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_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_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 main(ctx_factory=cl.create_some_context,
snapshot_pattern="flame1d-{step:06d}-{rank:04d}.pkl",
restart_step=None,
use_profiling=False,
use_logmgr=False):
"""Drive the Y0 example."""
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = 0
rank = comm.Get_rank()
nparts = comm.Get_size()
"""logging and profiling"""
logmgr = initialize_logmgr(use_logmgr,
filename="flame1d.sqlite",
mode="wo",
mpi_comm=comm)
cl_ctx = ctx_factory()
if use_profiling:
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
actx = PyOpenCLProfilingArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
logmgr=logmgr)
else:
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
#nviz = 500
#nrestart = 500
nviz = 1
nrestart = 3
#current_dt = 5.0e-8 # stable with euler
current_dt = 5.0e-8 # stable with rk4
#current_dt = 4e-7 # stable with lrsrk144
t_final = 1.5e-7
dim = 2
order = 1
exittol = 1000000000000
#t_final = 0.001
current_cfl = 1.0
current_t = 0
constant_cfl = False
nstatus = 10000000000
rank = 0
checkpoint_t = current_t
current_step = 0
vel_burned = np.zeros(shape=(dim, ))
vel_unburned = np.zeros(shape=(dim, ))
# {{{ Set up initial state using Cantera
# Use Cantera for initialization
# -- Pick up a CTI for the thermochemistry config
# --- Note: Users may add their own CTI file by dropping it into
# --- mirgecom/mechanisms alongside the other CTI files.
from mirgecom.mechanisms import get_mechanism_cti
# uiuc C2H4
#mech_cti = get_mechanism_cti("uiuc")
# sanDiego H2
mech_cti = get_mechanism_cti("sanDiego")
cantera_soln = cantera.Solution(phase_id="gas", source=mech_cti)
nspecies = cantera_soln.n_species
# Initial temperature, pressure, and mixutre mole fractions are needed to
# set up the initial state in Cantera.
temp_unburned = 300.0
temp_ignition = 1500.0
# Parameters for calculating the amounts of fuel, oxidizer, and inert species
equiv_ratio = 1.0
ox_di_ratio = 0.21
# H2
stoich_ratio = 0.5
#C2H4
#stoich_ratio = 3.0
# Grab the array indices for the specific species, ethylene, oxygen, and nitrogen
# C2H4
#i_fu = cantera_soln.species_index("C2H4")
# H2
i_fu = cantera_soln.species_index("H2")
i_ox = cantera_soln.species_index("O2")
i_di = cantera_soln.species_index("N2")
x = np.zeros(nspecies)
# Set the species mole fractions according to our desired fuel/air mixture
x[i_fu] = (ox_di_ratio * equiv_ratio) / (stoich_ratio +
ox_di_ratio * equiv_ratio)
x[i_ox] = stoich_ratio * x[i_fu] / equiv_ratio
x[i_di] = (1.0 - ox_di_ratio) * x[i_ox] / ox_di_ratio
# Uncomment next line to make pylint fail when it can't find cantera.one_atm
one_atm = cantera.one_atm # pylint: disable=no-member
# one_atm = 101325.0
pres_unburned = one_atm
# Let the user know about how Cantera is being initilized
print(f"Input state (T,P,X) = ({temp_unburned}, {pres_unburned}, {x}")
# Set Cantera internal gas temperature, pressure, and mole fractios
cantera_soln.TPX = temp_unburned, pres_unburned, x
# Pull temperature, total density, mass fractions, and pressure from Cantera
# We need total density, and mass fractions to initialize the fluid/gas state.
y_unburned = np.zeros(nspecies)
can_t, rho_unburned, y_unburned = cantera_soln.TDY
can_p = cantera_soln.P
# *can_t*, *can_p* should not differ (significantly) from user's initial data,
# but we want to ensure that we use exactly the same starting point as Cantera,
# so we use Cantera's version of these data.
# now find the conditions for the burned gas
cantera_soln.equilibrate('TP')
temp_burned, rho_burned, y_burned = cantera_soln.TDY
pres_burned = cantera_soln.P
casename = "flame1d"
pyrometheus_mechanism = pyro.get_thermochem_class(cantera_soln)(actx.np)
# C2H4
mu = 1.e-5
kappa = 1.6e-5 # Pr = mu*rho/alpha = 0.75
# H2
mu = 1.e-5
kappa = mu * 0.08988 / 0.75 # Pr = mu*rho/alpha = 0.75
species_diffusivity = 1.e-5 * np.ones(nspecies)
transport_model = SimpleTransport(viscosity=mu,
thermal_conductivity=kappa,
species_diffusivity=species_diffusivity)
eos = PyrometheusMixture(pyrometheus_mechanism,
temperature_guess=temp_unburned,
transport_model=transport_model)
species_names = pyrometheus_mechanism.species_names
print(f"Pyrometheus mechanism species names {species_names}")
print(
f"Unburned state (T,P,Y) = ({temp_unburned}, {pres_unburned}, {y_unburned}"
)
print(f"Burned state (T,P,Y) = ({temp_burned}, {pres_burned}, {y_burned}")
flame_start_loc = 0.05
flame_speed = 1000
# use the burned conditions with a lower temperature
bulk_init = PlanarDiscontinuity(dim=dim,
disc_location=flame_start_loc,
sigma=0.01,
nspecies=nspecies,
temperature_left=temp_ignition,
temperature_right=temp_unburned,
pressure_left=pres_burned,
pressure_right=pres_unburned,
velocity_left=vel_burned,
velocity_right=vel_unburned,
species_mass_left=y_burned,
species_mass_right=y_unburned)
inflow_init = MixtureInitializer(dim=dim,
nspecies=nspecies,
pressure=pres_burned,
temperature=temp_ignition,
massfractions=y_burned,
velocity=vel_burned)
outflow_init = MixtureInitializer(dim=dim,
nspecies=nspecies,
pressure=pres_unburned,
temperature=temp_unburned,
massfractions=y_unburned,
velocity=vel_unburned)
inflow = PrescribedViscousBoundary(q_func=inflow_init)
outflow = PrescribedViscousBoundary(q_func=outflow_init)
wall = PrescribedViscousBoundary(
) # essentially a "dummy" use the interior solution for the exterior
from grudge import sym
boundaries = {
sym.DTAG_BOUNDARY("Inflow"): inflow,
sym.DTAG_BOUNDARY("Outflow"): outflow,
sym.DTAG_BOUNDARY("Wall"): wall
}
if restart_step is None:
char_len = 0.001
box_ll = (0.0, 0.0)
box_ur = (0.25, 0.01)
num_elements = (int((box_ur[0] - box_ll[0]) / char_len),
int((box_ur[1] - box_ll[1]) / char_len))
from meshmode.mesh.generation import generate_regular_rect_mesh
generate_mesh = partial(generate_regular_rect_mesh,
a=box_ll,
b=box_ur,
n=num_elements,
mesh_type="X",
boundary_tag_to_face={
"Inflow": ["-x"],
"Outflow": ["+x"],
"Wall": ["+y", "-y"]
})
local_mesh, global_nelements = generate_and_distribute_mesh(
comm, generate_mesh)
local_nelements = local_mesh.nelements
else: # Restart
with open(snapshot_pattern.format(step=restart_step, rank=rank),
"rb") as f:
restart_data = pickle.load(f)
local_mesh = restart_data["local_mesh"]
local_nelements = local_mesh.nelements
global_nelements = restart_data["global_nelements"]
assert comm.Get_size() == restart_data["num_parts"]
if rank == 0:
logging.info("Making discretization")
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
nodes = thaw(actx, discr.nodes())
if restart_step is None:
if rank == 0:
logging.info("Initializing soln.")
# for Discontinuity initial conditions
current_state = bulk_init(t=0., x_vec=nodes, eos=eos)
# for uniform background initial condition
#current_state = bulk_init(nodes, eos=eos)
else:
current_t = restart_data["t"]
current_step = restart_step
current_state = unflatten(
actx, discr.discr_from_dd("vol"),
obj_array_vectorize(actx.from_numpy, restart_data["state"]))
vis_timer = None
if logmgr:
logmgr_add_cl_device_info(logmgr, queue)
logmgr_add_many_discretization_quantities(logmgr, discr, dim,
extract_vars_for_logging,
units_for_logging)
logmgr.add_watches([
"step.max", "t_sim.max", "t_step.max", "t_log.max", "min_pressure",
"max_pressure", "min_temperature", "max_temperature"
])
try:
logmgr.add_watches(
["memory_usage_python.max", "memory_usage_gpu.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["pyopencl_array_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
visualizer = make_visualizer(discr, order)
# initname = initializer.__class__.__name__
initname = "flame1d"
eosname = eos.__class__.__name__
init_message = make_init_message(dim=dim,
order=order,
nelements=local_nelements,
global_nelements=global_nelements,
dt=current_dt,
t_final=t_final,
nstatus=nstatus,
nviz=nviz,
cfl=current_cfl,
constant_cfl=constant_cfl,
initname=initname,
eosname=eosname,
casename=casename)
if rank == 0:
logger.info(init_message)
#timestepper = rk4_step
#timestepper = lsrk54_step
#timestepper = lsrk144_step
timestepper = euler_step
get_timestep = partial(inviscid_sim_timestep,
discr=discr,
t=current_t,
dt=current_dt,
cfl=current_cfl,
eos=eos,
t_final=t_final,
constant_cfl=constant_cfl)
def my_rhs(t, state):
# check for some troublesome output types
inf_exists = not np.isfinite(discr.norm(state, np.inf))
if inf_exists:
if rank == 0:
logging.info(
"Non-finite values detected in simulation, exiting...")
# dump right now
sim_checkpoint(discr=discr,
visualizer=visualizer,
eos=eos,
q=state,
vizname=casename,
step=999999999,
t=t,
dt=current_dt,
nviz=1,
exittol=exittol,
constant_cfl=constant_cfl,
comm=comm,
vis_timer=vis_timer,
overwrite=True,
s0=s0_sc,
kappa=kappa_sc)
exit()
cv = split_conserved(dim=dim, q=state)
return (
ns_operator(discr, q=state, t=t, boundaries=boundaries, eos=eos) +
eos.get_species_source_terms(cv))
def my_checkpoint(step, t, dt, state):
write_restart = (check_step(step, nrestart)
if step != restart_step else False)
if write_restart is True:
with open(snapshot_pattern.format(step=step, rank=rank),
"wb") as f:
pickle.dump(
{
"local_mesh": local_mesh,
"state": obj_array_vectorize(actx.to_numpy,
flatten(state)),
"t": t,
"step": step,
"global_nelements": global_nelements,
"num_parts": nparts,
}, f)
def loc_fn(t):
return flame_start_loc + flame_speed * t
exact_soln = PlanarDiscontinuity(dim=dim,
disc_location=loc_fn,
sigma=0.0000001,
nspecies=nspecies,
temperature_left=temp_ignition,
temperature_right=temp_unburned,
pressure_left=pres_burned,
pressure_right=pres_unburned,
velocity_left=vel_burned,
velocity_right=vel_unburned,
species_mass_left=y_burned,
species_mass_right=y_unburned)
cv = split_conserved(dim, state)
reaction_rates = eos.get_production_rates(cv)
viz_fields = [("reaction_rates", reaction_rates)]
return sim_checkpoint(discr=discr,
visualizer=visualizer,
eos=eos,
q=state,
vizname=casename,
step=step,
t=t,
dt=dt,
nstatus=nstatus,
nviz=nviz,
exittol=exittol,
constant_cfl=constant_cfl,
comm=comm,
vis_timer=vis_timer,
overwrite=True,
exact_soln=exact_soln,
viz_fields=viz_fields)
if rank == 0:
logging.info("Stepping.")
(current_step, current_t, current_state) = \
advance_state(rhs=my_rhs, timestepper=timestepper,
checkpoint=my_checkpoint,
get_timestep=get_timestep, state=current_state,
t_final=t_final, t=current_t, istep=current_step,
logmgr=logmgr,eos=eos,dim=dim)
if rank == 0:
logger.info("Checkpointing final state ...")
my_checkpoint(current_step,
t=current_t,
dt=(current_t - checkpoint_t),
state=current_state)
if current_t - t_final < 0:
raise ValueError("Simulation exited abnormally")
if logmgr:
logmgr.close()
elif use_profiling:
print(actx.tabulate_profiling_data())
exit()
def main(ctx_factory=cl.create_some_context,
casename="flame1d",
user_input_file=None,
snapshot_pattern="{casename}-{step:06d}-{rank:04d}.pkl",
restart_step=None,
restart_name=None,
use_profiling=False,
use_logmgr=False,
use_lazy_eval=False):
"""Drive the 1D Flame example."""
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = 0
rank = comm.Get_rank()
nparts = comm.Get_size()
if restart_name is None:
restart_name = casename
"""logging and profiling"""
logmgr = initialize_logmgr(use_logmgr,
filename=(f"{casename}.sqlite"),
mode="wo",
mpi_comm=comm)
cl_ctx = ctx_factory()
if use_profiling:
if use_lazy_eval:
raise RuntimeError("Cannot run lazy with profiling.")
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
actx = PyOpenCLProfilingArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
logmgr=logmgr)
else:
queue = cl.CommandQueue(cl_ctx)
if use_lazy_eval:
actx = PytatoArrayContext(queue)
else:
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
# default input values that will be read from input (if they exist)
nviz = 100
nrestart = 100
nhealth = 100
nstatus = 1
current_dt = 1e-9
t_final = 1.e-3
order = 1
integrator = "rk4"
if user_input_file:
if rank == 0:
with open(user_input_file) as f:
input_data = yaml.load(f, Loader=yaml.FullLoader)
else:
input_data = None
input_data = comm.bcast(input_data, root=0)
#print(input_data)
try:
nviz = int(input_data["nviz"])
except KeyError:
pass
try:
nrestart = int(input_data["nrestart"])
except KeyError:
pass
try:
nhealth = int(input_data["nhealth"])
except KeyError:
pass
try:
nstatus = int(input_data["nstatus"])
except KeyError:
pass
try:
current_dt = float(input_data["current_dt"])
except KeyError:
pass
try:
t_final = float(input_data["t_final"])
except KeyError:
pass
try:
order = int(input_data["order"])
except KeyError:
pass
try:
integrator = input_data["integrator"]
except KeyError:
pass
# param sanity check
allowed_integrators = ["rk4", "euler", "lsrk54", "lsrk144"]
if (integrator not in allowed_integrators):
error_message = "Invalid time integrator: {}".format(integrator)
raise RuntimeError(error_message)
timestepper = rk4_step
if integrator == "euler":
timestepper = euler_step
if integrator == "lsrk54":
timestepper = lsrk54_step
if integrator == "lsrk144":
timestepper = lsrk144_step
if (rank == 0):
print(f'#### Simluation control data: ####')
print(f'\tnviz = {nviz}')
print(f'\tnrestart = {nrestart}')
print(f'\tnhealth = {nhealth}')
print(f'\tnstatus = {nstatus}')
print(f'\tcurrent_dt = {current_dt}')
print(f'\tt_final = {t_final}')
print(f'\torder = {order}')
print(f"\tTime integration {integrator}")
print(f'#### Simluation control data: ####')
restart_path = 'restart_data/'
viz_path = 'viz_data/'
#if(rank == 0):
#if not os.path.exists(restart_path):
#os.makedirs(restart_path)
#if not os.path.exists(viz_path):
#os.makedirs(viz_path)
dim = 2
exittol = .09
current_cfl = 1.0
current_t = 0
constant_cfl = False
checkpoint_t = current_t
current_step = 0
vel_burned = np.zeros(shape=(dim, ))
vel_unburned = np.zeros(shape=(dim, ))
# {{{ Set up initial state using Cantera
# Use Cantera for initialization
# -- Pick up a CTI for the thermochemistry config
# --- Note: Users may add their own CTI file by dropping it into
# --- mirgecom/mechanisms alongside the other CTI files.
fuel = "H2"
allowed_fuels = ["H2", "C2H4"]
if (fuel not in allowed_fuels):
error_message = "Invalid fuel selection: {}".format(fuel)
raise RuntimeError(error_message)
if rank == 0:
print(f"Fuel: {fuel}")
from mirgecom.mechanisms import get_mechanism_cti
if fuel == "C2H4":
mech_cti = get_mechanism_cti("uiuc")
elif fuel == "H2":
mech_cti = get_mechanism_cti("sanDiego")
cantera_soln = cantera.Solution(phase_id="gas", source=mech_cti)
nspecies = cantera_soln.n_species
# Initial temperature, pressure, and mixutre mole fractions are needed to
# set up the initial state in Cantera.
temp_unburned = 300.0
temp_ignition = 1500.0
# Parameters for calculating the amounts of fuel, oxidizer, and inert species
if fuel == "C2H4":
stoich_ratio = 3.0
if fuel == "H2":
stoich_ratio = 0.5
equiv_ratio = 1.0
ox_di_ratio = 0.21
# Grab the array indices for the specific species, ethylene, oxygen, and nitrogen
i_fu = cantera_soln.species_index(fuel)
i_ox = cantera_soln.species_index("O2")
i_di = cantera_soln.species_index("N2")
x = np.zeros(nspecies)
# Set the species mole fractions according to our desired fuel/air mixture
x[i_fu] = (ox_di_ratio * equiv_ratio) / (stoich_ratio +
ox_di_ratio * equiv_ratio)
x[i_ox] = stoich_ratio * x[i_fu] / equiv_ratio
x[i_di] = (1.0 - ox_di_ratio) * x[i_ox] / ox_di_ratio
# Uncomment next line to make pylint fail when it can't find cantera.one_atm
one_atm = cantera.one_atm # pylint: disable=no-member
# one_atm = 101325.0
pres_unburned = one_atm
# Let the user know about how Cantera is being initilized
print(f"Input state (T,P,X) = ({temp_unburned}, {pres_unburned}, {x}")
# Set Cantera internal gas temperature, pressure, and mole fractios
cantera_soln.TPX = temp_unburned, pres_unburned, x
# Pull temperature, total density, mass fractions, and pressure from Cantera
# We need total density, and mass fractions to initialize the fluid/gas state.
y_unburned = np.zeros(nspecies)
can_t, rho_unburned, y_unburned = cantera_soln.TDY
can_p = cantera_soln.P
# *can_t*, *can_p* should not differ (significantly) from user's initial data,
# but we want to ensure that we use exactly the same starting point as Cantera,
# so we use Cantera's version of these data.
# now find the conditions for the burned gas
cantera_soln.equilibrate('TP')
temp_burned, rho_burned, y_burned = cantera_soln.TDY
pres_burned = cantera_soln.P
pyrometheus_mechanism = pyro.get_thermochem_class(cantera_soln)(actx.np)
kappa = 1.6e-5 # Pr = mu*rho/alpha = 0.75
mu = 1.e-5
species_diffusivity = 1.e-5 * np.ones(nspecies)
transport_model = SimpleTransport(viscosity=mu,
thermal_conductivity=kappa,
species_diffusivity=species_diffusivity)
eos = PyrometheusMixture(pyrometheus_mechanism,
temperature_guess=temp_unburned,
transport_model=transport_model)
species_names = pyrometheus_mechanism.species_names
print(f"Pyrometheus mechanism species names {species_names}")
print(
f"Unburned state (T,P,Y) = ({temp_unburned}, {pres_unburned}, {y_unburned}"
)
print(f"Burned state (T,P,Y) = ({temp_burned}, {pres_burned}, {y_burned}")
flame_start_loc = 0.10
flame_speed = 1000
# use the burned conditions with a lower temperature
#bulk_init = PlanarDiscontinuity(dim=dim, disc_location=flame_start_loc, sigma=0.01, nspecies=nspecies,
#temperature_left=temp_ignition, temperature_right=temp_unburned,
#pressure_left=pres_burned, pressure_right=pres_unburned,
#velocity_left=vel_burned, velocity_right=vel_unburned,
#species_mass_left=y_burned, species_mass_right=y_unburned)
bulk_init = PlanarDiscontinuity(dim=dim,
disc_location=flame_start_loc,
sigma=0.0005,
nspecies=nspecies,
temperature_right=temp_ignition,
temperature_left=temp_unburned,
pressure_right=pres_burned,
pressure_left=pres_unburned,
velocity_right=vel_burned,
velocity_left=vel_unburned,
species_mass_right=y_burned,
species_mass_left=y_unburned)
inflow_init = MixtureInitializer(dim=dim,
nspecies=nspecies,
pressure=pres_burned,
temperature=temp_ignition,
massfractions=y_burned,
velocity=vel_burned)
outflow_init = MixtureInitializer(dim=dim,
nspecies=nspecies,
pressure=pres_unburned,
temperature=temp_unburned,
massfractions=y_unburned,
velocity=vel_unburned)
def symmetry(nodes, eos, cv=None, **kwargs):
dim = len(nodes)
if cv is not None:
#cv = split_conserved(dim, q)
mass = cv.mass
momentum = cv.momentum
momentum[1] = -1.0 * momentum[1]
ke = .5 * np.dot(cv.momentum, cv.momentum) / cv.mass
energy = cv.energy
species_mass = cv.species_mass
return make_conserved(dim=dim,
mass=mass,
momentum=momentum,
energy=energy,
species_mass=species_mass)
def dummy(nodes, eos, cv=None, **kwargs):
dim = len(nodes)
if cv is not None:
#cv = split_conserved(dim, q)
mass = cv.mass
momentum = cv.momentum
ke = .5 * np.dot(cv.momentum, cv.momentum) / cv.mass
energy = cv.energy
species_mass = cv.species_mass
return make_conserved(dim=dim,
mass=mass,
momentum=momentum,
energy=energy,
species_mass=species_mass)
inflow = PrescribedViscousBoundary(q_func=inflow_init)
outflow = PrescribedViscousBoundary(q_func=outflow_init)
wall_symmetry = PrescribedViscousBoundary(q_func=symmetry)
wall_dummy = PrescribedViscousBoundary(q_func=dummy)
wall = PrescribedViscousBoundary(
) # essentially a "dummy" use the interior solution for the exterior
boundaries = {
DTAG_BOUNDARY("Inflow"): inflow,
DTAG_BOUNDARY("Outflow"): outflow,
#DTAG_BOUNDARY("Wall"): wall_dummy}
DTAG_BOUNDARY("Wall"): wall_symmetry
}
if restart_step is None:
char_len = 0.0001
box_ll = (0.0, 0.0)
box_ur = (0.2, 0.00125)
num_elements = (int((box_ur[0] - box_ll[0]) / char_len),
int((box_ur[1] - box_ll[1]) / char_len))
from meshmode.mesh.generation import generate_regular_rect_mesh
generate_mesh = partial(generate_regular_rect_mesh,
a=box_ll,
b=box_ur,
n=num_elements,
boundary_tag_to_face={
"Inflow": ["+x"],
"Outflow": ["-x"],
"Wall": ["+y", "-y"]
})
local_mesh, global_nelements = generate_and_distribute_mesh(
comm, generate_mesh)
local_nelements = local_mesh.nelements
else: # Restart
from mirgecom.restart import read_restart_data
restart_file = restart_path + snapshot_pattern.format(
casename=restart_name, step=restart_step, rank=rank)
restart_data = read_restart_data(actx, restart_file)
local_mesh = restart_data["local_mesh"]
local_nelements = local_mesh.nelements
global_nelements = restart_data["global_nelements"]
assert comm.Get_size() == restart_data["num_parts"]
if rank == 0:
logging.info("Making discretization")
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
nodes = thaw(actx, discr.nodes())
if restart_step is None:
if rank == 0:
logging.info("Initializing soln.")
# for Discontinuity initial conditions
current_state = bulk_init(x_vec=nodes, eos=eos, time=0.)
# for uniform background initial condition
#current_state = bulk_init(nodes, eos=eos)
else:
current_t = restart_data["t"]
current_step = restart_step
#current_state = make_fluid_restart_state(actx, discr.discr_from_dd("vol"), restart_data["state"])
current_state = restart_data["state"]
vis_timer = None
log_cfl = LogUserQuantity(name="cfl", value=current_cfl)
if logmgr:
logmgr_add_cl_device_info(logmgr, queue)
logmgr_add_many_discretization_quantities(logmgr, discr, dim,
extract_vars_for_logging,
units_for_logging)
logmgr_set_time(logmgr, current_step, current_t)
logmgr.add_quantity(log_cfl, interval=nstatus)
#logmgr_add_package_versions(logmgr)
logmgr.add_watches([
("step.max", "step = {value}, "),
("t_sim.max", "sim time: {value:1.6e} s, "),
("cfl.max", "cfl = {value:1.4f}\n"),
("min_pressure", "------- P (min, max) (Pa) = ({value:1.9e}, "),
("max_pressure", "{value:1.9e})\n"),
("min_temperature", "------- T (min, max) (K) = ({value:7g}, "),
("max_temperature", "{value:7g})\n"),
("t_step.max", "------- step walltime: {value:6g} s, "),
("t_log.max", "log walltime: {value:6g} s")
])
try:
logmgr.add_watches(["memory_usage.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["pyopencl_array_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
visualizer = make_visualizer(discr)
initname = "flame1d"
eosname = eos.__class__.__name__
init_message = make_init_message(dim=dim,
order=order,
nelements=local_nelements,
global_nelements=global_nelements,
dt=current_dt,
t_final=t_final,
nstatus=nstatus,
nviz=nviz,
cfl=current_cfl,
constant_cfl=constant_cfl,
initname=initname,
eosname=eosname,
casename=casename)
if rank == 0:
logger.info(init_message)
get_timestep = partial(inviscid_sim_timestep,
discr=discr,
t=current_t,
dt=current_dt,
cfl=current_cfl,
eos=eos,
t_final=t_final,
constant_cfl=constant_cfl)
def my_rhs(t, state):
return (
ns_operator(discr, cv=state, t=t, boundaries=boundaries, eos=eos) +
eos.get_species_source_terms(cv=state))
def my_checkpoint(step, t, dt, state, force=False):
do_health = force or check_step(step, nhealth) and step > 0
do_viz = force or check_step(step, nviz)
do_restart = force or check_step(step, nrestart)
do_status = force or check_step(step, nstatus)
if do_viz or do_health:
dv = eos.dependent_vars(state)
errors = False
if do_health:
health_message = ""
if check_naninf_local(discr, "vol", dv.pressure):
errors = True
health_message += "Invalid pressure data found.\n"
elif check_range_local(discr,
"vol",
dv.pressure,
min_value=1,
max_value=2.e6):
errors = True
health_message += "Pressure data failed health check.\n"
errors = comm.allreduce(errors, MPI.LOR)
if errors:
if rank == 0:
logger.info("Fluid solution failed health check.")
if health_message:
logger.info(f"{rank=}: {health_message}")
#if check_step(step, nrestart) and step != restart_step and not errors:
if do_restart or errors:
filename = restart_path + snapshot_pattern.format(
step=step, rank=rank, casename=casename)
restart_dictionary = {
"local_mesh": local_mesh,
"order": order,
"state": state,
"t": t,
"step": step,
"global_nelements": global_nelements,
"num_parts": nparts
}
write_restart_file(actx, restart_dictionary, filename, comm)
if do_status or do_viz or errors:
local_cfl = get_inviscid_cfl(discr, eos=eos, dt=dt, cv=state)
max_cfl = nodal_max(discr, "vol", local_cfl)
log_cfl.set_quantity(max_cfl)
#if ((check_step(step, nviz) and step != restart_step) or errors):
if do_viz or errors:
def loc_fn(t):
return flame_start_loc + flame_speed * t
#exact_soln = PlanarDiscontinuity(dim=dim, disc_location=loc_fn,
#sigma=0.0000001, nspecies=nspecies,
#temperature_left=temp_ignition, temperature_right=temp_unburned,
#pressure_left=pres_burned, pressure_right=pres_unburned,
#velocity_left=vel_burned, velocity_right=vel_unburned,
#species_mass_left=y_burned, species_mass_right=y_unburned)
reaction_rates = eos.get_production_rates(cv=state)
# conserved quantities
viz_fields = [
#("cv", state),
("CV_rho", state.mass),
("CV_rhoU", state.momentum[0]),
("CV_rhoV", state.momentum[1]),
("CV_rhoE", state.energy)
]
# species mass fractions
viz_fields.extend(
("Y_" + species_names[i], state.species_mass[i] / state.mass)
for i in range(nspecies))
# dependent variables
viz_fields.extend([
("DV", eos.dependent_vars(state)),
#("exact_soln", exact_soln),
("reaction_rates", reaction_rates),
("cfl", local_cfl)
])
write_visfile(discr,
viz_fields,
visualizer,
vizname=viz_path + casename,
step=step,
t=t,
overwrite=True,
vis_timer=vis_timer)
if errors:
raise RuntimeError("Error detected by user checkpoint, exiting.")
if rank == 0:
logging.info("Stepping.")
(current_step, current_t, current_state) = \
advance_state(rhs=my_rhs, timestepper=timestepper,
checkpoint=my_checkpoint,
get_timestep=get_timestep, state=current_state,
t_final=t_final, t=current_t, istep=current_step,
logmgr=logmgr,eos=eos,dim=dim)
if rank == 0:
logger.info("Checkpointing final state ...")
my_checkpoint(current_step,
t=current_t,
dt=(current_t - checkpoint_t),
state=current_state,
force=True)
if logmgr:
logmgr.close()
elif use_profiling:
print(actx.tabulate_profiling_data())
exit()
def run_init(
ctx_factory=cl.create_some_context,
snapshot_pattern="flame1d-{step:06d}-{rank:04d}.pkl",
):
"""Drive the Y0 example."""
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = 0
rank = comm.Get_rank()
nparts = comm.Get_size()
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
dim = 2
order = 1
vel_burned = np.zeros(shape=(dim, ))
vel_unburned = np.zeros(shape=(dim, ))
# {{{ Set up initial state using Cantera
# Use Cantera for initialization
# -- Pick up a CTI for the thermochemistry config
# --- Note: Users may add their own CTI file by dropping it into
# --- mirgecom/mechanisms alongside the other CTI files.
from mirgecom.mechanisms import get_mechanism_cti
# uiuc C2H4
#mech_cti = get_mechanism_cti("uiuc")
# sanDiego H2
mech_cti = get_mechanism_cti("sanDiego")
cantera_soln = cantera.Solution(phase_id="gas", source=mech_cti)
nspecies = cantera_soln.n_species
# Initial temperature, pressure, and mixutre mole fractions are needed to
# set up the initial state in Cantera.
temp_unburned = 300.0
temp_ignition = 1500.0
# Parameters for calculating the amounts of fuel, oxidizer, and inert species
equiv_ratio = 1.0
ox_di_ratio = 0.21
# H2
stoich_ratio = 0.5
#C2H4
#stoich_ratio = 3.0
# Grab the array indices for the specific species, ethylene, oxygen, and nitrogen
# C2H4
#i_fu = cantera_soln.species_index("C2H4")
# H2
i_fu = cantera_soln.species_index("H2")
i_ox = cantera_soln.species_index("O2")
i_di = cantera_soln.species_index("N2")
x = np.zeros(nspecies)
# Set the species mole fractions according to our desired fuel/air mixture
x[i_fu] = (ox_di_ratio * equiv_ratio) / (stoich_ratio +
ox_di_ratio * equiv_ratio)
x[i_ox] = stoich_ratio * x[i_fu] / equiv_ratio
x[i_di] = (1.0 - ox_di_ratio) * x[i_ox] / ox_di_ratio
# Uncomment next line to make pylint fail when it can't find cantera.one_atm
one_atm = cantera.one_atm # pylint: disable=no-member
# one_atm = 101325.0
pres_unburned = one_atm
# Let the user know about how Cantera is being initilized
print(f"Input state (T,P,X) = ({temp_unburned}, {pres_unburned}, {x}")
# Set Cantera internal gas temperature, pressure, and mole fractios
cantera_soln.TPX = temp_unburned, pres_unburned, x
# Pull temperature, total density, mass fractions, and pressure from Cantera
# We need total density, and mass fractions to initialize the fluid/gas state.
y_unburned = np.zeros(nspecies)
can_t, rho_unburned, y_unburned = cantera_soln.TDY
can_p = cantera_soln.P
# *can_t*, *can_p* should not differ (significantly) from user's initial data,
# but we want to ensure that we use exactly the same starting point as Cantera,
# so we use Cantera's version of these data.
# now find the conditions for the burned gas
cantera_soln.equilibrate('TP')
temp_burned, rho_burned, y_burned = cantera_soln.TDY
pres_burned = cantera_soln.P
casename = "flame1d"
pyrometheus_mechanism = pyro.get_thermochem_class(cantera_soln)(actx.np)
# C2H4
mu = 1.e-5
kappa = 1.6e-5 # Pr = mu*rho/alpha = 0.75
# H2
mu = 1.e-5
kappa = mu * 0.08988 / 0.75 # Pr = mu*rho/alpha = 0.75
species_diffusivity = 1.e-5 * np.ones(nspecies)
transport_model = SimpleTransport(viscosity=mu,
thermal_conductivity=kappa,
species_diffusivity=species_diffusivity)
eos = PyrometheusMixture(pyrometheus_mechanism,
temperature_guess=temp_unburned,
transport_model=transport_model)
species_names = pyrometheus_mechanism.species_names
print(f"Pyrometheus mechanism species names {species_names}")
print(
f"Unburned state (T,P,Y) = ({temp_unburned}, {pres_unburned}, {y_unburned}"
)
print(f"Burned state (T,P,Y) = ({temp_burned}, {pres_burned}, {y_burned}")
flame_start_loc = 0.05
flame_speed = 1000
# use the burned conditions with a lower temperature
bulk_init = PlanarDiscontinuity(dim=dim,
disc_location=flame_start_loc,
sigma=0.01,
nspecies=nspecies,
temperature_left=temp_ignition,
temperature_right=temp_unburned,
pressure_left=pres_burned,
pressure_right=pres_unburned,
velocity_left=vel_burned,
velocity_right=vel_unburned,
species_mass_left=y_burned,
species_mass_right=y_unburned)
char_len = 0.001
box_ll = (0.0, 0.0)
box_ur = (0.25, 0.01)
num_elements = (int((box_ur[0] - box_ll[0]) / char_len),
int((box_ur[1] - box_ll[1]) / char_len))
from meshmode.mesh.generation import generate_regular_rect_mesh
generate_mesh = partial(generate_regular_rect_mesh,
a=box_ll,
b=box_ur,
n=num_elements,
mesh_type="X",
boundary_tag_to_face={
"Inflow": ["-x"],
"Outflow": ["+x"],
"Wall": ["+y", "-y"]
})
local_mesh, global_nelements = generate_and_distribute_mesh(
comm, generate_mesh)
local_nelements = local_mesh.nelements
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
nodes = thaw(actx, discr.nodes())
# for Discontinuity initial conditions
state = bulk_init(t=0., x_vec=nodes, eos=eos)
# for uniform background initial condition
#current_state = bulk_init(nodes, eos=eos)
visualizer = make_visualizer(discr, order)
with open(snapshot_pattern.format(step=0, rank=rank), "wb") as f:
pickle.dump(
{
"local_mesh": local_mesh,
"state": obj_array_vectorize(actx.to_numpy, flatten(state)),
"t": 0.,
"step": 0,
"global_nelements": global_nelements,
"num_parts": nparts,
}, f)
cv = split_conserved(dim, state)
reaction_rates = eos.get_production_rates(cv)
viz_fields = [("reaction_rates", reaction_rates)]
sim_checkpoint(discr=discr,
visualizer=visualizer,
eos=eos,
q=state,
vizname=casename,
nviz=0,
comm=comm,
overwrite=True,
viz_fields=viz_fields)
exit()
def test_diffusive_heat_flux(actx_factory):
"""Test diffusive heat flux 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])
# assemble y so that each one has simple, but unique grad components
nspecies = 2 * dim
y = make_obj_array([ones for _ in range(nspecies)])
for idim in range(dim):
ispec = 2 * idim
y[ispec] = (ispec + 1) * (idim * dim + 1) * sum(
[(iidim + 1) * nodes[iidim] for iidim in range(dim)])
y[ispec + 1] = -y[ispec]
massval = 2
mass = massval * ones
energy = zeros + 2.5
mom = mass * velocity
species_mass = mass * y
cv = make_conserved(dim,
mass=mass,
energy=energy,
momentum=mom,
species_mass=species_mass)
grad_cv = op.local_grad(discr, cv)
mu_b = 1.0
mu = 0.5
kappa = 5.0
# assemble d_alpha so that every species has a unique j
d_alpha = np.array([(ispec + 1) for ispec in range(nspecies)])
tv_model = SimpleTransport(bulk_viscosity=mu_b,
viscosity=mu,
thermal_conductivity=kappa,
species_diffusivity=d_alpha)
eos = IdealSingleGas()
gas_model = GasModel(eos=eos, transport=tv_model)
fluid_state = make_fluid_state(cv, gas_model)
from mirgecom.viscous import diffusive_flux
j = diffusive_flux(fluid_state, grad_cv)
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
tol = 1e-10
for idim in range(dim):
ispec = 2 * idim
exact_dy = np.array([((ispec + 1) * (idim * dim + 1)) * (iidim + 1)
for iidim in range(dim)])
exact_j = -massval * d_alpha[ispec] * exact_dy
assert inf_norm(j[ispec] - exact_j) < tol
exact_j = massval * d_alpha[ispec + 1] * exact_dy
assert inf_norm(j[ispec + 1] - exact_j) < tol
def test_poiseuille_fluxes(actx_factory, order, kappa):
"""Test the viscous fluxes using a Poiseuille input state."""
actx = actx_factory()
dim = 2
from pytools.convergence import EOCRecorder
e_eoc_rec = EOCRecorder()
p_eoc_rec = EOCRecorder()
base_pressure = 100000.0
pressure_ratio = 1.001
mu = 42 # arbitrary
left_boundary_location = 0
right_boundary_location = 0.1
ybottom = 0.
ytop = .02
nspecies = 0
spec_diffusivity = 0 * np.ones(nspecies)
transport_model = SimpleTransport(viscosity=mu,
thermal_conductivity=kappa,
species_diffusivity=spec_diffusivity)
xlen = right_boundary_location - left_boundary_location
p_low = base_pressure
p_hi = pressure_ratio * base_pressure
dpdx = (p_low - p_hi) / xlen
rho = 1.0
eos = IdealSingleGas()
gas_model = GasModel(eos=eos, transport=transport_model)
from mirgecom.initializers import PlanarPoiseuille
initializer = PlanarPoiseuille(density=rho, mu=mu)
def _elbnd_flux(discr, compute_interior_flux, compute_boundary_flux,
int_tpair, boundaries):
return (compute_interior_flux(int_tpair) +
sum(compute_boundary_flux(btag) for btag in boundaries))
from mirgecom.flux import gradient_flux_central
def cv_flux_interior(int_tpair):
normal = thaw(actx, discr.normal(int_tpair.dd))
flux_weak = gradient_flux_central(int_tpair, normal)
dd_all_faces = int_tpair.dd.with_dtag("all_faces")
return discr.project(int_tpair.dd, dd_all_faces, flux_weak)
def cv_flux_boundary(btag):
boundary_discr = discr.discr_from_dd(btag)
bnd_nodes = thaw(actx, boundary_discr.nodes())
cv_bnd = initializer(x_vec=bnd_nodes, eos=eos)
bnd_nhat = thaw(actx, discr.normal(btag))
from grudge.trace_pair import TracePair
bnd_tpair = TracePair(btag, interior=cv_bnd, exterior=cv_bnd)
flux_weak = gradient_flux_central(bnd_tpair, bnd_nhat)
dd_all_faces = bnd_tpair.dd.with_dtag("all_faces")
return discr.project(bnd_tpair.dd, dd_all_faces, flux_weak)
for nfac in [1, 2, 4]:
npts_axis = nfac * (11, 21)
box_ll = (left_boundary_location, ybottom)
box_ur = (right_boundary_location, ytop)
mesh = _get_box_mesh(2, a=box_ll, b=box_ur, n=npts_axis)
logger.info(f"Number of {dim}d elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
def inf_norm(x):
return actx.to_numpy(discr.norm(x, np.inf))
# compute max element size
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(discr)
# form exact cv
cv = initializer(x_vec=nodes, eos=eos)
cv_int_tpair = interior_trace_pair(discr, cv)
boundaries = [BTAG_ALL]
cv_flux_bnd = _elbnd_flux(discr, cv_flux_interior, cv_flux_boundary,
cv_int_tpair, boundaries)
from mirgecom.operators import grad_operator
from grudge.dof_desc import as_dofdesc
dd_vol = as_dofdesc("vol")
dd_faces = as_dofdesc("all_faces")
grad_cv = grad_operator(discr, dd_vol, dd_faces, cv, cv_flux_bnd)
xp_grad_cv = initializer.exact_grad(x_vec=nodes, eos=eos, cv_exact=cv)
xp_grad_v = 1 / cv.mass * xp_grad_cv.momentum
xp_tau = mu * (xp_grad_v + xp_grad_v.transpose())
# sanity check the gradient:
relerr_scale_e = 1.0 / inf_norm(xp_grad_cv.energy)
relerr_scale_p = 1.0 / inf_norm(xp_grad_cv.momentum)
graderr_e = inf_norm(grad_cv.energy - xp_grad_cv.energy)
graderr_p = inf_norm(grad_cv.momentum - xp_grad_cv.momentum)
graderr_e *= relerr_scale_e
graderr_p *= relerr_scale_p
assert graderr_e < 5e-7
assert graderr_p < 5e-11
zeros = discr.zeros(actx)
ones = zeros + 1
pressure = eos.pressure(cv)
# grad of p should be dp/dx
xp_grad_p = make_obj_array([dpdx * ones, zeros])
grad_p = op.local_grad(discr, pressure)
dpscal = 1.0 / np.abs(dpdx)
temperature = eos.temperature(cv)
tscal = rho * eos.gas_const() * dpscal
xp_grad_t = xp_grad_p / (cv.mass * eos.gas_const())
grad_t = op.local_grad(discr, temperature)
# sanity check
assert inf_norm(grad_p - xp_grad_p) * dpscal < 5e-9
assert inf_norm(grad_t - xp_grad_t) * tscal < 5e-9
fluid_state = make_fluid_state(cv, gas_model)
# verify heat flux
from mirgecom.viscous import conductive_heat_flux
heat_flux = conductive_heat_flux(fluid_state, grad_t)
xp_heat_flux = -kappa * xp_grad_t
assert inf_norm(heat_flux - xp_heat_flux) < 2e-8
xp_e_flux = np.dot(xp_tau, cv.velocity) - xp_heat_flux
xp_mom_flux = xp_tau
from mirgecom.viscous import viscous_flux
vflux = viscous_flux(fluid_state, grad_cv, grad_t)
efluxerr = (inf_norm(vflux.energy - xp_e_flux) / inf_norm(xp_e_flux))
momfluxerr = (inf_norm(vflux.momentum - xp_mom_flux) /
inf_norm(xp_mom_flux))
assert inf_norm(vflux.mass) == 0
e_eoc_rec.add_data_point(actx.to_numpy(h_max), efluxerr)
p_eoc_rec.add_data_point(actx.to_numpy(h_max), momfluxerr)
assert (e_eoc_rec.order_estimate() >= order - 0.5
or e_eoc_rec.max_error() < 3e-9)
assert (p_eoc_rec.order_estimate() >= order - 0.5
or p_eoc_rec.max_error() < 2e-12)