def test_slipwall_identity(actx_factory, dim):
"""Identity test - check for the expected boundary solution.
Checks that the slipwall implements the expected boundary solution:
rho_plus = rho_minus
v_plus = v_minus - 2 * (n_hat . v_minus) * n_hat
mom_plus = rho_plus * v_plus
E_plus = E_minus
"""
actx = actx_factory()
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())
eos = IdealSingleGas()
orig = np.zeros(shape=(dim, ))
nhat = thaw(actx, discr.normal(BTAG_ALL))
gas_model = GasModel(eos=eos)
logger.info(f"Number of {dim}d elems: {mesh.nelements}")
# for velocity going along each direction
for vdir in range(dim):
vel = np.zeros(shape=(dim, ))
# for velocity directions +1, and -1
for parity in [1.0, -1.0]:
vel[vdir] = parity # Check incoming normal
initializer = Lump(dim=dim, center=orig, velocity=vel, rhoamp=0.0)
wall = AdiabaticSlipBoundary()
uniform_state = initializer(nodes)
fluid_state = make_fluid_state(uniform_state, gas_model)
def bnd_norm(vec):
return actx.to_numpy(discr.norm(vec, p=np.inf, dd=BTAG_ALL))
interior_soln = \
project_fluid_state(discr, "vol", BTAG_ALL, gas_model=gas_model,
state=fluid_state)
bnd_soln = \
wall.adiabatic_slip_state(discr, btag=BTAG_ALL, gas_model=gas_model,
state_minus=interior_soln)
from grudge.trace_pair import TracePair
bnd_pair = TracePair(BTAG_ALL,
interior=interior_soln.cv,
exterior=bnd_soln.cv)
# check that mass and energy are preserved
mass_resid = bnd_pair.int.mass - bnd_pair.ext.mass
mass_err = bnd_norm(mass_resid)
assert mass_err == 0.0
energy_resid = bnd_pair.int.energy - bnd_pair.ext.energy
energy_err = bnd_norm(energy_resid)
assert energy_err == 0.0
# check that exterior momentum term is mom_interior - 2 * mom_normal
mom_norm_comp = np.dot(bnd_pair.int.momentum, nhat)
mom_norm = nhat * mom_norm_comp
expected_mom_ext = bnd_pair.int.momentum - 2.0 * mom_norm
mom_resid = bnd_pair.ext.momentum - expected_mom_ext
mom_err = bnd_norm(mom_resid)
assert mom_err == 0.0
def test_slipwall_flux(actx_factory, dim, order):
"""Check for zero boundary flux.
Check for vanishing flux across the slipwall.
"""
actx = actx_factory()
wall = AdiabaticSlipBoundary()
eos = IdealSingleGas()
gas_model = GasModel(eos=eos)
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for nel_1d in [4, 8, 12]:
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)
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
nhat = thaw(actx, discr.normal(BTAG_ALL))
h = 1.0 / nel_1d
def bnd_norm(vec):
return actx.to_numpy(discr.norm(vec, p=np.inf, dd=BTAG_ALL))
logger.info(f"Number of {dim}d elems: {mesh.nelements}")
# for velocities in each direction
err_max = 0.0
for vdir in range(dim):
vel = np.zeros(shape=(dim, ))
# for velocity directions +1, and -1
for parity in [1.0, -1.0]:
vel[vdir] = parity
from mirgecom.initializers import Uniform
initializer = Uniform(dim=dim, velocity=vel)
uniform_state = initializer(nodes)
fluid_state = make_fluid_state(uniform_state, gas_model)
interior_soln = project_fluid_state(discr,
"vol",
BTAG_ALL,
state=fluid_state,
gas_model=gas_model)
bnd_soln = wall.adiabatic_slip_state(discr,
btag=BTAG_ALL,
gas_model=gas_model,
state_minus=interior_soln)
from grudge.trace_pair import TracePair
bnd_pair = TracePair(BTAG_ALL,
interior=interior_soln.cv,
exterior=bnd_soln.cv)
state_pair = TracePair(BTAG_ALL,
interior=interior_soln,
exterior=bnd_soln)
# Check the total velocity component normal
# to each surface. It should be zero. The
# numerical fluxes cannot be zero.
avg_state = 0.5 * (bnd_pair.int + bnd_pair.ext)
err_max = max(err_max,
bnd_norm(np.dot(avg_state.momentum, nhat)))
from mirgecom.inviscid import inviscid_facial_flux
bnd_flux = inviscid_facial_flux(discr, state_pair, local=True)
err_max = max(err_max, bnd_norm(bnd_flux.mass),
bnd_norm(bnd_flux.energy))
eoc.add_data_point(h, err_max)
message = (f"EOC:\n{eoc}")
logger.info(message)
assert (eoc.order_estimate() >= order - 0.5 or eoc.max_error() < 1e-12)