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):
"""Drive example."""
cl_ctx = ctx_factory()
if casename is None:
casename = "mirgecom"
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
nproc = comm.Get_size()
logmgr = initialize_logmgr(use_logmgr,
filename=f"{casename}.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)))
# Some discretization parameters
dim = 2
nel_1d = 8
order = 1
# {{{ Time stepping control
# This example runs only 3 steps by default (to keep CI ~short)
# With the mixture defined below, equilibrium is achieved at ~40ms
# To run to equlibrium, set t_final >= 40ms.
# Time stepper selection
if use_leap:
from leap.rk import RK4MethodBuilder
timestepper = RK4MethodBuilder("state")
else:
timestepper = rk4_step
# Time loop control parameters
current_step = 0
t_final = 1e-8
current_cfl = 1.0
current_dt = 1e-9
current_t = 0
constant_cfl = False
# i.o frequencies
nstatus = 1
nviz = 5
nhealth = 1
nrestart = 5
# }}} Time stepping control
debug = False
rst_path = "restart_data/"
rst_pattern = (rst_path + "{cname}-{step:04d}-{rank:04d}.pkl")
if rst_filename: # read the grid from restart data
rst_filename = f"{rst_filename}-{rank:04d}.pkl"
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(actx, rst_filename)
local_mesh = restart_data["local_mesh"]
local_nelements = local_mesh.nelements
global_nelements = restart_data["global_nelements"]
assert restart_data["num_parts"] == nproc
rst_time = restart_data["t"]
rst_step = restart_data["step"]
rst_order = restart_data["order"]
else: # generate the grid from scratch
from meshmode.mesh.generation import generate_regular_rect_mesh
box_ll = -0.005
box_ur = 0.005
generate_mesh = partial(generate_regular_rect_mesh,
a=(box_ll, ) * dim,
b=(box_ur, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
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())
vis_timer = None
if logmgr:
logmgr_add_device_name(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr_add_many_discretization_quantities(logmgr, discr, dim,
extract_vars_for_logging,
units_for_logging)
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
logmgr.add_watches([
("step.max", "step = {value}, "),
("t_sim.max", "sim time: {value:1.6e} s\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")
])
# {{{ 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
mech_cti = get_mechanism_cti("uiuc")
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.
init_temperature = 1500.0 # Initial temperature hot enough to burn
# Parameters for calculating the amounts of fuel, oxidizer, and inert species
equiv_ratio = 1.0
ox_di_ratio = 0.21
stoich_ratio = 3.0
# Grab the array indices for the specific species, ethylene, oxygen, and nitrogen
i_fu = cantera_soln.species_index("C2H4")
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
# Let the user know about how Cantera is being initilized
print(f"Input state (T,P,X) = ({init_temperature}, {one_atm}, {x}")
# Set Cantera internal gas temperature, pressure, and mole fractios
cantera_soln.TPX = init_temperature, one_atm, x
# Pull temperature, total density, mass fractions, and pressure from Cantera
# We need total density, and mass fractions to initialize the fluid/gas state.
can_t, can_rho, can_y = 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.
# }}}
# {{{ Create Pyrometheus thermochemistry object & EOS
# Create a Pyrometheus EOS with the Cantera soln. Pyrometheus uses Cantera and
# generates a set of methods to calculate chemothermomechanical properties and
# states for this particular mechanism.
pyrometheus_mechanism = pyro.get_thermochem_class(cantera_soln)(actx.np)
eos = PyrometheusMixture(pyrometheus_mechanism,
temperature_guess=init_temperature)
# }}}
# {{{ MIRGE-Com state initialization
# Initialize the fluid/gas state with Cantera-consistent data:
# (density, pressure, temperature, mass_fractions)
print(f"Cantera state (rho,T,P,Y) = ({can_rho}, {can_t}, {can_p}, {can_y}")
velocity = np.zeros(shape=(dim, ))
initializer = MixtureInitializer(dim=dim,
nspecies=nspecies,
pressure=can_p,
temperature=can_t,
massfractions=can_y,
velocity=velocity)
my_boundary = AdiabaticSlipBoundary()
boundaries = {BTAG_ALL: my_boundary}
if rst_filename:
current_step = rst_step
current_t = rst_time
if logmgr:
from mirgecom.logging_quantities import logmgr_set_time
logmgr_set_time(logmgr, current_step, current_t)
if order == rst_order:
current_state = restart_data["state"]
else:
rst_state = restart_data["state"]
old_discr = EagerDGDiscretization(actx,
local_mesh,
order=rst_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"))
current_state = connection(rst_state)
else:
# Set the current state from time 0
current_state = initializer(eos=eos, x_vec=nodes)
# Inspection at physics debugging time
if debug:
print("Initial MIRGE-Com state:")
print(f"{current_state=}")
print(f"Initial DV pressure: {eos.pressure(current_state)}")
print(f"Initial DV temperature: {eos.temperature(current_state)}")
# }}}
visualizer = make_visualizer(discr)
initname = initializer.__class__.__name__
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)
# Cantera equilibrate calculates the expected end state @ chemical equilibrium
# i.e. the expected state after all reactions
cantera_soln.equilibrate("UV")
eq_temperature, eq_density, eq_mass_fractions = cantera_soln.TDY
eq_pressure = cantera_soln.P
# Report the expected final state to the user
if rank == 0:
logger.info(init_message)
logger.info(f"Expected equilibrium state:"
f" {eq_pressure=}, {eq_temperature=},"
f" {eq_density=}, {eq_mass_fractions=}")
def my_write_status(dt, cfl):
status_msg = f"------ {dt=}" if constant_cfl else f"----- {cfl=}"
if rank == 0:
logger.info(status_msg)
def my_write_viz(step,
t,
dt,
state,
ts_field=None,
dv=None,
production_rates=None,
cfl=None):
if dv is None:
dv = eos.dependent_vars(state)
if production_rates is None:
production_rates = eos.get_production_rates(state)
if ts_field is None:
ts_field, cfl, dt = my_get_timestep(t=t, dt=dt, state=state)
viz_fields = [("cv", state), ("dv", dv),
("production_rates", production_rates),
("dt" if constant_cfl else "cfl", ts_field)]
write_visfile(discr,
viz_fields,
visualizer,
vizname=casename,
step=step,
t=t,
overwrite=True,
vis_timer=vis_timer)
def my_write_restart(step, t, state):
rst_fname = rst_pattern.format(cname=casename, step=step, rank=rank)
if rst_fname == rst_filename:
if rank == 0:
logger.info("Skipping overwrite of restart file.")
else:
rst_data = {
"local_mesh": local_mesh,
"state": state,
"t": t,
"step": step,
"order": order,
"global_nelements": global_nelements,
"num_parts": nproc
}
from mirgecom.restart import write_restart_file
write_restart_file(actx, rst_data, rst_fname, comm)
def my_health_check(dv):
health_error = False
from mirgecom.simutil import check_naninf_local, check_range_local
if check_naninf_local(discr, "vol", dv.pressure) \
or check_range_local(discr, "vol", dv.pressure, 1e5, 2.4e5):
health_error = True
logger.info(f"{rank=}: Invalid pressure data found.")
if check_range_local(discr, "vol", dv.temperature, 1.498e3, 1.52e3):
health_error = True
logger.info(f"{rank=}: Invalid temperature data found.")
return health_error
def my_get_timestep(t, dt, state):
# richer interface to calculate {dt,cfl} returns node-local estimates
t_remaining = max(0, t_final - t)
if constant_cfl:
from mirgecom.inviscid import get_inviscid_timestep
ts_field = current_cfl * get_inviscid_timestep(
discr, eos=eos, cv=state)
from grudge.op import nodal_min
dt = nodal_min(discr, "vol", ts_field)
cfl = current_cfl
else:
from mirgecom.inviscid import get_inviscid_cfl
ts_field = get_inviscid_cfl(discr, eos=eos, dt=dt, cv=state)
from grudge.op import nodal_max
cfl = nodal_max(discr, "vol", ts_field)
return ts_field, cfl, min(t_remaining, dt)
def my_pre_step(step, t, dt, state):
try:
dv = None
if logmgr:
logmgr.tick_before()
from mirgecom.simutil import check_step
do_viz = check_step(step=step, interval=nviz)
do_restart = check_step(step=step, interval=nrestart)
do_health = check_step(step=step, interval=nhealth)
do_status = check_step(step=step, interval=nstatus)
if do_health:
dv = eos.dependent_vars(state)
from mirgecom.simutil import allsync
health_errors = allsync(my_health_check(dv), comm, op=MPI.LOR)
if health_errors:
if rank == 0:
logger.info("Fluid solution failed health check.")
raise MyRuntimeError("Failed simulation health check.")
ts_field, cfl, dt = my_get_timestep(t=t, dt=dt, state=state)
if do_status:
my_write_status(dt, cfl)
if do_restart:
my_write_restart(step=step, t=t, state=state)
if do_viz:
production_rates = eos.get_production_rates(state)
if dv is None:
dv = eos.dependent_vars(state)
my_write_viz(step=step,
t=t,
dt=dt,
state=state,
dv=dv,
production_rates=production_rates,
ts_field=ts_field,
cfl=cfl)
except MyRuntimeError:
if rank == 0:
logger.info("Errors detected; attempting graceful exit.")
my_write_viz(step=step, t=t, dt=dt, state=state)
my_write_restart(step=step, t=t, state=state)
raise
return state, dt
def my_post_step(step, t, dt, state):
# Logmgr needs to know about EOS, dt, dim?
# imo this is a design/scope flaw
if logmgr:
set_dt(logmgr, dt)
set_sim_state(logmgr, dim, state, eos)
logmgr.tick_after()
return state, dt
def my_rhs(t, state):
return (euler_operator(
discr, cv=state, time=t, boundaries=boundaries, eos=eos) +
eos.get_species_source_terms(state))
current_dt = get_sim_timestep(discr, current_state, current_t, current_dt,
current_cfl, eos, t_final, constant_cfl)
current_step, current_t, current_state = \
advance_state(rhs=my_rhs, timestepper=timestepper,
pre_step_callback=my_pre_step,
post_step_callback=my_post_step, dt=current_dt,
state=current_state, t=current_t, t_final=t_final)
# Dump the final data
if rank == 0:
logger.info("Checkpointing final state ...")
final_dv = eos.dependent_vars(current_state)
final_dm = eos.get_production_rates(current_state)
ts_field, cfl, dt = my_get_timestep(t=current_t,
dt=current_dt,
state=current_state)
my_write_viz(step=current_step,
t=current_t,
dt=dt,
state=current_state,
dv=final_dv,
production_rates=final_dm,
ts_field=ts_field,
cfl=cfl)
my_write_status(dt=dt, cfl=cfl)
my_write_restart(step=current_step, t=current_t, state=current_state)
if logmgr:
logmgr.close()
elif use_profiling:
print(actx.tabulate_profiling_data())
finish_tol = 1e-16
assert np.abs(current_t - t_final) < finish_tol
def get_test_density(actx, density_discr):
nodes = thaw(actx, density_discr.nodes())
sigma = actx.np.sin(10 * nodes[0])
return sigma
def test_grad_operator(actx_factory, dim, order, sym_test_func_factory):
"""Test the gradient operator for sanity.
Check whether we get the right answers for gradients of analytic functions with
some simple input fields and states:
- constant
- multilinear funcs
- quadratic funcs
- trig funcs
- :class:`~mirgecom.fluid.ConservedVars` composed of funcs from above
"""
actx = actx_factory()
sym_test_func = sym_test_func_factory(dim)
tol = 1e-10 if dim < 3 else 1e-9
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for nfac in [1, 2, 4]:
npts_axis = (nfac * 4, ) * dim
box_ll = (0, ) * dim
box_ur = (1, ) * dim
mesh = _get_box_mesh(dim, 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)
# compute max element size
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(discr)
def sym_eval(expr, x_vec):
# FIXME: When pymbolic supports array containers
mapper = sym.EvaluationMapper({"x": x_vec})
from arraycontext import rec_map_array_container
result = rec_map_array_container(mapper, expr)
# If expressions don't depend on coords (e.g., order 0), evaluated result
# will be scalar-valued, so promote to DOFArray(s) before returning
return result * (0 * x_vec[0] + 1)
test_func = partial(sym_eval, sym_test_func)
grad_test_func = partial(sym_eval, sym_grad(dim, sym_test_func))
nodes = thaw(actx, discr.nodes())
int_flux = partial(central_flux_interior, actx, discr)
bnd_flux = partial(central_flux_boundary, actx, discr, test_func)
test_data = test_func(nodes)
exact_grad = grad_test_func(nodes)
from mirgecom.simutil import componentwise_norms
from arraycontext import flatten
err_scale = max(
flatten(componentwise_norms(discr, exact_grad, np.inf), actx))
if err_scale <= 1e-16:
err_scale = 1
print(f"{test_data=}")
print(f"{exact_grad=}")
test_data_int_tpair = interior_trace_pair(discr, test_data)
boundaries = [BTAG_ALL]
test_data_flux_bnd = _elbnd_flux(discr, int_flux, bnd_flux,
test_data_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")
test_grad = grad_operator(discr, dd_vol, dd_faces, test_data,
test_data_flux_bnd)
print(f"{test_grad=}")
grad_err = \
max(flatten(componentwise_norms(discr, test_grad - exact_grad, np.inf),
actx)) / err_scale
eoc.add_data_point(actx.to_numpy(h_max), actx.to_numpy(grad_err))
assert (eoc.order_estimate() >= order - 0.5 or eoc.max_error() < tol)
def gather_block_interaction_points(actx,
places,
source_dd,
indices,
radius_factor=None,
approx_nproxy=None,
max_nodes_in_box=None):
"""Generate sets of interaction points for each given range of indices
in the *source* discretization. For each input range of indices,
the corresponding output range of points is consists of:
- a set of proxy points (or balls) around the range, which
model farfield interactions. These are constructed using
:class:`ProxyGenerator`.
- a set of neighboring points that are inside the proxy balls, but
do not belong to the given range, which model nearby interactions.
These are constructed with :func:`gather_block_neighbor_points`.
:arg places: a :class:`~pytential.GeometryCollection`.
:arg source_dd: geometry in *places* for which to generate the
interaction points. This is a
:class:`~pytential.symbolic.primitives.DOFDescriptor` describing
the exact discretization.
:arg indices: a :class:`sumpy.tools.BlockIndexRanges` on the
discretization described by *source_dd*.
:return: a tuple ``(nodes, ranges)``, where each value is a
:class:`pyopencl.array.Array`. For a range :math:`i`, we can
get the slice using ``nodes[ranges[i]:ranges[i + 1]]``.
"""
@memoize_in(places, "concat_proxy_and_neighbors")
def knl():
loopy_knl = lp.make_kernel(
[
"{[irange, idim]: 0 <= irange < nranges and \
0 <= idim < dim}",
"{[ipxy, ingb]: 0 <= ipxy < npxyblock and \
0 <= ingb < nngbblock}"
],
"""
for irange
<> pxystart = pxyranges[irange]
<> pxyend = pxyranges[irange + 1]
<> npxyblock = pxyend - pxystart
<> ngbstart = nbrranges[irange]
<> ngbend = nbrranges[irange + 1]
<> nngbblock = ngbend - ngbstart
<> istart = pxyranges[irange] + nbrranges[irange]
nodes[idim, istart + ipxy] = \
proxies[idim, pxystart + ipxy] \
{id_prefix=write_pxy,nosync=write_ngb}
nodes[idim, istart + npxyblock + ingb] = \
sources[idim, nbrindices[ngbstart + ingb]] \
{id_prefix=write_ngb,nosync=write_pxy}
ranges[irange + 1] = ranges[irange] + npxyblock + nngbblock
end
""", [
lp.GlobalArg("sources",
None,
shape=(lpot_source.ambient_dim, "nsources"),
dim_tags="sep,C"),
lp.GlobalArg("proxies",
None,
shape=(lpot_source.ambient_dim, "nproxies"),
dim_tags="sep,C"),
lp.GlobalArg("nbrindices", None, shape="nnbrindices"),
lp.GlobalArg(
"nodes",
None,
shape=(lpot_source.ambient_dim, "nproxies + nnbrindices")),
lp.ValueArg("nsources", np.int),
lp.ValueArg("nproxies", np.int),
lp.ValueArg("nnbrindices", np.int), "..."
],
name="concat_proxy_and_neighbors",
default_offset=lp.auto,
silenced_warnings="write_race(write_*)",
fixed_parameters=dict(dim=lpot_source.ambient_dim),
lang_version=MOST_RECENT_LANGUAGE_VERSION)
loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
loopy_knl = lp.split_iname(loopy_knl, "irange", 128, outer_tag="g.0")
return loopy_knl
lpot_source = places.get_geometry(source_dd.geometry)
generator = ProxyGenerator(places,
radius_factor=radius_factor,
approx_nproxy=approx_nproxy)
proxies, pxyranges, pxycenters, pxyradii = \
generator(actx, source_dd, indices)
discr = places.get_discretization(source_dd.geometry,
source_dd.discr_stage)
neighbors = gather_block_neighbor_points(actx,
discr,
indices,
pxycenters,
pxyradii,
max_nodes_in_box=max_nodes_in_box)
from meshmode.dof_array import flatten, thaw
ranges = actx.zeros(indices.nblocks + 1, dtype=np.int)
_, (nodes, ranges) = knl()(actx.queue,
sources=flatten(thaw(actx, discr.nodes())),
proxies=proxies,
pxyranges=pxyranges,
nbrindices=neighbors.indices,
nbrranges=neighbors.ranges,
ranges=ranges)
return actx.freeze(nodes), actx.freeze(ranges)
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, n=(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))
# normal_mag = actx.np.sqrt(np.dot(normal, normal))
# nhat_mult = 1.0 / normal_mag
# nhat = normal * make_obj_array([nhat_mult])
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(center=orig, velocity=vel, rhoamp=0.0)
wall = AdiabaticSlipBoundary()
uniform_state = initializer(0, nodes)
from functools import partial
bnd_norm = partial(discr.norm, p=np.inf, dd=BTAG_ALL)
bnd_pair = wall.boundary_pair(discr, uniform_state, t=0.0,
btag=BTAG_ALL, eos=eos)
bnd_cv_int = split_conserved(dim, bnd_pair.int)
bnd_cv_ext = split_conserved(dim, bnd_pair.ext)
# check that mass and energy are preserved
mass_resid = bnd_cv_int.mass - bnd_cv_ext.mass
mass_err = bnd_norm(mass_resid)
assert mass_err == 0.0
energy_resid = bnd_cv_int.energy - bnd_cv_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_cv_int.momentum, nhat)
mom_norm = nhat * mom_norm_comp
expected_mom_ext = bnd_cv_int.momentum - 2.0 * mom_norm
mom_resid = bnd_cv_ext.momentum - expected_mom_ext
mom_err = bnd_norm(mom_resid)
assert mom_err == 0.0
def map_int_g(self, expr):
lpot_source = self.places.get_geometry(expr.source.geometry)
source_discr = self.places.get_discretization(expr.source.geometry,
expr.source.discr_stage)
target_discr = self.places.get_discretization(expr.target.geometry,
expr.target.discr_stage)
if source_discr is not target_discr:
raise NotImplementedError
result = 0
for kernel, density in zip(expr.source_kernels, expr.densities):
rec_density = self._blk_mapper.rec(density)
if is_zero(rec_density):
continue
if not np.isscalar(rec_density):
raise NotImplementedError
actx = self.array_context
kernel_args = _get_layer_potential_args(self._mat_mapper, expr)
from sumpy.expansion.local import LineTaylorLocalExpansion
local_expn = LineTaylorLocalExpansion(
expr.target_kernel.get_base_kernel(), lpot_source.qbx_order)
from sumpy.qbx import LayerPotentialMatrixBlockGenerator
mat_gen = LayerPotentialMatrixBlockGenerator(
actx.context,
local_expn,
source_kernels=(kernel, ),
target_kernels=(expr.target_kernel, ))
assert abs(expr.qbx_forced_limit) > 0
from pytential import bind, sym
radii = bind(
self.places,
sym.expansion_radii(source_discr.ambient_dim,
dofdesc=expr.target))(actx)
centers = bind(
self.places,
sym.expansion_centers(source_discr.ambient_dim,
expr.qbx_forced_limit,
dofdesc=expr.target))(actx)
from meshmode.dof_array import flatten, thaw
_, (mat, ) = mat_gen(
actx.queue,
targets=flatten(thaw(actx, target_discr.nodes())),
sources=flatten(thaw(actx, source_discr.nodes())),
centers=flatten(centers),
expansion_radii=flatten(radii),
index_set=self.index_set,
**kernel_args)
waa = bind(
self.places,
sym.weights_and_area_elements(source_discr.ambient_dim,
dofdesc=expr.source))(actx)
waa = flatten(waa)
mat *= waa[self.index_set.linear_col_indices]
result += rec_density * actx.to_numpy(mat)
return result
def test_target_specific_qbx(ctx_factory, op, helmholtz_k, qbx_order):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
target_order = 4
fmm_tol = 1e-3
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(1, target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder
qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order=qbx_order,
fmm_level_to_order=SimpleExpansionOrderFinder(fmm_tol),
fmm_backend="fmmlib",
_expansions_in_tree_have_extent=True,
_expansion_stick_out_factor=0.9,
_use_target_specific_qbx=False,
)
kernel_length_scale = 5 / abs(helmholtz_k) if helmholtz_k else None
places = {
"qbx": qbx,
"qbx_target_specific": qbx.copy(_use_target_specific_qbx=True)
}
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(places, auto_where="qbx")
places = refine_geometry_collection(
places, kernel_length_scale=kernel_length_scale)
density_discr = places.get_discretization("qbx")
from meshmode.dof_array import thaw
nodes = thaw(actx, density_discr.nodes())
u_dev = actx.np.sin(nodes[0])
if helmholtz_k == 0:
kernel = LaplaceKernel(3)
kernel_kwargs = {}
else:
kernel = HelmholtzKernel(3, allow_evanescent=True)
kernel_kwargs = {"k": sym.var("k")}
u_sym = sym.var("u")
if op == "S":
op = sym.S
elif op == "D":
op = sym.D
elif op == "Sp":
op = sym.Sp
else:
raise ValueError("unknown operator: '%s'" % op)
expr = op(kernel, u_sym, qbx_forced_limit=-1, **kernel_kwargs)
from meshmode.dof_array import flatten
bound_op = bind(places, expr)
pot_ref = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k)))
bound_op = bind(places, expr, auto_where="qbx_target_specific")
pot_tsqbx = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k)))
assert np.allclose(pot_tsqbx, pot_ref, atol=1e-13, rtol=1e-13)
def test_diffusion_compare_to_nodal_dg(actx_factory, problem, order,
print_err=False):
"""Compares diffusion operator to Hesthaven/Warburton Nodal-DG code."""
pytest.importorskip("oct2py")
actx = actx_factory()
p = problem
assert p.dim == 1
assert p.sym_alpha == 1.
from meshmode.interop.nodal_dg import download_nodal_dg_if_not_present
download_nodal_dg_if_not_present()
sym_diffusion_u = sym_diffusion(p.dim, p.sym_alpha, p.sym_u)
for n in [4, 8, 16, 32, 64]:
mesh = p.get_mesh(n)
from meshmode.interop.nodal_dg import NodalDGContext
with NodalDGContext("./nodal-dg/Codes1.1") as ndgctx:
ndgctx.set_mesh(mesh, order=order)
t = 1.23456789
from grudge.eager import EagerDGDiscretization
discr_mirgecom = EagerDGDiscretization(actx, mesh, order=order)
nodes_mirgecom = thaw(actx, discr_mirgecom.nodes())
def sym_eval_mirgecom(expr):
return sym.EvaluationMapper({"x": nodes_mirgecom, "t": t})(expr)
u_mirgecom = sym_eval_mirgecom(p.sym_u)
diffusion_u_mirgecom = diffusion_operator(discr_mirgecom,
quad_tag=DISCR_TAG_BASE, alpha=discr_mirgecom.zeros(actx)+1.,
boundaries=p.get_boundaries(discr_mirgecom, actx, t), u=u_mirgecom)
discr_ndg = ndgctx.get_discr(actx)
nodes_ndg = thaw(actx, discr_ndg.nodes())
def sym_eval_ndg(expr):
return sym.EvaluationMapper({"x": nodes_ndg, "t": t})(expr)
u_ndg = sym_eval_ndg(p.sym_u)
ndgctx.push_dof_array("u", u_ndg)
ndgctx.octave.push("t", t)
ndgctx.octave.eval("[rhs] = HeatCRHS1D(u,t)", verbose=False)
diffusion_u_ndg = ndgctx.pull_dof_array(actx, "rhs")
def inf_norm(f):
return actx.np.linalg.norm(f, np.inf)
err = (inf_norm(diffusion_u_mirgecom-diffusion_u_ndg)
/ inf_norm(diffusion_u_ndg))
if print_err:
diffusion_u_exact = sym_eval_mirgecom(sym_diffusion_u)
err_exact = (inf_norm(diffusion_u_mirgecom-diffusion_u_exact)
/ inf_norm(diffusion_u_exact))
print(err, err_exact)
assert err < 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 test_diffusion_accuracy(actx_factory, problem, nsteps, dt, scales, order,
visualize=False):
"""
Checks the accuracy of the diffusion operator by solving the heat equation for a
given problem setup.
"""
actx = actx_factory()
p = problem
sym_diffusion_u = sym_diffusion(p.dim, p.sym_alpha, p.sym_u)
# In order to support manufactured solutions, we modify the heat equation
# to add a source term f. If the solution is exact, this term should be 0.
sym_t = pmbl.var("t")
sym_f = sym.diff(sym_t)(p.sym_u) - sym_diffusion_u
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in scales:
mesh = p.get_mesh(n)
from grudge.eager import EagerDGDiscretization
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
PolynomialWarpAndBlendGroupFactory
discr = EagerDGDiscretization(
actx, mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3*order),
}
)
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"x": nodes, "t": t})(expr)
alpha = sym_eval(p.sym_alpha, 0.)
if isinstance(alpha, DOFArray):
discr_tag = DISCR_TAG_QUAD
else:
discr_tag = DISCR_TAG_BASE
def get_rhs(t, u):
return (diffusion_operator(discr, quad_tag=discr_tag, alpha=alpha,
boundaries=p.get_boundaries(discr, actx, t), u=u)
+ sym_eval(sym_f, t))
t = 0.
u = sym_eval(p.sym_u, t)
from mirgecom.integrators import rk4_step
for _ in range(nsteps):
u = rk4_step(u, t, dt, get_rhs)
t += dt
expected_u = sym_eval(p.sym_u, t)
rel_linf_err = (
discr.norm(u - expected_u, np.inf)
/ discr.norm(expected_u, 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+3)
vis.write_vtk_file("diffusion_accuracy_{order}_{n}.vtu".format(
order=order, n=n), [
("u", u),
("expected_u", expected_u),
])
print("L^inf error:")
print(eoc_rec)
# Expected convergence rates from Hesthaven/Warburton book
expected_order = order+1 if order % 2 == 0 else order
assert(eoc_rec.order_estimate() >= expected_order - 0.5
or eoc_rec.max_error() < 1e-11)
def test_diffusion_discontinuous_alpha(actx_factory, order, visualize=False):
"""
Checks the accuracy of the diffusion operator for an alpha field that has a
jump across an element face.
"""
actx = actx_factory()
n = 8
mesh = get_box_mesh(1, -1, 1, n)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Set up a 1D heat equation interface problem, apply the diffusion operator to
# the exact steady state solution, and check that it's zero
lower_mask_np = np.empty((n, order+1), dtype=int)
lower_mask_np[:, :] = 0
lower_mask_np[:int(n/2), :] = 1
lower_mask = DOFArray(actx, (actx.from_numpy(lower_mask_np),))
upper_mask_np = np.empty((n, order+1), dtype=int)
upper_mask_np[:, :] = 0
upper_mask_np[int(n/2):, :] = 1
upper_mask = DOFArray(actx, (actx.from_numpy(upper_mask_np),))
alpha_lower = 0.5
alpha_upper = 1
alpha = alpha_lower * lower_mask + alpha_upper * upper_mask
boundaries = {
DTAG_BOUNDARY("-0"): DirichletDiffusionBoundary(0.),
DTAG_BOUNDARY("+0"): DirichletDiffusionBoundary(1.),
}
flux = -alpha_lower*alpha_upper/(alpha_lower + alpha_upper)
u_steady = (
-flux/alpha_lower * (nodes[0] + 1) * lower_mask # noqa: E126, E221
+ (1 - flux/alpha_upper * (nodes[0] - 1)) * upper_mask) # noqa: E131
def get_rhs(t, u):
return diffusion_operator(
discr, quad_tag=DISCR_TAG_BASE, alpha=alpha, boundaries=boundaries, u=u)
rhs = get_rhs(0, u_steady)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order+3)
vis.write_vtk_file("diffusion_discontinuous_alpha_rhs_{order}.vtu"
.format(order=order), [
("alpha", alpha),
("u_steady", u_steady),
("rhs", rhs),
])
linf_err = discr.norm(rhs, np.inf)
assert(linf_err < 1e-11)
# Now check stability
from numpy.random import rand
perturb_np = np.empty((n, order+1), dtype=float)
for i in range(n):
perturb_np[i, :] = 0.1*(rand()-0.5)
perturb = DOFArray(actx, (actx.from_numpy(perturb_np),))
u = u_steady + perturb
dt = 1e-3 / order**2
t = 0
from mirgecom.integrators import rk4_step
for _ in range(50):
u = rk4_step(u, t, dt, get_rhs)
t += dt
if visualize:
vis.write_vtk_file("diffusion_disc_alpha_stability_{order}.vtu"
.format(order=order), [
("alpha", alpha),
("u", u),
("u_steady", u_steady),
])
linf_diff = discr.norm(u - u_steady, np.inf)
assert linf_diff < 0.1
def run_exterior_stokes_2d(
ctx_factory,
nelements,
mesh_order=4,
target_order=4,
qbx_order=4,
fmm_order=False, # FIXME: FMM is slower than direct eval
mu=1,
circle_rad=1.5,
visualize=False):
# This program tests an exterior Stokes flow in 2D using the
# compound representation given in Hsiao & Kress,
# ``On an integral equation for the two-dimensional exterior Stokes problem,''
# Applied Numerical Mathematics 1 (1985).
logging.basicConfig(level=logging.INFO)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
ovsmp_target_order = 4 * target_order
# {{{ geometries
from meshmode.mesh.generation import ( # noqa
make_curve_mesh, starfish, ellipse, drop)
mesh = make_curve_mesh(lambda t: circle_rad * ellipse(1, t),
np.linspace(0, 1, nelements + 1), target_order)
coarse_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
target_association_tolerance = 0.05
qbx = QBXLayerPotentialSource(
coarse_density_discr,
fine_order=ovsmp_target_order,
qbx_order=qbx_order,
fmm_order=fmm_order,
target_association_tolerance=target_association_tolerance,
_expansions_in_tree_have_extent=True,
)
def circle_mask(test_points, radius):
return (test_points[0, :]**2 + test_points[1, :]**2 > radius**2)
def outside_circle(test_points, radius):
mask = circle_mask(test_points, radius)
return np.array([row[mask] for row in test_points])
from pytential.target import PointsTarget
nsamp = 30
eval_points_1d = np.linspace(-3., 3., nsamp)
eval_points = np.zeros((2, len(eval_points_1d)**2))
eval_points[0, :] = np.tile(eval_points_1d, len(eval_points_1d))
eval_points[1, :] = np.repeat(eval_points_1d, len(eval_points_1d))
eval_points = outside_circle(eval_points, radius=circle_rad)
point_targets = PointsTarget(eval_points)
fplot = FieldPlotter(np.zeros(2), extent=6, npoints=100)
plot_targets = PointsTarget(outside_circle(fplot.points,
radius=circle_rad))
places = GeometryCollection({
sym.DEFAULT_SOURCE: qbx,
sym.DEFAULT_TARGET: qbx.density_discr,
"point_target": point_targets,
"plot_target": plot_targets,
})
density_discr = places.get_discretization(sym.DEFAULT_SOURCE)
normal = bind(places, sym.normal(2).as_vector())(actx)
path_length = bind(places, sym.integral(2, 1, 1))(actx)
# }}}
# {{{ describe bvp
from pytential.symbolic.stokes import StressletWrapper, StokesletWrapper
dim = 2
cse = sym.cse
sigma_sym = sym.make_sym_vector("sigma", dim)
meanless_sigma_sym = cse(sigma_sym - sym.mean(2, 1, sigma_sym))
int_sigma = sym.Ones() * sym.integral(2, 1, sigma_sym)
nvec_sym = sym.make_sym_vector("normal", dim)
mu_sym = sym.var("mu")
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = 1
stresslet_obj = StressletWrapper(dim=2)
stokeslet_obj = StokesletWrapper(dim=2)
bdry_op_sym = (-loc_sign * 0.5 * sigma_sym - stresslet_obj.apply(
sigma_sym, nvec_sym, mu_sym, qbx_forced_limit="avg") +
stokeslet_obj.apply(
meanless_sigma_sym, mu_sym, qbx_forced_limit="avg") -
(0.5 / np.pi) * int_sigma)
# }}}
bound_op = bind(places, bdry_op_sym)
# {{{ fix rhs and solve
def fund_soln(x, y, loc, strength):
#with direction (1,0) for point source
r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2)
scaling = strength / (4 * np.pi * mu)
xcomp = (-actx.np.log(r) + (x - loc[0])**2 / r**2) * scaling
ycomp = ((x - loc[0]) * (y - loc[1]) / r**2) * scaling
return [xcomp, ycomp]
def rotlet_soln(x, y, loc):
r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2)
xcomp = -(y - loc[1]) / r**2
ycomp = (x - loc[0]) / r**2
return [xcomp, ycomp]
def fund_and_rot_soln(x, y, loc, strength):
#with direction (1,0) for point source
r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2)
scaling = strength / (4 * np.pi * mu)
xcomp = ((-actx.np.log(r) + (x - loc[0])**2 / r**2) * scaling -
(y - loc[1]) * strength * 0.125 / r**2 + 3.3)
ycomp = (((x - loc[0]) * (y - loc[1]) / r**2) * scaling +
(x - loc[0]) * strength * 0.125 / r**2 + 1.5)
return make_obj_array([xcomp, ycomp])
from meshmode.dof_array import unflatten, flatten, thaw
nodes = flatten(thaw(actx, density_discr.nodes()))
fund_soln_loc = np.array([0.5, -0.2])
strength = 100.
bc = unflatten(
actx, density_discr,
fund_and_rot_soln(nodes[0], nodes[1], fund_soln_loc, strength))
omega_sym = sym.make_sym_vector("omega", dim)
u_A_sym_bdry = stokeslet_obj.apply( # noqa: N806
omega_sym, mu_sym, qbx_forced_limit=1)
from pytential.utils import unflatten_from_numpy
omega = unflatten_from_numpy(
actx, density_discr,
make_obj_array([(strength / path_length) * np.ones(len(nodes[0])),
np.zeros(len(nodes[0]))]))
bvp_rhs = bind(places,
sym.make_sym_vector("bc", dim) + u_A_sym_bdry)(actx,
bc=bc,
mu=mu,
omega=omega)
gmres_result = gmres(bound_op.scipy_op(actx,
"sigma",
np.float64,
mu=mu,
normal=normal),
bvp_rhs,
x0=bvp_rhs,
tol=1e-9,
progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
sigma_int_val_sym = sym.make_sym_vector("sigma_int_val", 2)
int_val = bind(places, sym.integral(2, 1, sigma_sym))(actx, sigma=sigma)
int_val = -int_val / (2 * np.pi)
print("int_val = ", int_val)
u_A_sym_vol = stokeslet_obj.apply( # noqa: N806
omega_sym, mu_sym, qbx_forced_limit=2)
representation_sym = (
-stresslet_obj.apply(sigma_sym, nvec_sym, mu_sym, qbx_forced_limit=2) +
stokeslet_obj.apply(meanless_sigma_sym, mu_sym, qbx_forced_limit=2) -
u_A_sym_vol + sigma_int_val_sym)
where = (sym.DEFAULT_SOURCE, "point_target")
vel = bind(places, representation_sym,
auto_where=where)(actx,
sigma=sigma,
mu=mu,
normal=normal,
sigma_int_val=int_val,
omega=omega)
print("@@@@@@@@")
plot_vel = bind(places,
representation_sym,
auto_where=(sym.DEFAULT_SOURCE,
"plot_target"))(actx,
sigma=sigma,
mu=mu,
normal=normal,
sigma_int_val=int_val,
omega=omega)
def get_obj_array(obj_array):
return make_obj_array([ary.get() for ary in obj_array])
exact_soln = fund_and_rot_soln(actx.from_numpy(eval_points[0]),
actx.from_numpy(eval_points[1]),
fund_soln_loc, strength)
vel = get_obj_array(vel)
err = vel - get_obj_array(exact_soln)
# FIXME: Pointwise relative errors don't make sense!
rel_err = err / (get_obj_array(exact_soln))
if 0:
print("@@@@@@@@")
print("vel[0], err[0], rel_err[0] ***** vel[1], err[1], rel_err[1]: ")
for i in range(len(vel[0])):
print(
"{:15.8e}, {:15.8e}, {:15.8e} ***** {:15.8e}, {:15.8e}, {:15.8e}"
.format(vel[0][i], err[0][i], rel_err[0][i], vel[1][i],
err[1][i], rel_err[1][i]))
print("@@@@@@@@")
l2_err = np.sqrt((6. / (nsamp - 1))**2 * np.sum(err[0] * err[0]) +
(6. / (nsamp - 1))**2 * np.sum(err[1] * err[1]))
l2_rel_err = np.sqrt((6. /
(nsamp - 1))**2 * np.sum(rel_err[0] * rel_err[0]) +
(6. /
(nsamp - 1))**2 * np.sum(rel_err[1] * rel_err[1]))
print("L2 error estimate: ", l2_err)
print("L2 rel error estimate: ", l2_rel_err)
print("max error at sampled points: ", max(abs(err[0])), max(abs(err[1])))
print("max rel error at sampled points: ", max(abs(rel_err[0])),
max(abs(rel_err[1])))
if visualize:
import matplotlib.pyplot as plt
full_pot = np.zeros_like(fplot.points) * float("nan")
mask = circle_mask(fplot.points, radius=circle_rad)
for i, vel in enumerate(plot_vel):
full_pot[i, mask] = vel.get()
plt.quiver(fplot.points[0],
fplot.points[1],
full_pot[0],
full_pot[1],
linewidth=0.1)
plt.savefig("exterior-2d-field.pdf")
# }}}
h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx)
return h_max, l2_err
def main(mesh_name="ellipse", visualize=False):
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
if mesh_name == "ellipse":
mesh = make_curve_mesh(
partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
mesh_order)
elif mesh_name == "ellipse_array":
base_mesh = make_curve_mesh(
partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
nx = 2
ny = 2
dx = 2 / nx
meshes = [
affine_map(
base_mesh,
A=np.diag([dx*0.25, dx*0.25]),
b=np.array([dx*(ix-nx/2), dx*(iy-ny/2)]))
for ix in range(nx)
for iy in range(ny)]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if visualize:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
else:
raise ValueError("unknown mesh name: {}".format(mesh_name))
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx = QBXLayerPotentialSource(
pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
targets = actx.from_numpy(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection({
"qbx": qbx,
"qbx_high_target_assoc_tol": qbx.copy(target_association_tolerance=0.05),
"targets": PointsTarget(targets)
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel, HelmholtzKernel
kernel = HelmholtzKernel(2)
sigma_sym = sym.var("sigma")
sqrt_w = sym.sqrt_jac_q_weight(2)
inv_sqrt_w_sigma = sym.cse(sigma_sym/sqrt_w)
# Brakhage-Werner parameter
alpha = 1j
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
k_sym = sym.var("k")
bdry_op_sym = (-loc_sign*0.5*sigma_sym
+ sqrt_w*(
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=k_sym,
qbx_forced_limit=+1)
- sym.D(kernel, inv_sqrt_w_sigma, k=k_sym,
qbx_forced_limit="avg")
))
# }}}
bound_op = bind(places, bdry_op_sym)
# {{{ fix rhs and solve
from meshmode.dof_array import thaw
nodes = thaw(actx, density_discr.nodes())
k_vec = np.array([2, 1])
k_vec = k * k_vec / la.norm(k_vec, 2)
def u_incoming_func(x):
return actx.np.exp(
1j * (x[0] * k_vec[0] + x[1] * k_vec[1]))
bc = -u_incoming_func(nodes)
bvp_rhs = bind(places, sqrt_w*sym.var("bc"))(actx, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(actx, sigma_sym.name, dtype=np.complex128, k=k),
bvp_rhs, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
repr_kwargs = dict(
source="qbx_high_target_assoc_tol",
target="targets",
qbx_forced_limit=None)
representation_sym = (
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs)
- sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs))
u_incoming = u_incoming_func(targets)
ones_density = density_discr.zeros(actx)
for elem in ones_density:
elem.fill(1)
indicator = actx.to_numpy(
bind(places, sym.D(LaplaceKernel(2), sigma_sym, **repr_kwargs))(
actx, sigma=ones_density))
try:
fld_in_vol = actx.to_numpy(
bind(places, representation_sym)(
actx, sigma=gmres_result.solution, k=k))
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("helmholtz-dirichlet-failed-targets.vts", [
("failed", e.failed_target_flags.get(queue))
])
raise
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("helmholtz-dirichlet-potential.vts", [
("potential", fld_in_vol),
("indicator", indicator),
("u_incoming", actx.to_numpy(u_incoming)),
])
def get_density(actx, discr):
from meshmode.dof_array import thaw
nodes = thaw(actx, discr.nodes())
return actx.np.sin(10 * nodes[0])
def main(ctx_factory=cl.create_some_context,
snapshot_pattern="y0euler-{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="y0euler.sqlite",
mode="wu", 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 = 100
nrestart = 100
current_dt = 2.5e-8
t_final = 5.e-1
dim = 3
order = 1
exittol = .09
#t_final = 0.001
current_cfl = 1.0
vel_init = np.zeros(shape=(dim,))
vel_inflow = np.zeros(shape=(dim,))
vel_outflow = np.zeros(shape=(dim,))
orig = np.zeros(shape=(dim,))
orig[0] = 0.83
orig[2] = 0.001
#vel[0] = 340.0
#vel_inflow[0] = 100.0 # m/s
current_t = 0
casename = "y0euler"
constant_cfl = False
nstatus = 10000000000
rank = 0
checkpoint_t = current_t
current_step = 0
# working gas: CO2 #
# gamma = 1.289
# MW=44.009 g/mol
# cp = 37.135 J/mol-K,
# rho= 1.977 kg/m^3 @298K
gamma_CO2 = 1.289
R_CO2 = 8314.59/44.009
# background
# 100 Pa
# 298 K
# rho = 1.77619667e-3 kg/m^3
# velocity = 0,0,0
rho_bkrnd=1.77619667e-3
pres_bkrnd=100
temp_bkrnd=298
# nozzle inflow #
#
# stagnation tempertuare 298 K
# stagnation pressure 1.5e Pa
#
# isentropic expansion based on the area ratios between the inlet (r=13e-3m) and the throat (r=6.3e-3)
#
# MJA, this is calculated offline, add some code to do it for us
#
# Mach number=0.139145
# pressure=148142
# temperature=297.169
# density=2.63872
# gamma=1.289
# calculate the inlet Mach number from the area ratio
nozzleInletRadius = 13.e-3
nozzleThroatRadius = 6.3e-3
nozzleInletArea = math.pi*nozzleInletRadius*nozzleInletRadius
nozzleThroatArea = math.pi*nozzleThroatRadius*nozzleThroatRadius
inletAreaRatio = nozzleInletArea/nozzleThroatArea
def getMachFromAreaRatio(area_ratio, gamma, mach_guess=0.01):
error=1.e-8
nextError=1.e8
g=gamma
M0=mach_guess
while nextError > error:
R = ((2/(g+1)+((g-1)/(g+1)*M0*M0))**(((g+1)/(2*g-2))))/M0-area_ratio
dRdM = (2*((2/(g+1)+((g-1)/(g+1)*M0*M0))**(((g+1)/(2*g-2))))/
(2*g-2)*(g-1)/(2/(g+1)+((g-1)/(g+1)*M0*M0))-
((2/(g+1)+((g-1)/(g+1)*M0*M0))**(((g+1)/(2*g-2))))* M0**(-2))
M1=M0-R/dRdM
nextError=abs(R)
M0=M1
return M1
def getIsentropicPressure(mach, P0, gamma):
pressure=(1.+(gamma-1.)*0.5*math.pow(mach,2))
pressure=P0*math.pow(pressure,(-gamma/(gamma-1.)))
return pressure
def getIsentropicTemperature(mach, T0, gamma):
temperature=(1.+(gamma-1.)*0.5*math.pow(mach,2))
temperature=T0*math.pow(temperature,-1.0)
return temperature
inlet_mach = getMachFromAreaRatio(area_ratio = inletAreaRatio, gamma=gamma_CO2, mach_guess = 0.01);
# ramp the stagnation pressure
start_ramp_pres = 1000
ramp_interval = 1.e-2
t_ramp_start = 1e5
pres_inflow = getIsentropicPressure(mach=inlet_mach, P0=start_ramp_pres, gamma=gamma_CO2)
temp_inflow = getIsentropicTemperature(mach=inlet_mach, T0=298, gamma=gamma_CO2)
rho_inflow = pres_inflow/temp_inflow/R_CO2
print(f'inlet Mach number {inlet_mach}')
print(f'inlet temperature {temp_inflow}')
print(f'inlet pressure {pres_inflow}')
end_ramp_pres = 150000
pres_inflow_final = getIsentropicPressure(mach=inlet_mach, P0=end_ramp_pres, gamma=gamma_CO2)
print(f'final inlet pressure {pres_inflow_final}')
#pres_inflow=148142
#temp_inflow=297.169
#rho_inflow=2.63872
#mach_inflow=infloM = 0.139145
vel_inflow[0] = inlet_mach*math.sqrt(gamma_CO2*pres_inflow/rho_inflow)
# starting pressure for the inflow ramp
#timestepper = rk4_step
timestepper = euler_step
eos = IdealSingleGas(gamma=gamma_CO2, gas_const=R_CO2)
bulk_init = Discontinuity(dim=dim, x0=-.30,sigma=0.005,
#bulk_init = Discontinuity(dim=dim, x0=-.31,sigma=0.04,
rhol=rho_inflow, rhor=rho_bkrnd,
pl=pres_inflow, pr=pres_bkrnd,
ul=vel_inflow, ur=vel_outflow)
#inflow_init = Lump(dim=dim, rho0=rho_inflow, p0=pres_inflow,
#center=orig, velocity=vel_inflow, rhoamp=0.0)
#outflow_init = Lump(dim=dim, rho0=rho_bkrnd, p0=pres_bkrnd,
#center=orig, velocity=vel_outflow, rhoamp=0.0)
# pressure ramp function
def inflow_ramp_pressure(t, startP=start_ramp_pres, finalP=end_ramp_pres,
ramp_interval=ramp_interval, t_ramp_start=t_ramp_start):
if t > t_ramp_start:
rampPressure = min(finalP, startP+(t-t_ramp_start)/ramp_interval*(finalP-startP))
else:
rampPressure = startP
return rampPressure
class IsentropicInflow:
def __init__(self, *, dim=1, direc=0, T0=298, P0=1e5, mach= 0.01, p_fun = None):
self._P0 = P0
self._T0 = T0
self._dim = dim
self._direc = direc
self._mach = mach
if p_fun is not None:
self._p_fun = p_fun
def __call__(self, x_vec, *, t=0, eos):
if self._p_fun is not None:
P0 = self._p_fun(t)
else:
P0 = self._P0
T0 = self._T0
gamma = eos.gamma()
gas_const = eos.gas_const()
pressure = getIsentropicPressure(mach=self._mach, P0=P0, gamma=gamma)
temperature = getIsentropicTemperature(mach=self._mach, T0=T0, gamma=gamma)
rho = pressure/temperature/gas_const
#print(f'ramp Mach number {self._mach}')
#print(f'ramp stagnation pressure {P0}')
#print(f'ramp stagnation temperature {T0}')
#print(f'ramp pressure {pressure}')
#print(f'ramp temperature {temperature}')
velocity = np.zeros(shape=(self._dim,))
velocity[self._direc] = self._mach*math.sqrt(gamma*pressure/rho)
mass = 0.0*x_vec[0] + rho
mom = velocity*mass
energy = (pressure/(gamma - 1.0)) + np.dot(mom, mom)/(2.0*mass)
from mirgecom.euler import join_conserved
return join_conserved(dim=self._dim, mass=mass, momentum=mom, energy=energy)
inflow_init = IsentropicInflow(dim=dim, T0=298, P0=start_ramp_pres,
mach = inlet_mach , p_fun=inflow_ramp_pressure)
outflow_init = Uniform(dim=dim, rho=rho_bkrnd, p=pres_bkrnd,
velocity=vel_outflow)
inflow = PrescribedBoundary(inflow_init)
outflow = PrescribedBoundary(outflow_init)
wall = AdiabaticSlipBoundary()
dummy = DummyBoundary()
alpha_sc = 0.5
# s0 is ~p^-4
#s0_sc = -11.0
s0_sc = -5.0
# kappa is empirical ...
kappa_sc = 0.5
print(f"Shock capturing parameters: alpha {alpha_sc}, s0 {s0_sc}, kappa {kappa_sc}")
# timestep estimate
#wave_speed = max(mach2*c_bkrnd,c_shkd+velocity2[0])
#char_len = 0.001
#area=char_len*char_len/2
#perimeter = 2*char_len+math.sqrt(2*char_len*char_len)
#h = 2*area/perimeter
#dt_est = 1/(wave_speed*order*order/h)
#print(f"Time step estimate {dt_est}\n")
#
#dt_est_visc = 1/(wave_speed*order*order/h+alpha_sc*order*order*order*order/h/h)
#print(f"Viscous timestep estimate {dt_est_visc}\n")
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:
local_mesh, global_nelements = create_parallel_grid(comm, get_pseudo_y0_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(0, 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_device_name(logmgr, queue)
logmgr_add_many_discretization_quantities(logmgr, discr, dim,
extract_vars_for_logging, units_for_logging)
#logmgr_add_package_versions(logmgr)
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.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, discr.order + 3
if discr.dim == 2 else discr.order)
# initname = initializer.__class__.__name__
initname = "pseudoY0"
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 inviscid_operator(discr, eos=eos, boundaries=boundaries, q=state, t=t)
return ( inviscid_operator(discr, q=state, t=t,boundaries=boundaries, eos=eos)
+ artificial_viscosity(discr,t=t, r=state, eos=eos, boundaries=boundaries,
alpha=alpha_sc, s0=s0_sc, kappa=kappa_sc))
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)
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,s0=s0_sc,kappa=kappa_sc)
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())
def main(ctx_factory=cl.create_some_context):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
dim = 1
nel_1d = 24
order = 1
# tolerate large errors; case is unstable
exittol = .2
t_final = 0.01
current_cfl = 1.0
current_dt = .0001
current_t = 0
eos = IdealSingleGas()
initializer = SodShock1D(dim)
casename = "sod1d"
boundaries = {BTAG_ALL: PrescribedBoundary(initializer)}
constant_cfl = False
nstatus = 10
nviz = 10
rank = 0
checkpoint_t = current_t
current_step = 0
timestepper = rk4_step
box_ll = -5.0
box_ur = 5.0
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
from meshmode.mesh.generation import generate_regular_rect_mesh
generate_grid = partial(generate_regular_rect_mesh,
a=(box_ll, ) * dim,
b=(box_ur, ) * dim,
n=(nel_1d, ) * dim)
local_mesh, global_nelements = create_parallel_grid(comm, generate_grid)
local_nelements = local_mesh.nelements
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
nodes = thaw(actx, discr.nodes())
current_state = initializer(0, nodes)
visualizer = make_visualizer(
discr, discr.order + 3 if discr.dim == 2 else discr.order)
initname = initializer.__class__.__name__
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 inviscid_operator(discr,
q=state,
t=t,
boundaries=boundaries,
eos=eos)
def my_checkpoint(step, t, dt, state):
return sim_checkpoint(discr,
visualizer,
eos,
q=state,
exact_soln=initializer,
vizname=casename,
step=step,
t=t,
dt=dt,
nstatus=nstatus,
nviz=nviz,
exittol=exittol,
constant_cfl=constant_cfl,
comm=comm)
try:
(current_step, current_t, current_state) = \
advance_state(rhs=my_rhs, timestepper=timestepper,
checkpoint=my_checkpoint,
get_timestep=get_timestep, state=current_state,
t=current_t, t_final=t_final)
except ExactSolutionMismatch as ex:
current_step = ex.step
current_t = ex.t
current_state = ex.state
# if current_t != checkpoint_t:
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")
def map_int_g(self, expr):
lpot_source = self.places.get_geometry(expr.source.geometry)
source_discr = self.places.get_discretization(expr.source.geometry,
expr.source.discr_stage)
target_discr = self.places.get_discretization(expr.target.geometry,
expr.target.discr_stage)
result = 0
for kernel, density in zip(expr.source_kernels, expr.densities):
rec_density = self.rec(density)
if is_zero(rec_density):
continue
assert isinstance(rec_density, np.ndarray)
if not self.is_kind_matrix(rec_density):
raise NotImplementedError("layer potentials on non-variables")
actx = self.array_context
kernel_args = _get_layer_potential_args(self, expr)
from sumpy.expansion.local import LineTaylorLocalExpansion
local_expn = LineTaylorLocalExpansion(
expr.target_kernel.get_base_kernel(), lpot_source.qbx_order)
from sumpy.qbx import LayerPotentialMatrixGenerator
mat_gen = LayerPotentialMatrixGenerator(
actx.context,
expansion=local_expn,
source_kernels=(kernel, ),
target_kernels=(expr.target_kernel, ))
assert abs(expr.qbx_forced_limit) > 0
from pytential import bind, sym
radii = bind(
self.places,
sym.expansion_radii(source_discr.ambient_dim,
dofdesc=expr.target))(actx)
centers = bind(
self.places,
sym.expansion_centers(source_discr.ambient_dim,
expr.qbx_forced_limit,
dofdesc=expr.target))(actx)
from meshmode.dof_array import flatten, thaw
_, (mat, ) = mat_gen(
actx.queue,
targets=flatten(thaw(actx, target_discr.nodes())),
sources=flatten(thaw(actx, source_discr.nodes())),
centers=flatten(centers),
expansion_radii=flatten(radii),
**kernel_args)
mat = actx.to_numpy(mat)
waa = bind(
self.places,
sym.weights_and_area_elements(source_discr.ambient_dim,
dofdesc=expr.source))(actx)
mat[:, :] *= actx.to_numpy(flatten(waa))
mat = mat.dot(rec_density)
result += mat
return result
def main(ctx_factory=cl.create_some_context,
snapshot_pattern="y0euler-{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,
use_profiling,
filename="y0euler.sqlite",
mode="wu",
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 = 50
nrestart = 10000000
current_dt = 2.5e-7
#t_final = 5.e-7
t_final = 3e-4
dim = 2
order = 1
exittol = 10000000 # do never exit when comparing to exact solution
#t_final = 0.001
current_cfl = 1.0
vel_init = np.zeros(shape=(dim, ))
vel_inflow = np.zeros(shape=(dim, ))
vel_outflow = np.zeros(shape=(dim, ))
orig = np.zeros(shape=(dim, ))
#vel[0] = 340.0
#vel_inflow[0] = 100.0 # m/s
current_t = 0
casename = "y0euler"
constant_cfl = False
# no internal euler status messages
nstatus = 1000000000
checkpoint_t = current_t
current_step = 0
# working gas: CO2 #
# gamma = 1.289
# MW=44.009 g/mol
# cp = 37.135 J/mol-K,
# rho= 1.977 kg/m^3 @298K
gamma_CO2 = 1.289
R_CO2 = 8314.59 / 44.009
# background
# 100 Pa
# 298 K
# rho = 1.77619667e-3 kg/m^3
# velocity = 0,0,0
rho_bkrnd = 1.77619667e-3
pres_bkrnd = 100
temp_bkrnd = 298
c_bkrnd = math.sqrt(gamma_CO2 * pres_bkrnd / rho_bkrnd)
# isentropic shock relations #
# lab frame, moving shock
# state 1 is behind (downstream) the shock, state 2 is in front (upstream) of the shock
mach = 2.0
pressure_ratio = (2. * gamma_CO2 * mach * mach -
(gamma_CO2 - 1.)) / (gamma_CO2 + 1.)
density_ratio = (gamma_CO2 + 1.) * mach * mach / (
(gamma_CO2 - 1.) * mach * mach + 2.)
mach2 = math.sqrt(((gamma_CO2 - 1.) * mach * mach + 2.) /
(2. * gamma_CO2 * mach * mach - (gamma_CO2 - 1.)))
rho1 = rho_bkrnd
pressure1 = pres_bkrnd
rho2 = rho1 * density_ratio
pressure2 = pressure1 * pressure_ratio
velocity1 = 0.
velocity2 = -mach * c_bkrnd * (1 / density_ratio - 1)
c_shkd = math.sqrt(gamma_CO2 * pressure2 / rho2)
vel_inflow[0] = velocity2
timestepper = rk4_step
eos = IdealSingleGas(gamma=gamma_CO2, gas_const=R_CO2)
bulk_init = Discontinuity(dim=dim,
x0=.05,
sigma=0.01,
rhol=rho2,
rhor=rho1,
pl=pressure2,
pr=pressure1,
ul=vel_inflow[0],
ur=0.)
inflow_init = Lump(dim=dim,
rho0=rho2,
p0=pressure2,
center=orig,
velocity=vel_inflow,
rhoamp=0.0)
outflow_init = Lump(dim=dim,
rho0=rho1,
p0=pressure1,
center=orig,
velocity=vel_outflow,
rhoamp=0.0)
inflow = PrescribedBoundary(inflow_init)
outflow = PrescribedBoundary(outflow_init)
wall = AdiabaticSlipBoundary()
dummy = DummyBoundary()
# shock capturing parameters
# sonic conditions
density_ratio = (gamma_CO2 + 1.) * 1.0 / ((gamma_CO2 - 1.) + 2.)
density_star = rho1 * density_ratio
shock_thickness = 20 * 0.001 # on the order of 3 elements, should match what is in mesh generator
# alpha is ~h/p (spacing/order)
#alpha_sc = shock_thickness*abs(velocity1-velocity2)*density_star
alpha_sc = 0.05
# sigma is ~p^-4
sigma_sc = -11.0
# kappa is empirical ...
kappa_sc = 0.5
print(
f"Shock capturing parameters: alpha {alpha_sc}, s0 {sigma_sc}, kappa {kappa_sc}"
)
# timestep estimate
wave_speed = max(mach2 * c_bkrnd, c_shkd + velocity2)
char_len = 0.001
area = char_len * char_len / 2
perimeter = 2 * char_len + math.sqrt(2 * char_len * char_len)
h = 2 * area / perimeter
dt_est = 1 / (wave_speed * order * order / h)
print(f"Time step estimate {dt_est}\n")
dt_est_visc = 1 / (wave_speed * order * order / h +
alpha_sc * order * order * order * order / h / h)
print(f"Viscous timestep estimate {dt_est_visc}\n")
from grudge import sym
# boundaries = {BTAG_ALL: DummyBoundary}
boundaries = {
sym.DTAG_BOUNDARY("Inflow"): inflow,
sym.DTAG_BOUNDARY("Outflow"): outflow,
sym.DTAG_BOUNDARY("Wall"): wall
}
#local_mesh, global_nelements = create_parallel_grid(comm,
#get_pseudo_y0_mesh)
#
#local_nelements = local_mesh.nelements
if restart_step is None:
local_mesh, global_nelements = create_parallel_grid(comm, get_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.")
current_state = bulk_init(0, 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_device_name(logmgr, queue)
logmgr_add_discretization_quantities(logmgr, discr, eos, dim)
#logmgr_add_package_versions(logmgr)
logmgr.add_watches([
"step.max", "t_sim.max", "t_step.max", "min_pressure",
"max_pressure", "min_temperature", "max_temperature"
])
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, discr.order + 3
#if discr.dim == 2 else discr.order)
visualizer = make_visualizer(discr, discr.order)
# initname = initializer.__class__.__name__
initname = "pseudoY0"
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 inviscid_operator(discr, eos=eos, boundaries=boundaries, q=state, t=t)
return (inviscid_operator(
discr, q=state, t=t, boundaries=boundaries, eos=eos) +
artificial_viscosity(discr,
t=t,
r=state,
eos=eos,
boundaries=boundaries,
alpha=alpha_sc,
sigma=sigma_sc,
kappa=kappa_sc))
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)
#x0=f(time)
exact_soln = Discontinuity(dim=dim,
x0=.05,
sigma=0.00001,
rhol=rho2,
rhor=rho1,
pl=pressure2,
pr=pressure1,
ul=vel_inflow[0],
ur=0.,
uc=mach * c_bkrnd)
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,
sigma=sigma_sc,
kappa=kappa_sc)
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())
def discr_and_nodes(stage):
density_discr = places.get_discretization(where.geometry, stage)
return density_discr, np.array([
actx.to_numpy(flatten(axis))
for axis in thaw(actx, density_discr.nodes())])
def test_chained_to_direct(actx_factory,
ndim,
chain_type,
nelements=128,
visualize=False):
import time
from meshmode.discretization.connection.chained import \
flatten_chained_connection
actx = actx_factory()
discr = create_discretization(actx, ndim, nelements=nelements)
connections = []
if chain_type == 1:
conn = create_refined_connection(actx, discr)
connections.append(conn)
conn = create_refined_connection(actx, conn.to_discr)
connections.append(conn)
elif chain_type == 2:
conn = create_refined_connection(actx, discr)
connections.append(conn)
conn = create_refined_connection(actx, conn.to_discr)
connections.append(conn)
conn = create_refined_connection(actx, conn.to_discr)
connections.append(conn)
elif chain_type == 3 and ndim == 3:
conn = create_refined_connection(actx, discr, threshold=np.inf)
connections.append(conn)
conn = create_face_connection(actx, conn.to_discr)
connections.append(conn)
else:
raise ValueError("unknown test case")
from meshmode.discretization.connection import \
ChainedDiscretizationConnection
chained = ChainedDiscretizationConnection(connections)
t_start = time.time()
direct = flatten_chained_connection(actx, chained)
t_end = time.time()
if visualize:
print("[TIME] Flatten: {:.5e}".format(t_end - t_start))
if chain_type < 3:
to_element_indices = np.full(direct.to_discr.mesh.nelements,
0,
dtype=np.int)
for grp in direct.groups:
for batch in grp.batches:
for i in batch.to_element_indices.get(actx.queue):
to_element_indices[i] += 1
assert np.min(to_element_indices) > 0
def f(x):
from functools import reduce
return 0.1 * reduce(lambda x, y: x * actx.np.sin(5 * y), x)
x = thaw(actx, connections[0].from_discr.nodes())
fx = f(x)
t_start = time.time()
f1 = actx.to_numpy(flatten(direct(fx)))
t_end = time.time()
if visualize:
print("[TIME] Direct: {:.5e}".format(t_end - t_start))
t_start = time.time()
f2 = actx.to_numpy(flatten(chained(fx)))
t_end = time.time()
if visualize:
print("[TIME] Chained: {:.5e}".format(t_end - t_start))
if visualize and ndim == 2:
import matplotlib.pyplot as pt
pt.figure(figsize=(10, 8), dpi=300)
pt.plot(f1, label="Direct")
pt.plot(f2, label="Chained")
pt.ylim([np.min(f2) - 0.1, np.max(f2) + 0.1])
pt.legend()
pt.savefig("test_chained_to_direct.png")
pt.clf()
assert np.allclose(f1, f2)
def __call__(self, actx, source_dd, indices, **kwargs):
"""Generate proxy points for each given range of source points in
the discretization in *source_dd*.
:arg actx: a :class:`~meshmode.array_context.ArrayContext`.
:arg source_dd: a :class:`~pytential.symbolic.primitives.DOFDescriptor`
for the discretization on which the proxy points are to be
generated.
:arg indices: a :class:`sumpy.tools.BlockIndexRanges`.
:return: a tuple of ``(proxies, pxyranges, pxycenters, pxyranges)``,
where each element is a :class:`pyopencl.array.Array`. The
sizes of the arrays are as follows: ``pxycenters`` is of size
``(2, nranges)``, ``pxyradii`` is of size ``(nranges,)``,
``pxyranges`` is of size ``(nranges + 1,)`` and ``proxies`` is
of size ``(2, nranges * nproxy)``. The proxy points in a range
:math:`i` can be obtained by a slice
``proxies[pxyranges[i]:pxyranges[i + 1]]`` and are all at a
distance ``pxyradii[i]`` from the range center ``pxycenters[i]``.
"""
def _affine_map(v, A, b):
return np.dot(A, v) + b
from pytential import bind, sym
source_dd = sym.as_dofdesc(source_dd)
discr = self.places.get_discretization(source_dd.geometry,
source_dd.discr_stage)
radii = bind(self.places,
sym.expansion_radii(self.ambient_dim,
dofdesc=source_dd))(actx)
center_int = bind(
self.places,
sym.expansion_centers(self.ambient_dim, -1,
dofdesc=source_dd))(actx)
center_ext = bind(
self.places,
sym.expansion_centers(self.ambient_dim, +1,
dofdesc=source_dd))(actx)
from meshmode.dof_array import flatten, thaw
knl = self.get_kernel()
_, (
centers_dev,
radii_dev,
) = knl(actx.queue,
sources=flatten(thaw(actx, discr.nodes())),
center_int=flatten(center_int),
center_ext=flatten(center_ext),
expansion_radii=flatten(radii),
srcindices=indices.indices,
srcranges=indices.ranges,
**kwargs)
from pytential.utils import flatten_to_numpy
centers = flatten_to_numpy(actx, centers_dev)
radii = flatten_to_numpy(actx, radii_dev)
proxies = np.empty(indices.nblocks, dtype=np.object)
for i in range(indices.nblocks):
proxies[i] = _affine_map(self.ref_points,
A=(radii[i] * np.eye(self.ambient_dim)),
b=centers[:, i].reshape(-1, 1))
pxyranges = actx.from_numpy(
np.arange(0,
proxies.shape[0] * proxies[0].shape[1] + 1,
proxies[0].shape[1],
dtype=indices.ranges.dtype))
proxies = make_obj_array([
actx.freeze(actx.from_numpy(np.hstack([p[idim] for p in proxies])))
for idim in range(self.ambient_dim)
])
centers = make_obj_array([
actx.freeze(centers_dev[idim]) for idim in range(self.ambient_dim)
])
assert pxyranges[-1] == proxies[0].shape[0]
return proxies, actx.freeze(pxyranges), centers, actx.freeze(radii_dev)
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
target_order = 16
qbx_order = 3
nelements = 60
mode_nr = 0
k = 0
if k:
kernel = HelmholtzKernel(2)
else:
kernel = LaplaceKernel(2)
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements + 1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
unaccel_qbx = QBXLayerPotentialSource(
pre_density_discr,
fine_order=2 * target_order,
qbx_order=qbx_order,
fmm_order=False,
target_association_tolerance=.05,
)
from pytential.target import PointsTarget
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600)
from pytential import GeometryCollection
places = GeometryCollection({
"unaccel_qbx": unaccel_qbx,
"qbx": unaccel_qbx.copy(fmm_order=10),
"targets": PointsTarget(fplot.points)
})
density_discr = places.get_discretization("unaccel_qbx")
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
from pytential import bind, sym
if k:
kernel_kwargs = {"k": sym.var("k")}
else:
kernel_kwargs = {}
def get_op():
kwargs = dict(qbx_forced_limit=None)
kwargs.update(kernel_kwargs)
# return sym.d_dx(2, sym.S(kernel, sym.var("sigma"), **kwargs))
# return sym.D(kernel, sym.var("sigma"), **kwargs)
return sym.S(kernel, sym.var("sigma"), **kwargs)
op = get_op()
sigma = actx.np.cos(mode_nr * angle)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
fld_in_vol = bind(places, op,
auto_where=("unaccel_qbx", "targets"))(actx,
sigma=sigma,
k=k).get()
fmm_fld_in_vol = bind(places, op,
auto_where=("qbx", "targets"))(actx,
sigma=sigma,
k=k).get()
err = fmm_fld_in_vol - fld_in_vol
try:
import matplotlib
except ImportError:
return
matplotlib.use("Agg")
im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17))
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-12, vmax=0))
import matplotlib.pyplot as pt
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathrm{Error})$")
pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
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()
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for np1 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, n=(np1,) * dim
)
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
nhat = thaw(actx, discr.normal(BTAG_ALL))
h = 1.0 / np1
from functools import partial
bnd_norm = partial(discr.norm, 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(numdim=dim, velocity=vel)
uniform_state = initializer(0, nodes)
bnd_pair = wall.boundary_pair(discr, uniform_state, t=0.0,
btag=BTAG_ALL, eos=eos)
# 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)
acv = split_conserved(dim, avg_state)
err_max = max(err_max, bnd_norm(np.dot(acv.momentum, nhat)))
from mirgecom.euler import _facial_flux
bnd_flux = split_conserved(dim, _facial_flux(discr, eos,
bnd_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
)
def main(mesh_name="ellipsoid"):
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
if mesh_name == "ellipsoid":
cad_file_name = "geometries/ellipsoid.step"
h = 0.6
elif mesh_name == "two-cylinders":
cad_file_name = "geometries/two-cylinders-smooth.step"
h = 0.4
else:
raise ValueError("unknown mesh name: %s" % mesh_name)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name),
2,
order=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h],
target_unit="MM")
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5 * (bbox_min + bbox_max)
bbox_size = max(bbox_max - bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15)
from pytential.target import PointsTarget
fplot = FieldPlotter(bbox_center, extent=3.5 * bbox_size, npoints=150)
from pytential import GeometryCollection
places = GeometryCollection(
{
"qbx": qbx,
"targets": PointsTarget(fplot.points)
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
if k:
kernel = HelmholtzKernel(3)
else:
kernel = LaplaceKernel(3)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = actx.np.cos(mode_nr * angle)
if 0:
from meshmode.dof_array import flatten, unflatten
sigma = flatten(0 * angle)
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
sigma = unflatten(actx, density_discr, sigma)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
fld_in_vol = actx.to_numpy(
bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma,
k=k))
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("layerpot-3d-potential.vts",
[("potential", fld_in_vol)])
bdry_normals = bind(places, sym.normal(
density_discr.ambient_dim))(actx).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(actx, density_discr, target_order)
bdry_vis.write_vtk_file("layerpot-3d-density.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
def map_q_weight(self, expr):
discr = self.places.get_discretization(expr.dofdesc.geometry,
expr.dofdesc.discr_stage)
return thaw(self.array_context, discr.quad_weights())
def eval_func_on_discr_nodes(queue, discr, func):
arr_ctx = PyOpenCLArrayContext(queue)
nodes = np.vstack([c.get() for c in flatten(thaw(arr_ctx, discr.nodes()))])
fvals = func(nodes)
return cl.array.to_device(queue, fvals)
def central_flux_interior(actx, discr, int_tpair):
"""Compute a central flux for interior faces."""
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 main(ctx_factory=cl.create_some_context, use_logmgr=True,
use_leap=False, use_profiling=False, casename=None,
rst_filename=None, actx_class=PyOpenCLArrayContext):
"""Drive example."""
cl_ctx = ctx_factory()
if casename is None:
casename = "mirgecom"
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
nparts = comm.Get_size()
logmgr = initialize_logmgr(use_logmgr,
filename=f"{casename}.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)))
# timestepping control
if use_leap:
from leap.rk import RK4MethodBuilder
timestepper = RK4MethodBuilder("state")
else:
timestepper = rk4_step
t_final = 0.01
current_cfl = 1.0
current_dt = .001
current_t = 0
current_step = 0
constant_cfl = False
# some i/o frequencies
nstatus = 1
nhealth = 1
nrestart = 10
nviz = 1
dim = 2
rst_path = "restart_data/"
rst_pattern = (
rst_path + "{cname}-{step:04d}-{rank:04d}.pkl"
)
if rst_filename: # read the grid from restart data
rst_filename = f"{rst_filename}-{rank:04d}.pkl"
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(actx, rst_filename)
local_mesh = restart_data["local_mesh"]
local_nelements = local_mesh.nelements
global_nelements = restart_data["global_nelements"]
assert restart_data["nparts"] == nparts
else: # generate the grid from scratch
box_ll = -5.0
box_ur = 5.0
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
generate_mesh = partial(generate_regular_rect_mesh, a=(box_ll,)*dim,
b=(box_ur,) * dim, nelements_per_axis=(nel_1d,)*dim)
local_mesh, global_nelements = generate_and_distribute_mesh(comm,
generate_mesh)
local_nelements = local_mesh.nelements
order = 3
discr = EagerDGDiscretization(
actx, local_mesh, order=order, mpi_communicator=comm
)
nodes = thaw(actx, discr.nodes())
vis_timer = None
if logmgr:
logmgr_add_device_name(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr_add_many_discretization_quantities(logmgr, discr, dim,
extract_vars_for_logging, units_for_logging)
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
logmgr.add_watches([
("step.max", "step = {value}, "),
("t_sim.max", "sim time: {value:1.6e} s\n"),
("min_pressure", "------- P (min, max) (Pa) = ({value:1.9e}, "),
("max_pressure", "{value:1.9e})\n"),
("t_step.max", "------- step walltime: {value:6g} s, "),
("t_log.max", "log walltime: {value:6g} s")
])
# soln setup, init
eos = IdealSingleGas()
vel = np.zeros(shape=(dim,))
orig = np.zeros(shape=(dim,))
vel[:dim] = 1.0
initializer = Lump(dim=dim, center=orig, velocity=vel)
boundaries = {
BTAG_ALL: PrescribedInviscidBoundary(fluid_solution_func=initializer)
}
if rst_filename:
current_t = restart_data["t"]
current_step = restart_data["step"]
current_state = restart_data["state"]
if logmgr:
from mirgecom.logging_quantities import logmgr_set_time
logmgr_set_time(logmgr, current_step, current_t)
else:
# Set the current state from time 0
current_state = initializer(nodes)
visualizer = make_visualizer(discr)
initname = initializer.__class__.__name__
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)
def my_write_viz(step, t, state, dv=None, exact=None, resid=None):
if dv is None:
dv = eos.dependent_vars(state)
if exact is None:
exact = initializer(x_vec=nodes, eos=eos, time=t)
if resid is None:
resid = state - exact
viz_fields = [("cv", state),
("dv", dv),
("exact", exact),
("residual", resid)]
from mirgecom.simutil import write_visfile
write_visfile(discr, viz_fields, visualizer, vizname=casename,
step=step, t=t, overwrite=True, vis_timer=vis_timer)
def my_write_restart(state, step, t):
rst_fname = rst_pattern.format(cname=casename, step=step, rank=rank)
if rst_fname != rst_filename:
rst_data = {
"local_mesh": local_mesh,
"state": state,
"t": t,
"step": step,
"order": order,
"global_nelements": global_nelements,
"num_parts": nparts
}
from mirgecom.restart import write_restart_file
write_restart_file(actx, rst_data, rst_fname, comm)
def my_health_check(dv, state, exact):
health_error = False
from mirgecom.simutil import check_naninf_local, check_range_local
if check_naninf_local(discr, "vol", dv.pressure) \
or check_range_local(discr, "vol", dv.pressure, .9999999999, 1.00000001):
health_error = True
logger.info(f"{rank=}: Invalid pressure data found.")
from mirgecom.simutil import compare_fluid_solutions
component_errors = compare_fluid_solutions(discr, state, exact)
exittol = .09
if max(component_errors) > exittol:
health_error = True
if rank == 0:
logger.info("Solution diverged from exact soln.")
return health_error
def my_pre_step(step, t, dt, state):
try:
dv = None
exact = None
if logmgr:
logmgr.tick_before()
from mirgecom.simutil import check_step
do_viz = check_step(step=step, interval=nviz)
do_restart = check_step(step=step, interval=nrestart)
do_health = check_step(step=step, interval=nhealth)
do_status = check_step(step=step, interval=nstatus)
if do_health:
dv = eos.dependent_vars(state)
exact = initializer(x_vec=nodes, eos=eos, time=t)
from mirgecom.simutil import allsync
health_errors = allsync(
my_health_check(dv=dv, state=state, exact=exact),
comm, op=MPI.LOR
)
if health_errors:
if rank == 0:
logger.info("Fluid solution failed health check.")
raise MyRuntimeError("Failed solution health check.")
if do_restart:
my_write_restart(step=step, t=t, state=state)
if do_viz:
if dv is None:
dv = eos.dependent_vars(state)
if exact is None:
exact = initializer(x_vec=nodes, eos=eos, time=t)
resid = state - exact
my_write_viz(step=step, t=t, dv=dv, state=state, exact=exact,
resid=resid)
if do_status:
if exact is None:
exact = initializer(x_vec=nodes, eos=eos, time=t)
from mirgecom.simutil import compare_fluid_solutions
component_errors = compare_fluid_solutions(discr, state, exact)
status_msg = (
"------- errors="
+ ", ".join("%.3g" % en for en in component_errors))
if rank == 0:
logger.info(status_msg)
except MyRuntimeError:
if rank == 0:
logger.info("Errors detected; attempting graceful exit.")
my_write_viz(step=step, t=t, state=state)
my_write_restart(step=step, t=t, state=state)
raise
dt = get_sim_timestep(discr, state, t, dt, current_cfl, eos, t_final,
constant_cfl)
return state, dt
def my_post_step(step, t, dt, state):
# Logmgr needs to know about EOS, dt, dim?
# imo this is a design/scope flaw
if logmgr:
set_dt(logmgr, dt)
set_sim_state(logmgr, dim, state, eos)
logmgr.tick_after()
return state, dt
def my_rhs(t, state):
return euler_operator(discr, cv=state, time=t,
boundaries=boundaries, eos=eos)
current_dt = get_sim_timestep(discr, current_state, current_t, current_dt,
current_cfl, eos, t_final, constant_cfl)
current_step, current_t, current_state = \
advance_state(rhs=my_rhs, timestepper=timestepper,
pre_step_callback=my_pre_step,
post_step_callback=my_post_step, dt=current_dt,
state=current_state, t=current_t, t_final=t_final)
# Dump the final data
if rank == 0:
logger.info("Checkpointing final state ...")
final_dv = eos.dependent_vars(current_state)
final_exact = initializer(x_vec=nodes, eos=eos, time=current_t)
final_resid = current_state - final_exact
my_write_viz(step=current_step, t=current_t, state=current_state, dv=final_dv,
exact=final_exact, resid=final_resid)
my_write_restart(step=current_step, t=current_t, state=current_state)
if logmgr:
logmgr.close()
elif use_profiling:
print(actx.tabulate_profiling_data())
finish_tol = 1e-16
time_err = current_t - t_final
if np.abs(time_err) > finish_tol:
raise ValueError(f"Simulation did not finish at expected time {time_err=}.")
)
places = GeometryCollection(qbx)
from pytential.qbx.refinement import refine_geometry_collection
kernel_length_scale = 5 / case.k if case.k else None
places = refine_geometry_collection(
places, kernel_length_scale=kernel_length_scale)
# {{{ compute values of a solution to the PDE
density_discr = places.get_discretization(places.auto_source.geometry)
from meshmode.dof_array import thaw, flatten, unflatten
nodes_host = [
actx.to_numpy(axis)
for axis in flatten(thaw(actx, density_discr.nodes()))
]
normal = bind(places, sym.normal(d))(actx).as_vector(np.object)
normal_host = [actx.to_numpy(axis) for axis in flatten(normal)]
if k != 0:
if d == 2:
angle = 0.3
wave_vec = np.array([np.cos(angle), np.sin(angle)])
u = np.exp(1j * k * np.tensordot(wave_vec, nodes_host, axes=1))
grad_u = 1j * k * wave_vec[:, np.newaxis] * u
elif d == 3:
center = np.array([3, 1, 2])
diff = nodes_host - center[:, np.newaxis]
r = la.norm(diff, axis=0)
u = np.exp(1j * k * r) / r
def sim_checkpoint(discr,
visualizer,
eos,
cv,
vizname,
exact_soln=None,
step=0,
t=0,
dt=0,
cfl=1.0,
nstatus=-1,
nviz=-1,
exittol=1e-16,
constant_cfl=False,
comm=None,
viz_fields=None,
overwrite=False,
vis_timer=None):
"""Check simulation health, status, viz dumps, and restart."""
do_viz = check_step(step=step, interval=nviz)
do_status = check_step(step=step, interval=nstatus)
if do_viz is False and do_status is False:
return 0
dependent_vars = eos.dependent_vars(cv)
rank = 0
if comm is not None:
rank = comm.Get_rank()
maxerr = 0.0
if exact_soln is not None:
actx = cv.mass.array_context
nodes = thaw(actx, discr.nodes())
expected_state = exact_soln(x_vec=nodes, t=t, eos=eos)
exp_resid = cv - expected_state
err_norms = [discr.norm(v, np.inf) for v in exp_resid.join()]
maxerr = discr.norm(exp_resid.join(), np.inf)
if do_viz:
io_fields = [("cv", cv), ("dv", dependent_vars)]
if exact_soln is not None:
exact_list = [
("exact_soln", expected_state),
]
io_fields.extend(exact_list)
if viz_fields is not None:
io_fields.extend(viz_fields)
from mirgecom.io import make_rank_fname, make_par_fname
rank_fn = make_rank_fname(basename=vizname, rank=rank, step=step, t=t)
from contextlib import nullcontext
if vis_timer:
ctm = vis_timer.start_sub_timer()
else:
ctm = nullcontext()
with ctm:
visualizer.write_parallel_vtk_file(
comm,
rank_fn,
io_fields,
overwrite=overwrite,
par_manifest_filename=make_par_fname(basename=vizname,
step=step,
t=t))
if do_status is True:
# if constant_cfl is False:
# current_cfl = get_inviscid_cfl(discr=discr, q=q,
# eos=eos, dt=dt)
statusmesg = make_status_message(discr=discr,
t=t,
step=step,
dt=dt,
cfl=cfl,
dependent_vars=dependent_vars)
if exact_soln is not None:
statusmesg += ("\n------- errors=" +
", ".join("%.3g" % en for en in err_norms))
if rank == 0:
logger.info(statusmesg)
if maxerr > exittol:
raise ExactSolutionMismatch(step, t=t, state=cv)