import matplotlib.pyplot as plt
import numpy as np
import pyro.compressible.unsplit_fluxes as flx
import pyro.mesh.boundary as bnd
from pyro.compressible import BC, derives, eos, riemann
from pyro.particles import particles
from pyro.simulation_null import NullSimulation, bc_setup, grid_setup
from pyro.util import msg, plot_tools
[docs]
class Variables:
"""
a container class for easy access to the different compressible
variable by an integer key
"""
def __init__(self, myd):
self.nvar = len(myd.names)
# conserved variables -- we set these when we initialize for
# they match the CellCenterData2d object
self.idens = myd.names.index("density")
self.ixmom = myd.names.index("x-momentum")
self.iymom = myd.names.index("y-momentum")
self.iener = myd.names.index("energy")
# if there are any additional variable, we treat them as
# passively advected scalars
self.naux = self.nvar - 4
if self.naux > 0:
self.irhox = 4
else:
self.irhox = -1
# primitive variables
self.nq = 4 + self.naux
self.irho = 0
self.iu = 1
self.iv = 2
self.ip = 3
if self.naux > 0:
self.ix = 4 # advected scalar
else:
self.ix = -1
[docs]
def cons_to_prim(U, gamma, ivars, myg):
""" convert an input vector of conserved variables to primitive variables """
q = myg.scratch_array(nvar=ivars.nq)
q[:, :, ivars.irho] = U[:, :, ivars.idens]
q[:, :, ivars.iu] = np.divide(U[:, :, ivars.ixmom], U[:, :, ivars.idens],
out=np.zeros_like(U[:, :, ivars.ixmom]),
where=(U[:, :, ivars.idens] != 0.0))
q[:, :, ivars.iv] = np.divide(U[:, :, ivars.iymom], U[:, :, ivars.idens],
out=np.zeros_like(U[:, :, ivars.iymom]),
where=(U[:, :, ivars.idens] != 0.0))
e = np.divide(U[:, :, ivars.iener] - 0.5 * q[:, :, ivars.irho] *
(q[:, :, ivars.iu]**2 + q[:, :, ivars.iv]**2),
q[:, :, ivars.irho],
out=np.zeros_like(U[:, :, ivars.iener]),
where=(U[:, :, ivars.idens] != 0.0))
q[:, :, ivars.ip] = eos.pres(gamma, q[:, :, ivars.irho], e)
if ivars.naux > 0:
for nq, nu in zip(range(ivars.ix, ivars.ix+ivars.naux),
range(ivars.irhox, ivars.irhox+ivars.naux)):
q[:, :, nq] = U[:, :, nu]/q[:, :, ivars.irho]
return q
[docs]
def prim_to_cons(q, gamma, ivars, myg):
""" convert an input vector of primitive variables to conserved variables """
U = myg.scratch_array(nvar=ivars.nvar)
U[:, :, ivars.idens] = q[:, :, ivars.irho]
U[:, :, ivars.ixmom] = q[:, :, ivars.iu]*U[:, :, ivars.idens]
U[:, :, ivars.iymom] = q[:, :, ivars.iv]*U[:, :, ivars.idens]
rhoe = eos.rhoe(gamma, q[:, :, ivars.ip])
U[:, :, ivars.iener] = rhoe + 0.5*q[:, :, ivars.irho]*(q[:, :, ivars.iu]**2 +
q[:, :, ivars.iv]**2)
if ivars.naux > 0:
for nq, nu in zip(range(ivars.ix, ivars.ix+ivars.naux),
range(ivars.irhox, ivars.irhox+ivars.naux)):
U[:, :, nu] = q[:, :, nq]*q[:, :, ivars.irho]
return U
[docs]
def get_external_sources(t, dt, U, ivars, rp, myg, *, U_old=None, problem_source=None):
"""compute the external sources, including gravity"""
_ = t # maybe unused
S = myg.scratch_array(nvar=ivars.nvar)
grav = rp.get_param("compressible.grav")
if U_old is None:
# we are just computing the sources from the current state U
if myg.coord_type == 1:
# gravity points in the radial direction for spherical
S[:, :, ivars.ixmom] = U[:, :, ivars.idens] * grav
S[:, :, ivars.iener] = U[:, :, ivars.ixmom] * grav
S[:, :, ivars.ixmom] += U[:, :, ivars.iymom]**2 / (U[:, :, ivars.idens] * myg.x2d)
S[:, :, ivars.iymom] += -U[:, :, ivars.ixmom] * U[:, :, ivars.iymom] / U[:, :, ivars.idens]
else:
# gravity points in the vertical (y) direction for Cartesian
S[:, :, ivars.iymom] = U[:, :, ivars.idens] * grav
S[:, :, ivars.iener] = U[:, :, ivars.iymom] * grav
else:
# we want to compute gravity using the time-updated momentum
# we assume that U is an approximation to U^{n+1}, which includes
# a full dt * S_old
if myg.coord_type == 1:
S[:, :, ivars.ixmom] = U[:, :, ivars.idens] * grav
S_old_xmom = U_old[:, :, ivars.idens] * grav
# we want the corrected xmom that has a time-centered source
xmom_new = U[:, :, ivars.ixmom] + 0.5 * dt * (S[:, :, ivars.ixmom] - S_old_xmom)
S[:, :, ivars.iener] = xmom_new * grav
S[:, :, ivars.ixmom] += U[:, :, ivars.iymom]**2 / (U[:, :, ivars.idens] * myg.x2d)
S[:, :, ivars.iymom] += -U[:, :, ivars.ixmom] * U[:, :, ivars.iymom] / U[:, :, ivars.idens]
else:
S[:, :, ivars.iymom] = U[:, :, ivars.idens] * grav
S_old_ymom = U_old[:, :, ivars.idens] * grav
# we want the corrected ymom that has a time-centered source
ymom_new = U[:, :, ivars.iymom] + 0.5 * dt * (S[:, :, ivars.iymom] - S_old_ymom)
S[:, :, ivars.iener] = ymom_new * grav
# now add the heating
if problem_source:
S_heating = problem_source(myg, U, ivars, rp)
S[...] += S_heating
return S
[docs]
class Simulation(NullSimulation):
"""The main simulation class for the corner transport upwind
compressible hydrodynamics solver
"""
[docs]
def initialize(self, *, extra_vars=None, ng=4):
"""
Initialize the grid and variables for compressible flow and set
the initial conditions for the chosen problem.
"""
my_grid = grid_setup(self.rp, ng=ng)
my_data = self.data_class(my_grid)
# Make sure we use CGF for riemann solver when we do SphericalPolar
try:
riemann_method = self.rp.get_param("compressible.riemann")
except KeyError:
msg.warning("ERROR: Riemann Solver is not set.")
if my_grid.coord_type == 1 and riemann_method == "HLLC":
msg.fail("ERROR: HLLC Riemann Solver is not supported " +
"with SphericalPolar Geometry")
# define solver specific boundary condition routines
bnd.define_bc("hse", BC.user, is_solid=False)
bnd.define_bc("ambient", BC.user, is_solid=False)
bnd.define_bc("ramp", BC.user, is_solid=False) # for double mach reflection problem
bc, bc_xodd, bc_yodd = bc_setup(self.rp)
# are we dealing with solid boundaries? we'll use these for
# the Riemann solver
self.solid = bnd.bc_is_solid(bc)
# density and energy
my_data.register_var("density", bc)
my_data.register_var("energy", bc)
my_data.register_var("x-momentum", bc_xodd)
my_data.register_var("y-momentum", bc_yodd)
# any extras?
if extra_vars is not None:
for v in extra_vars:
my_data.register_var(v, bc)
# store the EOS gamma as an auxiliary quantity so we can have a
# self-contained object stored in output files to make plots.
# store grav because we'll need that in some BCs
my_data.set_aux("gamma", self.rp.get_param("eos.gamma"))
my_data.set_aux("grav", self.rp.get_param("compressible.grav"))
my_data.create()
self.cc_data = my_data
if self.rp.get_param("particles.do_particles") == 1:
self.particles = particles.Particles(self.cc_data, bc, self.rp)
# some auxiliary data that we'll need to fill GC in, but isn't
# really part of the main solution
aux_data = self.data_class(my_grid)
aux_data.register_var("dens_src", bc)
aux_data.register_var("xmom_src", bc_xodd)
aux_data.register_var("ymom_src", bc_yodd)
aux_data.register_var("E_src", bc)
aux_data.create()
self.aux_data = aux_data
self.ivars = Variables(my_data)
# derived variables
self.cc_data.add_derived(derives.derive_primitives)
# initial conditions for the problem
self.problem_func(self.cc_data, self.rp)
if self.verbose > 0:
print(my_data)
[docs]
def method_compute_timestep(self):
"""
The timestep function computes the advective timestep (CFL)
constraint. The CFL constraint says that information cannot
propagate further than one zone per timestep.
We use the driver.cfl parameter to control what fraction of the
CFL step we actually take.
"""
cfl = self.rp.get_param("driver.cfl")
# get the variables we need
u, v, cs = self.cc_data.get_var(["velocity", "soundspeed"])
grid = self.cc_data.grid
# the timestep is min(dx/(|u| + cs), dy/(|v| + cs))
xtmp = grid.Lx / (abs(u) + cs)
ytmp = grid.Ly / (abs(v) + cs)
self.dt = cfl*float(min(xtmp.min(), ytmp.min()))
[docs]
def evolve(self):
"""
Evolve the equations of compressible hydrodynamics through a
timestep dt.
"""
tm_evolve = self.tc.timer("evolve")
tm_evolve.begin()
dens = self.cc_data.get_var("density")
xmom = self.cc_data.get_var("x-momentum")
ymom = self.cc_data.get_var("y-momentum")
ener = self.cc_data.get_var("energy")
gamma = self.rp.get_param("eos.gamma")
myg = self.cc_data.grid
# First get conserved states normal to the x and y interface
U_xl, U_xr, U_yl, U_yr = flx.interface_states(self.cc_data, self.rp,
self.ivars, self.tc, self.dt)
# Apply source terms to them.
# This includes external (gravity), geometric and pressure terms for SphericalPolar
# Only gravitional source for Cartesian2d
U_xl, U_xr, U_yl, U_yr = flx.apply_source_terms(U_xl, U_xr, U_yl, U_yr,
self.cc_data, self.aux_data, self.rp,
self.ivars, self.tc, self.dt,
problem_source=self.problem_source)
# Apply transverse corrections.
U_xl, U_xr, U_yl, U_yr = flx.apply_transverse_flux(U_xl, U_xr, U_yl, U_yr,
self.cc_data, self.rp, self.ivars,
self.solid, self.tc, self.dt)
# Get the actual interface conserved state after using Riemann Solver
# Then construct the corresponding fluxes using the conserved states
if myg.coord_type == 1:
# We need pressure from interface state for conservative update for
# SphericalPolar geometry. So we need interface conserved states.
F_x, U_x = riemann.riemann_flux(1, U_xl, U_xr,
self.cc_data, self.rp, self.ivars,
self.solid.xl, self.solid.xr, self.tc,
return_cons=True)
F_y, U_y = riemann.riemann_flux(2, U_yl, U_yr,
self.cc_data, self.rp, self.ivars,
self.solid.yl, self.solid.yr, self.tc,
return_cons=True)
# Find primitive variable since we need pressure in conservative update.
qx = cons_to_prim(U_x, gamma, self.ivars, myg)
qy = cons_to_prim(U_y, gamma, self.ivars, myg)
else:
# Directly calculate the interface flux using Riemann Solver
F_x = riemann.riemann_flux(1, U_xl, U_xr,
self.cc_data, self.rp, self.ivars,
self.solid.xl, self.solid.xr, self.tc,
return_cons=False)
F_y = riemann.riemann_flux(2, U_yl, U_yr,
self.cc_data, self.rp, self.ivars,
self.solid.yl, self.solid.yr, self.tc,
return_cons=False)
# Apply artificial viscosity to fluxes
q = cons_to_prim(self.cc_data.data, gamma, self.ivars, myg)
F_x, F_y = flx.apply_artificial_viscosity(F_x, F_y, q,
self.cc_data, self.rp,
self.ivars)
# save the old state (without ghost cells)
U_old = myg.scratch_array(nvar=self.ivars.nvar)
U_old[:, :, self.ivars.idens] = dens[:, :]
U_old[:, :, self.ivars.ixmom] = xmom[:, :]
U_old[:, :, self.ivars.iymom] = ymom[:, :]
U_old[:, :, self.ivars.iener] = ener[:, :]
# Conservative update
# Apply contribution due to fluxes
dtdV = self.dt / myg.V.v()
for n in range(self.ivars.nvar):
var = self.cc_data.get_var_by_index(n)
var.v()[:, :] += dtdV * \
(F_x.v(n=n)*myg.Ax.v() - F_x.ip(1, n=n)*myg.Ax.ip(1) +
F_y.v(n=n)*myg.Ay.v() - F_y.jp(1, n=n)*myg.Ay.jp(1))
# Now apply external sources
# For SphericalPolar (coord_type == 1) there are pressure
# gradients since we don't include pressure in xmom and ymom
# fluxes
if myg.coord_type == 1:
xmom.v()[:, :] -= self.dt * (qx.ip(1, n=self.ivars.ip) -
qx.v(n=self.ivars.ip)) / myg.Lx.v()
ymom.v()[:, :] -= self.dt * (qy.jp(1, n=self.ivars.ip) -
qy.v(n=self.ivars.ip)) / myg.Ly.v()
# now the external sources (including gravity). We are going
# to do a predictor-corrector here:
#
# * compute old sources using old state: S^n = S(U^n)
# * update state full dt using old sources: U^{n+1,*} += dt * S^n
# * compute new sources using this updated state: S^{n+1) = S(U^{n+1,*})
# * correct: U^{n+1} = U^{n+1,*} + dt/2 (S^{n+1} - S^n)
S_old = get_external_sources(self.cc_data.t, self.dt, U_old,
self.ivars, self.rp, myg,
problem_source=self.problem_source)
for n in range(self.ivars.nvar):
var = self.cc_data.get_var_by_index(n)
var.v()[:, :] += self.dt * S_old.v(n=n)
# now get the new time source
S_new = get_external_sources(self.cc_data.t, self.dt, self.cc_data.data,
self.ivars, self.rp, myg, U_old=U_old,
problem_source=self.problem_source)
# and correct
for n in range(self.ivars.nvar):
var = self.cc_data.get_var_by_index(n)
var.v()[:, :] += 0.5 * self.dt * (S_new.v(n=n) - S_old.v(n=n))
if self.particles is not None:
self.particles.update_particles(self.dt)
# increment the time
self.cc_data.t += self.dt
self.n += 1
tm_evolve.end()
[docs]
def dovis(self):
"""
Do runtime visualization.
"""
plt.clf()
plt.rc("font", size=10)
# we do this even though ivars is in self, so this works when
# we are plotting from a file
ivars = Variables(self.cc_data)
# access gamma from the cc_data object so we can use dovis
# outside of a running simulation.
gamma = self.cc_data.get_aux("gamma")
q = cons_to_prim(self.cc_data.data, gamma, ivars, self.cc_data.grid)
rho = q[:, :, ivars.irho]
u = q[:, :, ivars.iu]
v = q[:, :, ivars.iv]
p = q[:, :, ivars.ip]
e = eos.rhoe(gamma, p)/rho
magvel = np.sqrt(u**2 + v**2)
myg = self.cc_data.grid
fields = [rho, magvel, p, e]
field_names = [r"$\rho$", r"U", "p", "e"]
x = myg.scratch_array()
y = myg.scratch_array()
if myg.coord_type == 1:
x.v()[:, :] = myg.x2d.v()[:, :]*np.sin(myg.y2d.v()[:, :])
y.v()[:, :] = myg.x2d.v()[:, :]*np.cos(myg.y2d.v()[:, :])
else:
x.v()[:, :] = myg.x2d.v()[:, :]
y.v()[:, :] = myg.y2d.v()[:, :]
_, axes, cbar_title = plot_tools.setup_axes(myg, len(fields))
for n, ax in enumerate(axes):
v = fields[n]
img = ax.pcolormesh(x.v(), y.v(), v.v(),
shading="nearest", cmap=self.cm)
ax.set_xlabel("x")
ax.set_ylabel("y")
# needed for PDF rendering
cb = axes.cbar_axes[n].colorbar(img)
cb.solids.set_rasterized(True)
cb.solids.set_edgecolor("face")
if cbar_title:
cb.ax.set_title(field_names[n])
else:
ax.set_title(field_names[n])
if self.particles is not None:
ax = axes[0]
particle_positions = self.particles.get_positions()
# dye particles
colors = self.particles.get_init_positions()[:, 0]
# plot particles
ax.scatter(particle_positions[:, 0],
particle_positions[:, 1], s=5, c=colors, alpha=0.8, cmap="Greys")
if myg.coord_type == 1:
ax.set_xlim([np.min(x), np.max(x)])
ax.set_ylim([np.min(y), np.max(y)])
else:
ax.set_xlim([myg.xmin, myg.xmax])
ax.set_ylim([myg.ymin, myg.ymax])
plt.figtext(0.05, 0.0125, f"t = {self.cc_data.t:10.5g}")
plt.pause(0.001)
plt.draw()
