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_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_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_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_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_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 main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 16
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 = 3
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")
print("%d elements" % mesh.nelements)
discr = EagerDGDiscretization(actx, mesh, order=order)
fields = flat_obj_array(
bump(discr, actx),
[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)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
print(f"step: {istep} t: {t} L2: {discr.norm(fields[0])} "
f"sol max: {discr.nodal_max('vol', fields[0])}")
vis.write_vtk_file("fld-wave-eager-%04d.vtu" % istep,
[
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
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_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 = local_grad(discr, cv)
from mirgecom.fluid import species_mass_fraction_gradient
grad_y = species_mass_fraction_gradient(cv, grad_cv)
assert grad_y.shape == (nspecies, dim)
from meshmode.dof_array import DOFArray
assert type(grad_y[0, 0]) == DOFArray
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
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 inf_norm(grad_y[ispec] - exact_grad) < tol
assert inf_norm(grad_y[ispec+1] + exact_grad) < tol
def test_uniform_init(ctx_factory, dim, nspecies):
"""Test the uniform flow initializer.
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 = 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())
velocity = np.ones(shape=(dim, ))
from mirgecom.initializers import Uniform
mass_fracs = np.array([float(ispec + 1) for ispec in range(nspecies)])
initializer = Uniform(dim=dim, mass_fracs=mass_fracs, velocity=velocity)
cv = initializer(nodes)
def inf_norm(data):
if len(data) > 0:
return discr.norm(data, np.inf)
else:
return 0.0
p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass)
exp_p = 1.0
perrmax = inf_norm(p - exp_p)
exp_mass = 1.0
merrmax = inf_norm(cv.mass - exp_mass)
exp_energy = 2.5 + .5 * dim
eerrmax = inf_norm(cv.energy - exp_energy)
exp_species_mass = exp_mass * mass_fracs
mferrmax = inf_norm(cv.species_mass - exp_species_mass)
assert perrmax < 1e-15
assert merrmax < 1e-15
assert eerrmax < 1e-15
assert mferrmax < 1e-15
def test_idealsingle_lump(ctx_factory, dim):
"""Test IdealSingle 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)
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
logger.info(f"Number of elements {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
from meshmode.dof_array import thaw
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
center = np.zeros(shape=(dim, ))
velocity = np.zeros(shape=(dim, ))
velocity[0] = 1
lump = Lump(dim=dim, center=center, velocity=velocity)
eos = IdealSingleGas()
cv = lump(nodes)
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
p = eos.pressure(cv)
exp_p = 1.0
errmax = inf_norm(p - exp_p)
exp_ke = 0.5 * cv.mass
ke = eos.kinetic_energy(cv)
kerr = inf_norm(ke - exp_ke)
te = eos.total_energy(cv, p)
terr = inf_norm(te - cv.energy)
logger.info(f"lump_soln = {cv}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
assert kerr < 1e-15
assert terr < 1e-15
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_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, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
from meshmode.dof_array import thaw
nodes = thaw(actx, discr.nodes())
eos = IdealSingleGas()
# Init soln with Vortex
vortex = Vortex2D()
cv = vortex(nodes)
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
gamma = eos.gamma()
p = eos.pressure(cv)
exp_p = cv.mass**gamma
errmax = inf_norm(p - exp_p)
exp_ke = 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass
ke = eos.kinetic_energy(cv)
kerr = inf_norm(ke - exp_ke)
te = eos.total_energy(cv, p)
terr = inf_norm(te - cv.energy)
logger.info(f"vortex_soln = {cv}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
assert kerr < 1e-15
assert terr < 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 = local_grad(discr, cv)
grad_v = velocity_gradient(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
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
assert inf_norm(grad_v - exp_result) < tol
assert inf_norm(grad_v.T - exp_trans) < tol
assert inf_norm(np.trace(grad_v) - exp_trace) < tol
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_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_inviscid_flux(actx_factory, dim):
"""Identity test - directly check inviscid flux
routine :func:`mirgecom.euler.inviscid_flux` against the exact
expected result. This test is designed to fail
if the flux routine is broken.
The expected inviscid flux is:
F(q) = <rhoV, (E+p)V, rho(V.x.V) + pI>
"""
actx = actx_factory()
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
# for dim in [1, 2, 3]:
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
eos = IdealSingleGas()
logger.info(f"Number of {dim}d elems: {mesh.nelements}")
mass = cl.clrandom.rand(actx.queue, (mesh.nelements, ), dtype=np.float64)
energy = cl.clrandom.rand(actx.queue, (mesh.nelements, ), dtype=np.float64)
mom = make_obj_array([
cl.clrandom.rand(actx.queue, (mesh.nelements, ), dtype=np.float64)
for i in range(dim)
])
q = join_conserved(dim, mass=mass, energy=energy, momentum=mom)
cv = split_conserved(dim, q)
# {{{ create the expected result
p = eos.pressure(cv)
escale = (energy + p) / mass
expected_flux = np.zeros((dim + 2, dim), dtype=object)
expected_flux[0] = mom
expected_flux[1] = mom * make_obj_array([escale])
for i in range(dim):
for j in range(dim):
expected_flux[2 + i,
j] = (mom[i] * mom[j] / mass + (p if i == j else 0))
# }}}
from mirgecom.euler import inviscid_flux
flux = inviscid_flux(discr, eos, q)
flux_resid = flux - expected_flux
for i in range(dim + 2, dim):
for j in range(dim):
assert (la.norm(flux_resid[i, j].get())) == 0.0
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_idealsingle_lump(ctx_factory):
"""
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)
logger.info(f"lump_soln = {lump_soln}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
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_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,
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}")
from mirgecom.initializers import Uniform
initr = Uniform(dim=dim)
initsoln = initr(time=0.0, x_vec=nodes)
tol = 1e-15
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
assert inf_norm(initsoln.mass - 1.0) < tol
assert inf_norm(initsoln.energy - 2.5) < tol
print(f"Uniform Soln:{initsoln}")
eos = IdealSingleGas()
p = eos.pressure(initsoln)
print(f"Press:{p}")
assert inf_norm(p - 1.0) < tol
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 get_discr(order):
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * 2,
b=(0.5, ) * 2,
nelements_per_axis=(4, ) * 2,
boundary_tag_to_face={
"x": ["-x", "+x"],
"y": ["-y", "+y"]
})
from grudge.eager import EagerDGDiscretization
return EagerDGDiscretization(eager_actx, mesh, order=order)
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_analytic_comparison(actx_factory):
"""Quick test of state comparison routine."""
from mirgecom.initializers import Vortex2D
from mirgecom.simutil import compare_fluid_solutions, componentwise_norms
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 = actx.to_numpy(
flatten(componentwise_norms(discr, resid, order=np.inf),
actx)).tolist()
errors = compare_fluid_solutions(discr, cv, cv)
assert max(errors) == 0
errors = compare_fluid_solutions(discr, cv, vortex_soln)
assert errors == expected_errors
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_idealsingle_vortex(ctx_factory):
r"""
Tests that the IdealSingleGas EOS returns
the correct pressure (p) for the Vortex2D solution
field (i.e. :math:'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)
logger.info(f"vortex_soln = {vortex_soln}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
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=}")
