structure, verifying usability with other helper routines."""
from mirgecom.fluid import velocity_gradient
actx = actx_factory()
dim = 3
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(1.0,) * dim, b=(2.0,) * dim, nelements_per_axis=(nel_1d,) * dim
)
order = 1
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
ones = zeros + 1.0
mass = 2*ones
energy = zeros + 2.5
velocity_x = nodes[0] + 2*nodes[1] + 3*nodes[2]
velocity_y = 4*nodes[0] + 5*nodes[1] + 6*nodes[2]
velocity_z = 7*nodes[0] + 8*nodes[1] + 9*nodes[2]
velocity = make_obj_array([velocity_x, velocity_y, velocity_z])
mom = mass * velocity
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
from grudge.op import local_grad
grad_cv = make_conserved(dim,
q=local_grad(discr, cv.join()))
grad_v = velocity_gradient(discr, cv, grad_cv)
tol = 1e-11
exp_result = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
exp_trans = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
exp_trace = 15
assert grad_v.shape == (dim, dim)
from meshmode.dof_array import DOFArray
assert type(grad_v[0, 0]) == DOFArray
assert discr.norm(grad_v - exp_result, np.inf) < tol
assert discr.norm(grad_v.T - exp_trans, np.inf) < tol
assert discr.norm(np.trace(grad_v) - exp_trace, np.inf) < tol
def test_viscous_timestep(actx_factory, dim, mu, vel):
"""Test timestep size."""
actx = actx_factory()
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(1.0, ) * dim,
b=(2.0, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 1
discr = EagerDGDiscretization(actx, mesh, order=order)
zeros = discr.zeros(actx)
ones = zeros + 1.0
velocity = make_obj_array([zeros + vel for _ in range(dim)])
massval = 1
mass = massval * ones
# I *think* this energy should yield c=1.0
energy = zeros + 1.0 / (1.4 * .4)
mom = mass * velocity
species_mass = None
cv = make_conserved(dim,
mass=mass,
energy=energy,
momentum=mom,
species_mass=species_mass)
from grudge.dt_utils import characteristic_lengthscales
chlen = characteristic_lengthscales(actx, discr)
from grudge.op import nodal_min
chlen_min = nodal_min(discr, "vol", chlen)
mu = mu * chlen_min
if mu < 0:
mu = 0
tv_model = None
else:
tv_model = SimpleTransport(viscosity=mu)
eos = IdealSingleGas()
gas_model = GasModel(eos=eos, transport=tv_model)
fluid_state = make_fluid_state(cv, gas_model)
from mirgecom.viscous import get_viscous_timestep
dt_field = get_viscous_timestep(discr, fluid_state)
speed_total = fluid_state.wavespeed
dt_expected = chlen / (speed_total + (mu / chlen))
error = (dt_expected - dt_field) / dt_expected
assert actx.to_numpy(discr.norm(error, np.inf)) == 0
def test_lump_rhs(actx_factory, dim, order):
"""Test the inviscid rhs using the non-trivial mass lump case.
The case is tested against the analytic expressions of the RHS.
Checks several different orders and refinement levels to check error behavior.
"""
actx = actx_factory()
tolerance = 1e-10
maxxerr = 0.0
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for nel_1d in [4, 8, 12]:
from meshmode.mesh.generation import (
generate_regular_rect_mesh, )
mesh = generate_regular_rect_mesh(
a=(-5, ) * dim,
b=(5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim,
)
logger.info(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Lump and expected RHS = 0
center = np.zeros(shape=(dim, ))
velocity = np.zeros(shape=(dim, ))
lump = Lump(dim=dim, center=center, velocity=velocity)
lump_soln = lump(nodes)
boundaries = {
BTAG_ALL: PrescribedInviscidBoundary(fluid_solution_func=lump)
}
inviscid_rhs = euler_operator(discr,
eos=IdealSingleGas(),
boundaries=boundaries,
cv=lump_soln,
time=0.0)
expected_rhs = lump.exact_rhs(discr, cv=lump_soln, time=0)
err_max = discr.norm((inviscid_rhs - expected_rhs).join(), np.inf)
if err_max > maxxerr:
maxxerr = err_max
eoc_rec.add_data_point(1.0 / nel_1d, err_max)
logger.info(f"Max error: {maxxerr}")
logger.info(f"Error for (dim,order) = ({dim},{order}):\n" f"{eoc_rec}")
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < tolerance)
def test_viscous_stress_tensor(actx_factory, transport_model):
"""Test tau data structure and values against exact."""
actx = actx_factory()
dim = 3
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(1.0, ) * dim,
b=(2.0, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 1
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
ones = zeros + 1.0
# assemble velocities for simple, unique grad components
velocity_x = nodes[0] + 2 * nodes[1] + 3 * nodes[2]
velocity_y = 4 * nodes[0] + 5 * nodes[1] + 6 * nodes[2]
velocity_z = 7 * nodes[0] + 8 * nodes[1] + 9 * nodes[2]
velocity = make_obj_array([velocity_x, velocity_y, velocity_z])
mass = 2 * ones
energy = zeros + 2.5
mom = mass * velocity
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
grad_cv = op.local_grad(discr, cv)
if transport_model:
tv_model = SimpleTransport(bulk_viscosity=1.0, viscosity=0.5)
else:
tv_model = PowerLawTransport()
eos = IdealSingleGas()
gas_model = GasModel(eos=eos, transport=tv_model)
fluid_state = make_fluid_state(cv, gas_model)
mu = tv_model.viscosity(eos, cv)
lam = tv_model.volume_viscosity(eos, cv)
# Exact answer for tau
exp_grad_v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
exp_grad_v_t = np.array([[1, 4, 7], [2, 5, 8], [3, 6, 9]])
exp_div_v = 15
exp_tau = (mu * (exp_grad_v + exp_grad_v_t) + lam * exp_div_v * np.eye(3))
from mirgecom.viscous import viscous_stress_tensor
tau = viscous_stress_tensor(fluid_state, grad_cv)
# The errors come from grad_v
assert actx.to_numpy(discr.norm(tau - exp_tau, np.inf)) < 1e-12
def test_velocity_gradient_eoc(actx_factory, dim):
"""Test that the velocity gradient converges at the proper rate."""
from mirgecom.fluid import velocity_gradient
actx = actx_factory()
order = 3
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
nel_1d_0 = 4
for hn1 in [1, 2, 3, 4]:
nel_1d = hn1 * nel_1d_0
h = 1/nel_1d
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(1.0,) * dim, b=(2.0,) * dim, nelements_per_axis=(nel_1d,) * dim
)
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
energy = zeros + 2.5
mass = nodes[dim-1]*nodes[dim-1]
velocity = make_obj_array([actx.np.cos(nodes[i]) for i in range(dim)])
mom = mass*velocity
q = join_conserved(dim, mass=mass, energy=energy, momentum=mom)
cv = split_conserved(dim, q)
grad_q = obj_array_vectorize(discr.grad, q)
grad_cv = split_conserved(dim, grad_q)
grad_v = velocity_gradient(discr, cv, grad_cv)
def exact_grad_row(xdata, gdim, dim):
exact_grad_row = make_obj_array([zeros for _ in range(dim)])
exact_grad_row[gdim] = -actx.np.sin(xdata)
return exact_grad_row
comp_err = make_obj_array([
discr.norm(grad_v[i] - exact_grad_row(nodes[i], i, dim), np.inf)
for i in range(dim)])
err_max = comp_err.max()
eoc.add_data_point(h, err_max)
logger.info(eoc)
assert (
eoc.order_estimate() >= order - 0.5
or eoc.max_error() < 1e-9
)
def test_uniform(ctx_factory, dim):
"""
Simple test to check that Uniform initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nel_1d = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim)
order = 1
print(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
print(f"DIM = {dim}, {len(nodes)}")
print(f"Nodes={nodes}")
from mirgecom.initializers import Uniform
initr = Uniform(numdim=dim)
initsoln = initr(t=0.0, x_vec=nodes)
tol = 1e-15
ssoln = split_conserved(dim, initsoln)
assert discr.norm(ssoln.mass - 1.0, np.inf) < tol
assert discr.norm(ssoln.energy - 2.5, np.inf) < tol
print(f"Uniform Soln:{initsoln}")
eos = IdealSingleGas()
cv = split_conserved(dim, initsoln)
p = eos.pressure(cv)
print(f"Press:{p}")
assert discr.norm(p - 1.0, np.inf) < tol
def test_local_max_species_diffusivity(actx_factory, dim, array_valued):
"""Test the local maximum species diffusivity."""
actx = actx_factory()
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(1.0, ) * dim,
b=(2.0, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 1
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
ones = zeros + 1.0
vel = .32
velocity = make_obj_array([zeros + vel for _ in range(dim)])
massval = 1
mass = massval * ones
energy = zeros + 1.0 / (1.4 * .4)
mom = mass * velocity
species_mass = np.array([1., 2., 3.], dtype=object)
cv = make_conserved(dim,
mass=mass,
energy=energy,
momentum=mom,
species_mass=species_mass)
d_alpha_input = np.array([.1, .2, .3])
if array_valued:
f = 1 + 0.1 * actx.np.sin(nodes[0])
d_alpha_input *= f
tv_model = SimpleTransport(species_diffusivity=d_alpha_input)
eos = IdealSingleGas()
d_alpha = tv_model.species_diffusivity(eos, cv)
from mirgecom.viscous import get_local_max_species_diffusivity
expected = .3 * ones
if array_valued:
expected *= f
calculated = get_local_max_species_diffusivity(actx, d_alpha)
assert actx.to_numpy(discr.norm(calculated - expected, np.inf)) == 0
def test_vortex_rhs(actx_factory, order):
"""Tests the inviscid rhs using the non-trivial
2D isentropic vortex case configured to yield
rhs = 0. Checks several different orders
and refinement levels to check error
behavior.
"""
actx = actx_factory()
dim = 2
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
from meshmode.mesh.generation import generate_regular_rect_mesh
for nel_1d in [16, 32, 64]:
mesh = generate_regular_rect_mesh(
a=(-5, ) * dim,
b=(5, ) * dim,
n=(nel_1d, ) * dim,
)
logger.info(f"Number of {dim}d elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex and expected RHS = 0
vortex = Vortex2D(center=[0, 0], velocity=[0, 0])
vortex_soln = vortex(0, nodes)
boundaries = {BTAG_ALL: PrescribedBoundary(vortex)}
inviscid_rhs = inviscid_operator(discr,
eos=IdealSingleGas(),
boundaries=boundaries,
q=vortex_soln,
t=0.0)
err_max = discr.norm(inviscid_rhs, np.inf)
eoc_rec.add_data_point(1.0 / nel_1d, err_max)
message = (f"Error for (dim,order) = ({dim},{order}):\n" f"{eoc_rec}")
logger.info(message)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
def test_restart_cv(actx_factory, nspecies):
"""Test that restart can read a CV array container."""
actx = actx_factory()
nel_1d = 4
dim = 3
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
from meshmode.dof_array import thaw
nodes = thaw(actx, discr.nodes())
mass = nodes[0]
energy = nodes[1]
mom = make_obj_array([nodes[2] * (i + 3) for i in range(dim)])
species_mass = None
if nspecies > 0:
mass_fractions = make_obj_array(
[i * nodes[0] for i in range(nspecies)])
species_mass = mass * mass_fractions
rst_filename = f"test_{nspecies}.pkl"
from mirgecom.fluid import make_conserved
test_state = make_conserved(dim,
mass=mass,
energy=energy,
momentum=mom,
species_mass=species_mass)
rst_data = {"state": test_state}
from mirgecom.restart import write_restart_file
write_restart_file(actx, rst_data, rst_filename)
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(actx, rst_filename)
resid = test_state - restart_data["state"]
assert discr.norm(resid.join(), np.inf) == 0
def test_velocity_gradient_sanity(actx_factory, dim, mass_exp, vel_fac):
"""Test that the grad(v) returns {0, I} for v={constant, r_xyz}."""
from mirgecom.fluid import velocity_gradient
actx = actx_factory()
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(1.0, ) * dim,
b=(2.0, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
zeros = discr.zeros(actx)
ones = zeros + 1.0
mass = 1 * ones
for i in range(mass_exp):
mass *= (mass + i)
energy = zeros + 2.5
velocity = vel_fac * nodes
mom = mass * velocity
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
from grudge.op import local_grad
grad_cv = make_conserved(dim, q=local_grad(discr, cv.join()))
grad_v = velocity_gradient(discr, cv, grad_cv)
tol = 1e-11
exp_result = vel_fac * np.eye(dim) * ones
grad_v_err = [
discr.norm(grad_v[i] - exp_result[i], np.inf) for i in range(dim)
]
assert max(grad_v_err) < tol
def test_lump_init(ctx_factory):
"""
Simple test to check that Lump initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
n=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
center = np.zeros(shape=(dim, ))
velocity = np.zeros(shape=(dim, ))
center[0] = 5
velocity[0] = 1
lump = Lump(center=center, velocity=velocity)
lump_soln = lump(0, nodes)
cv = split_conserved(dim, lump_soln)
p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass)
exp_p = 1.0
errmax = discr.norm(p - exp_p, np.inf)
logger.info(f"lump_soln = {lump_soln}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
def test_shock_init(ctx_factory):
"""
Simple test to check that Shock1D initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nel_1d = 10
dim = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (1.0, )],
b=[(-0.5, ), (0.5, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
print(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
initr = SodShock1D()
initsoln = initr(time=0.0, x_vec=nodes)
print("Sod Soln:", initsoln)
xpl = 1.0
xpr = 0.1
tol = 1e-15
nodes_x = nodes[0]
eos = IdealSingleGas()
p = eos.pressure(initsoln)
assert actx.to_numpy(
discr.norm(actx.np.where(nodes_x < 0.5, p - xpl, p - xpr),
np.inf)) < tol
def test_analytic_comparison(actx_factory):
"""Quick test of state comparison routine."""
from mirgecom.initializers import Vortex2D
from mirgecom.simutil import compare_fluid_solutions
actx = actx_factory()
nel_1d = 4
dim = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(1.0,) * dim, b=(2.0,) * dim, nelements_per_axis=(nel_1d,) * dim
)
order = 2
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(discr.nodes(), actx)
zeros = discr.zeros(actx)
ones = zeros + 1.0
mass = ones
energy = ones
velocity = 2 * nodes
mom = mass * velocity
vortex_init = Vortex2D()
vortex_soln = vortex_init(x_vec=nodes, eos=IdealSingleGas())
cv = make_conserved(dim, mass=mass, energy=energy, momentum=mom)
resid = vortex_soln - cv
expected_errors = [discr.norm(v, np.inf) for v in resid.join()]
errors = compare_fluid_solutions(discr, cv, cv)
assert max(errors) == 0
errors = compare_fluid_solutions(discr, cv, vortex_soln)
assert errors == expected_errors
def main(ctx_factory=cl.create_some_context, use_logmgr=True,
use_leap=False, use_profiling=False, casename=None,
rst_filename=None, actx_class=PyOpenCLArrayContext):
"""Run the example."""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
logmgr = initialize_logmgr(use_logmgr,
filename="heat-source.sqlite", mode="wu", mpi_comm=comm)
if use_profiling:
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
else:
queue = cl.CommandQueue(cl_ctx)
actx = actx_class(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)))
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
t = 0
t_final = 0.0002
istep = 0
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(-0.5,)*dim,
b=(0.5,)*dim,
nelements_per_axis=(nel_1d,)*dim,
boundary_tag_to_face={
"dirichlet": ["+x", "-x"],
"neumann": ["+y", "-y"]
}
)
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element, num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
order = 3
discr = EagerDGDiscretization(actx, local_mesh, order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.0025/(nel_1d*order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
source_width = 0.2
from arraycontext import thaw
nodes = thaw(discr.nodes(), actx)
boundaries = {
DTAG_BOUNDARY("dirichlet"): DirichletDiffusionBoundary(0.),
DTAG_BOUNDARY("neumann"): NeumannDiffusionBoundary(0.)
}
u = discr.zeros(actx)
if logmgr:
logmgr_add_device_name(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr.add_watches(["step.max", "t_step.max", "t_log.max"])
try:
logmgr.add_watches(["memory_usage_python.max", "memory_usage_gpu.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["multiply_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
vis = make_visualizer(discr)
def rhs(t, u):
return (
diffusion_operator(
discr, quad_tag=DISCR_TAG_BASE,
alpha=1, boundaries=boundaries, u=u)
+ actx.np.exp(-np.dot(nodes, nodes)/source_width**2))
compiled_rhs = actx.compile(rhs)
rank = comm.Get_rank()
while t < t_final:
if logmgr:
logmgr.tick_before()
if istep % 10 == 0:
print(istep, t, actx.to_numpy(actx.np.linalg.norm(u[0])))
vis.write_vtk_file("fld-heat-source-mpi-%03d-%04d.vtu" % (rank, istep),
[
("u", u)
], overwrite=True)
u = rk4_step(u, t, dt, compiled_rhs)
t += dt
istep += 1
if logmgr:
set_dt(logmgr, dt)
logmgr.tick_after()
final_answer = discr.norm(u, np.inf)
resid = abs(final_answer - 0.00020620711665201585)
if resid > 1e-15:
raise ValueError(f"Run did not produce the expected result {resid=}")
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim,
boundary_tag_to_face={
"dirichlet": ["+x", "-x"],
"neumann": ["+y", "-y"]
})
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.0025 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
source_width = 0.2
nodes = thaw(actx, discr.nodes())
u = discr.zeros(actx)
vis = make_visualizer(discr, order + 3 if dim == 2 else order)
boundaries = {
grudge_sym.DTAG_BOUNDARY("dirichlet"): DirichletDiffusionBoundary(0.),
grudge_sym.DTAG_BOUNDARY("neumann"): NeumannDiffusionBoundary(0.)
}
def rhs(t, u):
return (
diffusion_operator(discr, alpha=1, boundaries=boundaries, u=u) +
actx.np.exp(-np.dot(nodes, nodes) / source_width**2))
rank = comm.Get_rank()
t = 0
t_final = 0.01
istep = 0
while True:
if istep % 10 == 0:
print(istep, t, discr.norm(u))
vis.write_vtk_file(
"fld-heat-source-mpi-%03d-%04d.vtu" % (rank, istep),
[("u", u)])
if t >= t_final:
break
u = rk4_step(u, t, dt, rhs)
t += dt
istep += 1
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim)
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.75 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.45 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
vis = make_visualizer(discr, order + 3 if dim == 2 else order)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
rank = comm.Get_rank()
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_vtk_file(
"fld-wave-eager-mpi-%03d-%04d.vtu" % (rank, istep), [
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def _euler_flow_stepper(actx, parameters):
"""
Implements a generic time stepping loop for testing an inviscid flow.
"""
logging.basicConfig(format="%(message)s", level=logging.INFO)
mesh = parameters["mesh"]
t = parameters["time"]
order = parameters["order"]
t_final = parameters["tfinal"]
initializer = parameters["initializer"]
exittol = parameters["exittol"]
casename = parameters["casename"]
boundaries = parameters["boundaries"]
eos = parameters["eos"]
cfl = parameters["cfl"]
dt = parameters["dt"]
constantcfl = parameters["constantcfl"]
nstepstatus = parameters["nstatus"]
if t_final <= t:
return (0.0)
rank = 0
dim = mesh.dim
istep = 0
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
fields = initializer(0, nodes)
sdt = get_inviscid_timestep(discr, eos=eos, cfl=cfl, q=fields)
initname = initializer.__class__.__name__
eosname = eos.__class__.__name__
message = (f"Num {dim}d order-{order} elements: {mesh.nelements}\n"
f"Timestep: {dt}\n"
f"Final time: {t_final}\n"
f"Status freq: {nstepstatus}\n"
f"Initialization: {initname}\n"
f"EOS: {eosname}")
logger.info(message)
vis = make_visualizer(discr, discr.order + 3 if dim == 2 else discr.order)
def write_soln(write_status=True):
cv = split_conserved(dim, fields)
dv = eos.dependent_vars(cv)
expected_result = initializer(t, nodes)
result_resid = fields - expected_result
maxerr = [
np.max(np.abs(result_resid[i].get())) for i in range(dim + 2)
]
mindv = [np.min(dvfld.get()) for dvfld in dv]
maxdv = [np.max(dvfld.get()) for dvfld in dv]
if write_status is True:
statusmsg = (f"Status: Step({istep}) Time({t})\n"
f"------ P({mindv[0]},{maxdv[0]})\n"
f"------ T({mindv[1]},{maxdv[1]})\n"
f"------ dt,cfl = ({dt},{cfl})\n"
f"------ Err({maxerr})")
logger.info(statusmsg)
io_fields = ["cv", split_conserved(dim, fields)]
io_fields += eos.split_fields(dim, dv)
io_fields.append(("exact_soln", expected_result))
io_fields.append(("residual", result_resid))
nameform = casename + "-{iorank:04d}-{iostep:06d}.vtu"
visfilename = nameform.format(iorank=rank, iostep=istep)
vis.write_vtk_file(visfilename, io_fields)
return maxerr
def rhs(t, q):
return inviscid_operator(discr,
eos=eos,
boundaries=boundaries,
q=q,
t=t)
while t < t_final:
if constantcfl is True:
dt = sdt
else:
cfl = dt / sdt
if nstepstatus > 0:
if istep % nstepstatus == 0:
write_soln()
fields = rk4_step(fields, t, dt, rhs)
t += dt
istep += 1
sdt = get_inviscid_timestep(discr, eos=eos, cfl=cfl, q=fields)
if nstepstatus > 0:
logger.info("Writing final dump.")
maxerr = max(write_soln(False))
else:
expected_result = initializer(t, nodes)
maxerr = discr.norm(fields - expected_result, np.inf)
logger.info(f"Max Error: {maxerr}")
if maxerr > exittol:
raise ValueError("Solution failed to follow expected result.")
return (maxerr)
def test_uniform_rhs(actx_factory, dim, order):
"""Tests the inviscid rhs using a trivial
constant/uniform state which should
yield rhs = 0 to FP. The test is performed
for 1, 2, and 3 dimensions.
"""
actx = actx_factory()
tolerance = 1e-9
maxxerr = 0.0
from pytools.convergence import EOCRecorder
eoc_rec0 = EOCRecorder()
eoc_rec1 = EOCRecorder()
# for nel_1d in [4, 8, 12]:
for nel_1d in [4, 8]:
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim)
logger.info(f"Number of {dim}d elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
mass_input = discr.zeros(actx) + 1
energy_input = discr.zeros(actx) + 2.5
mom_input = make_obj_array(
[discr.zeros(actx) for i in range(discr.dim)])
fields = join_conserved(dim,
mass=mass_input,
energy=energy_input,
momentum=mom_input)
expected_rhs = make_obj_array(
[discr.zeros(actx) for i in range(len(fields))])
boundaries = {BTAG_ALL: DummyBoundary()}
inviscid_rhs = inviscid_operator(discr,
eos=IdealSingleGas(),
boundaries=boundaries,
q=fields,
t=0.0)
rhs_resid = inviscid_rhs - expected_rhs
resid_split = split_conserved(dim, rhs_resid)
rho_resid = resid_split.mass
rhoe_resid = resid_split.energy
mom_resid = resid_split.momentum
rhs_split = split_conserved(dim, inviscid_rhs)
rho_rhs = rhs_split.mass
rhoe_rhs = rhs_split.energy
rhov_rhs = rhs_split.momentum
message = (f"rho_rhs = {rho_rhs}\n"
f"rhoe_rhs = {rhoe_rhs}\n"
f"rhov_rhs = {rhov_rhs}")
logger.info(message)
assert discr.norm(rho_resid, np.inf) < tolerance
assert discr.norm(rhoe_resid, np.inf) < tolerance
for i in range(dim):
assert discr.norm(mom_resid[i], np.inf) < tolerance
err_max = discr.norm(rhs_resid[i], np.inf)
eoc_rec0.add_data_point(1.0 / nel_1d, err_max)
assert (err_max < tolerance)
if err_max > maxxerr:
maxxerr = err_max
# set a non-zero, but uniform velocity component
for i in range(len(mom_input)):
mom_input[i] = discr.zeros(actx) + (-1.0)**i
boundaries = {BTAG_ALL: DummyBoundary()}
inviscid_rhs = inviscid_operator(discr,
eos=IdealSingleGas(),
boundaries=boundaries,
q=fields,
t=0.0)
rhs_resid = inviscid_rhs - expected_rhs
resid_split = split_conserved(dim, rhs_resid)
rho_resid = resid_split.mass
rhoe_resid = resid_split.energy
mom_resid = resid_split.momentum
assert discr.norm(rho_resid, np.inf) < tolerance
assert discr.norm(rhoe_resid, np.inf) < tolerance
for i in range(dim):
assert discr.norm(mom_resid[i], np.inf) < tolerance
err_max = discr.norm(rhs_resid[i], np.inf)
eoc_rec1.add_data_point(1.0 / nel_1d, err_max)
assert (err_max < tolerance)
if err_max > maxxerr:
maxxerr = err_max
message = (f"V == 0 Errors:\n{eoc_rec0}" f"V != 0 Errors:\n{eoc_rec1}")
print(message)
assert (eoc_rec0.order_estimate() >= order - 0.5
or eoc_rec0.max_error() < 1e-9)
assert (eoc_rec1.order_estimate() >= order - 0.5
or eoc_rec1.max_error() < 1e-9)
def test_diffusion_obj_array_vectorize(actx_factory):
"""
Checks that the diffusion operator can be called with either scalars or object
arrays for `u`.
"""
actx = actx_factory()
p = get_decaying_trig(1, 2.)
assert isinstance(p.sym_alpha, Number)
sym_u1 = p.sym_u
sym_u2 = 2 * p.sym_u
sym_diffusion_u1 = sym_diffusion(p.dim, p.sym_alpha, sym_u1)
sym_diffusion_u2 = sym_diffusion(p.dim, p.sym_alpha, sym_u2)
n = 128
mesh = p.get_mesh(n)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=4)
nodes = thaw(actx, discr.nodes())
t = 1.23456789
def sym_eval(expr):
return sym.EvaluationMapper({"x": nodes, "t": t})(expr)
alpha = sym_eval(p.sym_alpha)
u1 = sym_eval(sym_u1)
u2 = sym_eval(sym_u2)
boundaries = p.get_boundaries(discr, actx, t)
diffusion_u1 = diffusion_operator(discr,
quad_tag=DISCR_TAG_BASE,
alpha=alpha,
boundaries=boundaries,
u=u1)
assert isinstance(diffusion_u1, DOFArray)
expected_diffusion_u1 = sym_eval(sym_diffusion_u1)
rel_linf_err = (discr.norm(diffusion_u1 - expected_diffusion_u1, np.inf) /
discr.norm(expected_diffusion_u1, np.inf))
assert rel_linf_err < 1.e-5
boundaries_vector = [boundaries, boundaries]
u_vector = make_obj_array([u1, u2])
diffusion_u_vector = diffusion_operator(discr,
quad_tag=DISCR_TAG_BASE,
alpha=alpha,
boundaries=boundaries_vector,
u=u_vector)
assert isinstance(diffusion_u_vector, np.ndarray)
assert diffusion_u_vector.shape == (2, )
expected_diffusion_u_vector = make_obj_array(
[sym_eval(sym_diffusion_u1),
sym_eval(sym_diffusion_u2)])
rel_linf_err = (
discr.norm(diffusion_u_vector - expected_diffusion_u_vector, np.inf) /
discr.norm(expected_diffusion_u_vector, np.inf))
assert rel_linf_err < 1.e-5
def main(snapshot_pattern="wave-eager-{step:04d}-{rank:04d}.pkl",
restart_step=None):
"""Drive the example."""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
num_parts = comm.Get_size()
if restart_step is None:
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) *
dim)
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
fields = None
else:
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(
actx, snapshot_pattern.format(step=restart_step, rank=rank))
local_mesh = restart_data["local_mesh"]
nel_1d = restart_data["nel_1d"]
assert comm.Get_size() == restart_data["num_parts"]
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if local_mesh.dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.7 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.4 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
t_final = 3
if restart_step is None:
t = 0
istep = 0
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
else:
t = restart_data["t"]
istep = restart_step
assert istep == restart_step
restart_fields = restart_data["fields"]
old_order = restart_data["order"]
if old_order != order:
old_discr = EagerDGDiscretization(actx,
local_mesh,
order=old_order,
mpi_communicator=comm)
from meshmode.discretization.connection import make_same_mesh_connection
connection = make_same_mesh_connection(
actx, discr.discr_from_dd("vol"),
old_discr.discr_from_dd("vol"))
fields = connection(restart_fields)
else:
fields = restart_fields
vis = make_visualizer(discr)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
while t < t_final:
# restart must happen at beginning of step
if istep % 100 == 0 and (
# Do not overwrite the restart file that we just read.
istep != restart_step):
from mirgecom.restart import write_restart_file
write_restart_file(actx,
restart_data={
"local_mesh": local_mesh,
"order": order,
"fields": fields,
"t": t,
"step": istep,
"nel_1d": nel_1d,
"num_parts": num_parts
},
filename=snapshot_pattern.format(step=istep,
rank=rank),
comm=comm)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_parallel_vtk_file(
comm, "fld-wave-eager-mpi-%03d-%04d.vtu" % (rank, istep), [
("u", fields[0]),
("v", fields[1:]),
])
fields = rk4_step(fields, t, dt, rhs)
t += dt
istep += 1