def euler_operator(discr, eos, boundaries, cv, time=0.0):
r"""Compute RHS of the Euler flow equations.
Returns
-------
numpy.ndarray
The right-hand-side of the Euler flow equations:
.. math::
\dot{\mathbf{q}} = - \nabla\cdot\mathbf{F} +
(\mathbf{F}\cdot\hat{n})_{\partial\Omega}
Parameters
----------
cv: :class:`mirgecom.fluid.ConservedVars`
Fluid conserved state object with the conserved variables.
boundaries
Dictionary of boundary functions, one for each valid btag
time
Time
eos: mirgecom.eos.GasEOS
Implementing the pressure and temperature functions for
returning pressure and temperature as a function of the state q.
Returns
-------
numpy.ndarray
Agglomerated object array of DOF arrays representing the RHS of the Euler
flow equations.
"""
inviscid_flux_vol = inviscid_flux(discr, eos, cv)
inviscid_flux_bnd = (inviscid_facial_flux(
discr, eos=eos, cv_tpair=interior_trace_pair(discr, cv)) + sum(
inviscid_facial_flux(
discr,
eos=eos,
cv_tpair=TracePair(
part_tpair.dd,
interior=make_conserved(discr.dim, q=part_tpair.int),
exterior=make_conserved(discr.dim, q=part_tpair.ext)))
for part_tpair in cross_rank_trace_pairs(discr, cv.join())) +
sum(boundaries[btag].inviscid_boundary_flux(
discr, btag=btag, cv=cv, eos=eos, time=time)
for btag in boundaries))
q = -div_operator(discr, inviscid_flux_vol.join(),
inviscid_flux_bnd.join())
return make_conserved(discr.dim, q=q)
def op(u):
return div_operator(discr, dd_vol, dd_faces,
u, get_flux(interior_trace_pair(discr, u)))
def euler_operator(discr,
state,
gas_model,
boundaries,
time=0.0,
quadrature_tag=None):
r"""Compute RHS of the Euler flow equations.
Returns
-------
numpy.ndarray
The right-hand-side of the Euler flow equations:
.. math::
\dot{\mathbf{q}} = - \nabla\cdot\mathbf{F} +
(\mathbf{F}\cdot\hat{n})_{\partial\Omega}
Parameters
----------
state: :class:`~mirgecom.gas_model.FluidState`
Fluid state object with the conserved state, and dependent
quantities.
boundaries
Dictionary of boundary functions, one for each valid btag
time
Time
gas_model: :class:`~mirgecom.gas_model.GasModel`
Physical gas model including equation of state, transport,
and kinetic properties as required by fluid state
quadrature_tag
An optional identifier denoting a particular quadrature
discretization to use during operator evaluations.
The default value is *None*.
Returns
-------
:class:`mirgecom.fluid.ConservedVars`
"""
dd_base_vol = DOFDesc("vol")
dd_quad_vol = DOFDesc("vol", quadrature_tag)
dd_quad_faces = DOFDesc("all_faces", quadrature_tag)
# project pair to the quadrature discretization and update dd to quad
def _interp_to_surf_quad(utpair):
local_dd = utpair.dd
local_dd_quad = local_dd.with_discr_tag(quadrature_tag)
return TracePair(local_dd_quad,
interior=op.project(discr, local_dd, local_dd_quad,
utpair.int),
exterior=op.project(discr, local_dd, local_dd_quad,
utpair.ext))
boundary_states_quad = {
btag:
project_fluid_state(discr, dd_base_vol,
as_dofdesc(btag).with_discr_tag(quadrature_tag),
state, gas_model)
for btag in boundaries
}
# performs MPI communication of CV if needed
cv_interior_pairs = [
# Get the interior trace pairs onto the surface quadrature
# discretization (if any)
_interp_to_surf_quad(tpair)
for tpair in interior_trace_pairs(discr, state.cv)
]
tseed_interior_pairs = None
if state.is_mixture:
# If this is a mixture, we need to exchange the temperature field because
# mixture pressure (used in the inviscid flux calculations) depends on
# temperature and we need to seed the temperature calculation for the
# (+) part of the partition boundary with the remote temperature data.
tseed_interior_pairs = [
# Get the interior trace pairs onto the surface quadrature
# discretization (if any)
_interp_to_surf_quad(tpair)
for tpair in interior_trace_pairs(discr, state.temperature)
]
interior_states_quad = make_fluid_state_trace_pairs(
cv_interior_pairs, gas_model, tseed_interior_pairs)
# Interpolate the fluid state to the volume quadrature grid
# (this includes the conserved and dependent quantities)
vol_state_quad = project_fluid_state(discr, dd_base_vol, dd_quad_vol,
state, gas_model)
# Compute volume contributions
inviscid_flux_vol = inviscid_flux(vol_state_quad)
# Compute interface contributions
inviscid_flux_bnd = (
# Interior faces
sum(
inviscid_facial_flux(discr, state_pair)
for state_pair in interior_states_quad)
# Domain boundary faces
+ sum(boundaries[btag].inviscid_divergence_flux(
discr,
as_dofdesc(btag).with_discr_tag(quadrature_tag),
gas_model,
state_minus=boundary_states_quad[btag],
time=time) for btag in boundaries))
return -div_operator(discr, dd_quad_vol, dd_quad_faces, inviscid_flux_vol,
inviscid_flux_bnd)