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"]
f, axes, cbar_title = plot_tools.setup_axes(myg, len(fields))
for n, ax in enumerate(axes):
v = fields[n]
img = ax.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
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])
plt.figtext(0.05, 0.0125, "t = {:10.5g}".format(self.cc_data.t))
plt.pause(0.001)
plt.draw()
def test_eos_consistency():
dens = 1.0
eint = 1.0
gamma = 1.4
p = eos.pres(gamma, dens, eint)
dens_eos = eos.dens(gamma, p, eint)
assert_equal(dens, dens_eos)
rhoe_eos = eos.rhoe(gamma, p)
assert_equal(dens * eint, rhoe_eos)
def test_eos_consistency():
dens = 1.0
eint = 1.0
gamma = 1.4
p = eos.pres(gamma, dens, eint)
dens_eos = eos.dens(gamma, p, eint)
assert dens == dens_eos
rhoe_eos = eos.rhoe(gamma, p)
assert dens*eint == rhoe_eos
def test_eos_consistency():
dens = 1.0
eint = 1.0
gamma = 1.4
p = eos.pres(gamma, dens, eint)
dens_eos = eos.dens(gamma, p, eint)
assert dens == dens_eos
rhoe_eos = eos.rhoe(gamma, p)
assert dens*eint == rhoe_eos
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:
U[:, :, ivars.irhox] = q[:, :, ivars.ix] * q[:, :, ivars.irho]
return U
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
def unsplitFluxes(my_data, my_aux, rp, vars, solid, tc, dt):
"""
unsplitFluxes returns the fluxes through the x and y interfaces by
doing an unsplit reconstruction of the interface values and then
solving the Riemann problem through all the interfaces at once
currently we assume a gamma-law EOS
The runtime parameter grav is assumed to be the gravitational
acceleration in the y-direction
Parameters
----------
my_data : CellCenterData2d object
The data object containing the grid and advective scalar that
we are advecting.
rp : RuntimeParameters object
The runtime parameters for the simulation
vars : Variables object
The Variables object that tells us which indices refer to which
variables
tc : TimerCollection object
The timers we are using to profile
dt : float
The timestep we are advancing through.
Returns
-------
out : ndarray, ndarray
The fluxes on the x- and y-interfaces
"""
tm_flux = tc.timer("unsplitFluxes")
tm_flux.begin()
myg = my_data.grid
gamma = rp.get_param("eos.gamma")
#=========================================================================
# compute the primitive variables
#=========================================================================
# Q = (rho, u, v, p)
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
r = dens
# get the velocities
u = xmom/dens
v = ymom/dens
# get the pressure
e = (ener - 0.5*(xmom**2 + ymom**2)/dens)/dens
p = eos.pres(gamma, dens, e)
smallp = 1.e-10
p.d = p.d.clip(smallp) # apply a floor to the pressure
#=========================================================================
# compute the flattening coefficients
#=========================================================================
# there is a single flattening coefficient (xi) for all directions
use_flattening = rp.get_param("compressible.use_flattening")
if use_flattening:
delta = rp.get_param("compressible.delta")
z0 = rp.get_param("compressible.z0")
z1 = rp.get_param("compressible.z1")
xi_x = reconstruction_f.flatten(1, p.d, u.d, myg.qx, myg.qy, myg.ng, smallp, delta, z0, z1)
xi_y = reconstruction_f.flatten(2, p.d, v.d, myg.qx, myg.qy, myg.ng, smallp, delta, z0, z1)
xi = reconstruction_f.flatten_multid(xi_x, xi_y, p.d, myg.qx, myg.qy, myg.ng)
else:
xi = 1.0
# monotonized central differences in x-direction
tm_limit = tc.timer("limiting")
tm_limit.begin()
limiter = rp.get_param("compressible.limiter")
if limiter == 0:
limitFunc = reconstruction_f.nolimit
elif limiter == 1:
limitFunc = reconstruction_f.limit2
else:
limitFunc = reconstruction_f.limit4
ldelta_rx = xi*limitFunc(1, r.d, myg.qx, myg.qy, myg.ng)
ldelta_ux = xi*limitFunc(1, u.d, myg.qx, myg.qy, myg.ng)
ldelta_vx = xi*limitFunc(1, v.d, myg.qx, myg.qy, myg.ng)
ldelta_px = xi*limitFunc(1, p.d, myg.qx, myg.qy, myg.ng)
# monotonized central differences in y-direction
ldelta_ry = xi*limitFunc(2, r.d, myg.qx, myg.qy, myg.ng)
ldelta_uy = xi*limitFunc(2, u.d, myg.qx, myg.qy, myg.ng)
ldelta_vy = xi*limitFunc(2, v.d, myg.qx, myg.qy, myg.ng)
ldelta_py = xi*limitFunc(2, p.d, myg.qx, myg.qy, myg.ng)
tm_limit.end()
#=========================================================================
# x-direction
#=========================================================================
# left and right primitive variable states
tm_states = tc.timer("interfaceStates")
tm_states.begin()
V_l, V_r = interface_f.states(1, myg.qx, myg.qy, myg.ng, myg.dx, dt,
vars.nvar,
gamma,
r.d, u.d, v.d, p.d,
ldelta_rx, ldelta_ux, ldelta_vx, ldelta_px)
tm_states.end()
# transform interface states back into conserved variables
U_xl = myg.scratch_array(vars.nvar)
U_xr = myg.scratch_array(vars.nvar)
U_xl.d[:,:,vars.idens] = V_l[:,:,vars.irho]
U_xl.d[:,:,vars.ixmom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iu]
U_xl.d[:,:,vars.iymom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iv]
U_xl.d[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_xr.d[:,:,vars.idens] = V_r[:,:,vars.irho]
U_xr.d[:,:,vars.ixmom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iu]
U_xr.d[:,:,vars.iymom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iv]
U_xr.d[:,:,vars.iener] = eos.rhoe(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# y-direction
#=========================================================================
# left and right primitive variable states
tm_states.begin()
V_l, V_r = interface_f.states(2, myg.qx, myg.qy, myg.ng, myg.dy, dt,
vars.nvar,
gamma,
r.d, u.d, v.d, p.d,
ldelta_ry, ldelta_uy, ldelta_vy, ldelta_py)
tm_states.end()
# transform interface states back into conserved variables
U_yl = myg.scratch_array(vars.nvar)
U_yr = myg.scratch_array(vars.nvar)
U_yl.d[:,:,vars.idens] = V_l[:,:,vars.irho]
U_yl.d[:,:,vars.ixmom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iu]
U_yl.d[:,:,vars.iymom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iv]
U_yl.d[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_yr.d[:,:,vars.idens] = V_r[:,:,vars.irho]
U_yr.d[:,:,vars.ixmom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iu]
U_yr.d[:,:,vars.iymom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iv]
U_yr.d[:,:,vars.iener] = eos.rhoe(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# apply source terms
#=========================================================================
grav = rp.get_param("compressible.grav")
ymom_src = my_aux.get_var("ymom_src")
ymom_src.v()[:,:] = dens.v()*grav
my_aux.fill_BC("ymom_src")
E_src = my_aux.get_var("E_src")
E_src.v()[:,:] = ymom.v()*grav
my_aux.fill_BC("E_src")
# ymom_xl[i,j] += 0.5*dt*dens[i-1,j]*grav
U_xl.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.ip(-1, buf=1)
U_xl.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.ip(-1, buf=1)
# ymom_xr[i,j] += 0.5*dt*dens[i,j]*grav
U_xr.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.v(buf=1)
U_xr.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.v(buf=1)
# ymom_yl[i,j] += 0.5*dt*dens[i,j-1]*grav
U_yl.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.jp(-1, buf=1)
U_yl.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.jp(-1, buf=1)
# ymom_yr[i,j] += 0.5*dt*dens[i,j]*grav
U_yr.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.v(buf=1)
U_yr.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.v(buf=1)
#=========================================================================
# compute transverse fluxes
#=========================================================================
tm_riem = tc.timer("riemann")
tm_riem.begin()
riemann = rp.get_param("compressible.riemann")
if riemann == "HLLC":
riemannFunc = interface_f.riemann_hllc
elif riemann == "CGF":
riemannFunc = interface_f.riemann_cgf
else:
msg.fail("ERROR: Riemann solver undefined")
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.xl, solid.xr,
gamma, U_xl.d, U_xr.d)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.yl, solid.yr,
gamma, U_yl.d, U_yr.d)
F_x = patch.ArrayIndexer(d=_fx, grid=myg)
F_y = patch.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# construct the interface values of U now
#=========================================================================
"""
finally, we can construct the state perpendicular to the interface
by adding the central difference part to the trasverse flux
difference.
The states that we represent by indices i,j are shown below
(1,2,3,4):
j+3/2--+----------+----------+----------+
| | | |
| | | |
j+1 -+ | | |
| | | |
| | | | 1: U_xl[i,j,:] = U
j+1/2--+----------XXXXXXXXXXXX----------+ i-1/2,j,L
| X X |
| X X |
j -+ 1 X 2 X | 2: U_xr[i,j,:] = U
| X X | i-1/2,j,R
| X 4 X |
j-1/2--+----------XXXXXXXXXXXX----------+
| | 3 | | 3: U_yl[i,j,:] = U
| | | | i,j-1/2,L
j-1 -+ | | |
| | | |
| | | | 4: U_yr[i,j,:] = U
j-3/2--+----------+----------+----------+ i,j-1/2,R
| | | | | | |
i-1 i i+1
i-3/2 i-1/2 i+1/2 i+3/2
remember that the fluxes are stored on the left edge, so
F_x[i,j,:] = F_x
i-1/2, j
F_y[i,j,:] = F_y
i, j-1/2
"""
tm_transverse = tc.timer("transverse flux addition")
tm_transverse.begin()
dtdx = dt/myg.dx
dtdy = dt/myg.dy
b = (2,1)
for n in range(vars.nvar):
# U_xl[i,j,:] = U_xl[i,j,:] - 0.5*dt/dy * (F_y[i-1,j+1,:] - F_y[i-1,j,:])
U_xl.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.ip_jp(-1, 1, buf=b, n=n) - F_y.ip(-1, buf=b, n=n))
# U_xr[i,j,:] = U_xr[i,j,:] - 0.5*dt/dy * (F_y[i,j+1,:] - F_y[i,j,:])
U_xr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.jp(1, buf=b, n=n) - F_y.v(buf=b, n=n))
# U_yl[i,j,:] = U_yl[i,j,:] - 0.5*dt/dx * (F_x[i+1,j-1,:] - F_x[i,j-1,:])
U_yl.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip_jp(1, -1, buf=b, n=n) - F_x.jp(-1, buf=b, n=n))
# U_yr[i,j,:] = U_yr[i,j,:] - 0.5*dt/dx * (F_x[i+1,j,:] - F_x[i,j,:])
U_yr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip(1, buf=b, n=n) - F_x.v(buf=b, n=n))
tm_transverse.end()
#=========================================================================
# construct the fluxes normal to the interfaces
#=========================================================================
# up until now, F_x and F_y stored the transverse fluxes, now we
# overwrite with the fluxes normal to the interfaces
tm_riem.begin()
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.xl, solid.xr,
gamma, U_xl.d, U_xr.d)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.yl, solid.yr,
gamma, U_yl.d, U_yr.d)
F_x = patch.ArrayIndexer(d=_fx, grid=myg)
F_y = patch.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = rp.get_param("compressible.cvisc")
_ax, _ay = interface_f.artificial_viscosity(
myg.qx, myg.qy, myg.ng, myg.dx, myg.dy,
cvisc, u.d, v.d)
avisco_x = patch.ArrayIndexer(d=_ax, grid=myg)
avisco_y = patch.ArrayIndexer(d=_ay, grid=myg)
b = (2,1)
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
F_x.v(buf=b, n=vars.idens)[:,:] += \
avisco_x.v(buf=b)*(dens.ip(-1, buf=b) - dens.v(buf=b))
F_x.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_x.v(buf=b)*(xmom.ip(-1, buf=b) - xmom.v(buf=b))
F_x.v(buf=b, n=vars.iymom)[:,:] += \
avisco_x.v(buf=b)*(ymom.ip(-1, buf=b) - ymom.v(buf=b))
F_x.v(buf=b, n=vars.iener)[:,:] += \
avisco_x.v(buf=b)*(ener.ip(-1, buf=b) - ener.v(buf=b))
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y.v(buf=b, n=vars.idens)[:,:] += \
avisco_y.v(buf=b)*(dens.jp(-1, buf=b) - dens.v(buf=b))
F_y.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_y.v(buf=b)*(xmom.jp(-1, buf=b) - xmom.v(buf=b))
F_y.v(buf=b, n=vars.iymom)[:,:] += \
avisco_y.v(buf=b)*(ymom.jp(-1, buf=b) - ymom.v(buf=b))
F_y.v(buf=b, n=vars.iener)[:,:] += \
avisco_y.v(buf=b)*(ener.jp(-1, buf=b) - ener.v(buf=b))
tm_flux.end()
return F_x, F_y
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"]
_, axes, cbar_title = plot_tools.setup_axes(myg, len(fields))
for n, ax in enumerate(axes):
v = fields[n]
img = ax.imshow(np.transpose(v.v()),
interpolation="nearest", origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
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")
ax.set_xlim([myg.xmin, myg.xmax])
ax.set_ylim([myg.ymin, myg.ymax])
plt.figtext(0.05, 0.0125, "t = {:10.5g}".format(self.cc_data.t))
plt.pause(0.001)
plt.draw()
def user(bc_name, bc_edge, variable, my_data):
"""
A hydrostatic boundary. This integrates the equation of HSE into
the ghost cells to get the pressure and density under the assumption
that the specific internal energy is constant.
Upon exit, the ghost cells for the input variable will be set
Parameters
----------
bc_name : {'hse'}
The descriptive name for the boundary condition -- this allows
for pyro to have multiple types of user-supplied boundary
conditions. For this module, it needs to be 'hse'.
bc_edge : {'ylb', 'yrb'}
The boundary to update: ylb = lower y boundary; yrb = upper y
boundary.
variable : {'density', 'x-momentum', 'y-momentum', 'energy'}
The variable whose ghost cells we are filling
my_data : CellCenterData2d object
The data object
"""
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
grav = my_data.get_aux("grav")
gamma = my_data.get_aux("gamma")
myg = my_data.grid
if bc_name == "hse":
if bc_edge == "ylb":
# lower y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable == "density":
j = myg.jlo - 1
while j >= 0:
dens[:, j] = dens[:, myg.jlo]
j -= 1
elif variable == "x-momentum":
j = myg.jlo - 1
while j >= 0:
xmom[:, j] = xmom[:, myg.jlo]
j -= 1
elif variable == "y-momentum":
j = myg.jlo - 1
while j >= 0:
ymom[:, j] = ymom[:, myg.jlo]
j -= 1
elif variable == "energy":
dens_base = dens[:, myg.jlo]
ke_base = 0.5 * (xmom[:, myg.jlo] ** 2 + ymom[:, myg.jlo] ** 2) / dens[:, myg.jlo]
eint_base = (ener[:, myg.jlo] - ke_base) / dens[:, myg.jlo]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
j = myg.jlo - 1
while j >= 0:
pres_below = pres_base - grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_below)
ener[:, j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
msg.fail("error: variable not defined")
elif bc_edge == "yrb":
# upper y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable == "density":
j = myg.jhi + 1
while j <= myg.jhi + myg.ng:
dens[:, j] = dens[:, myg.jhi]
j += 1
elif variable == "x-momentum":
j = myg.jhi + 1
while j <= myg.jhi + myg.ng:
xmom[:, j] = xmom[:, myg.jhi]
j += 1
elif variable == "y-momentum":
j = myg.jhi + 1
while j <= myg.jhi + myg.ng:
ymom[:, j] = ymom[:, myg.jhi]
j += 1
elif variable == "energy":
dens_base = dens[:, myg.jhi]
ke_base = 0.5 * (xmom[:, myg.jhi] ** 2 + ymom[:, myg.jhi] ** 2) / dens[:, myg.jhi]
eint_base = (ener[:, myg.jhi] - ke_base) / dens[:, myg.jhi]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
j = myg.jhi + 1
while j <= myg.jhi + myg.ng:
pres_above = pres_base + grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_above)
ener[:, j] = rhoe + ke_base
pres_base = pres_above.copy()
j += 1
else:
msg.fail("error: variable not defined")
else:
msg.fail("error: hse BC not supported for xlb or xrb")
else:
msg.fail("error: bc type %s not supported" % (bc_name))
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
# figure out the geometry
L_x = self.cc_data.grid.xmax - self.cc_data.grid.xmin
L_y = self.cc_data.grid.ymax - self.cc_data.grid.ymin
f = plt.figure(1)
cbar_title = False
if L_x > 2 * L_y:
# we want 4 rows:
axes = AxesGrid(f,
111,
nrows_ncols=(4, 1),
share_all=True,
cbar_mode="each",
cbar_location="top",
cbar_pad="10%",
cbar_size="25%",
axes_pad=(0.25, 0.65),
add_all=True,
label_mode="L")
cbar_title = True
elif L_y > 2 * L_x:
# we want 4 columns: rho |U| p e
axes = AxesGrid(f,
111,
nrows_ncols=(1, 4),
share_all=True,
cbar_mode="each",
cbar_location="right",
cbar_pad="10%",
cbar_size="25%",
axes_pad=(0.65, 0.25),
add_all=True,
label_mode="L")
else:
# 2x2 grid of plots
axes = AxesGrid(f,
111,
nrows_ncols=(2, 2),
share_all=True,
cbar_mode="each",
cbar_location="right",
cbar_pad="2%",
axes_pad=(0.65, 0.25),
add_all=True,
label_mode="L")
fields = [rho, magvel, p, e]
field_names = [r"$\rho$", r"U", "p", "e"]
for n in range(4):
ax = axes[n]
v = fields[n]
img = ax.imshow(np.transpose(v.v()),
interpolation="nearest",
origin="lower",
extent=[myg.xmin, myg.xmax, myg.ymin, myg.ymax],
cmap=self.cm)
ax.set_xlabel("x")
ax.set_ylabel("y")
cb = axes.cbar_axes[n].colorbar(img)
if cbar_title:
cb.ax.set_title(field_names[n])
else:
ax.set_title(field_names[n])
plt.figtext(0.05, 0.0125, "t = {:10.5g}".format(self.cc_data.t))
plt.pause(0.001)
plt.draw()
def init_data(my_data, rp):
""" initialize the shu-osher problem """
msg.bold("initializing the sod problem...")
# make sure that we are passed a valid patch object
if not isinstance(my_data, patch.CellCenterData2d):
print("ERROR: patch invalid in shu_osher.py")
print(my_data.__class__)
sys.exit()
# get the shu_osher parameters
dens_left = rp.get_param("shu_osher.dens_left")
u_left = rp.get_param("shu_osher.u_left")
u_right = rp.get_param("shu_osher.u_right")
p_left = rp.get_param("shu_osher.p_left")
p_right = rp.get_param("shu_osher.p_right")
# get the density, momenta, and energy as separate variables
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
# initialize the components, remember, that ener here is rho*eint
# + 0.5*rho*v**2, where eint is the specific internal energy
# (erg/g)
xmin = rp.get_param("mesh.xmin")
xmax = rp.get_param("mesh.xmax")
ymin = rp.get_param("mesh.ymin")
ymax = rp.get_param("mesh.ymax")
gamma = rp.get_param("eos.gamma")
direction = rp.get_param("shu_osher.direction")
#xctr = 0.5*(xmin + xmax)
xctr = -4.0
yctr = 0.5 * (ymin + ymax)
myg = my_data.grid
if direction == "x":
# left
idxl = myg.x2d <= xctr
dens[idxl] = dens_left
xmom[idxl] = dens_left * u_left
ymom[idxl] = 0.0
ener[idxl] = eos.rhoe(dens[idxl], p_left *
np.ones(np.shape(dens[idxl]))) #/ dens[idxl]
#ener[idxl] = p_left/(gamma - 1.0) + 0.5*xmom[idxl]*u_left
# right
idxr = myg.x2d > xctr
xdat = idxr[:, 0]
xall = myg.x2d[:, 0]
rhocrit = dens_left / 3.857
for i in range(xdat.shape[0]):
if idxr[i].all() == True:
dens[i] = (1.0 +
0.2 * np.sin(5.0 * xall[i])) * rhocrit * np.ones(18)
xmom[i] = (1.0 + 0.2 * np.sin(5.0 * xall[i])
) * rhocrit * np.ones(18) * u_right
ymom[i] = np.ones(18) * 0.0
ener[i] = eos.rhoe((1.0 + 0.2 * np.sin(5.0 * xall[i])) *
rhocrit * np.ones(18),
p_right * np.ones(18))
keyboard()
#dens[idxr] = 1.0 + 0.2*np.sin(5.0*xall[xdat])
#xmom[idxr] = dens_right*u_right
#ymom[idxr] = 0.0
#ener[idxr] = eos.rhoe(dens[idxr], p_right*np.ones(np.shape(dens[idxr]))) #/ dens[idxr]
#ener[idxr] = p_right/(gamma - 1.0) + 0.5*xmom[idxr]*u_right
else:
# bottom
idxb = myg.y2d <= yctr
dens[idxb] = dens_left
xmom[idxb] = 0.0
ymom[idxb] = dens_left * u_left
ener[idxb] = eos.rhoe(dens[idxb], p_left *
np.ones(np.shape(dens[idxb]))) #/ dens[idxb]
#ener[idxb] = p_left/(gamma - 1.0) + 0.5*ymom[idxb]*u_left
# top
idxt = myg.y2d > yctr
dens[idxt] = dens_right
xmom[idxt] = 0.0
ymom[idxt] = dens_right * u_right
ener[idxt] = eos.rhoe(dens[idxt],
p_right *
np.ones(np.shape(dens[idxt]))) #/ dens[idxt]
def init_data(my_data, rp):
""" initialize the Kelvin-Helmholtz problem """
msg.bold("initializing the sedov problem...")
# make sure that we are passed a valid patch object
if not isinstance(my_data, patch.CellCenterData2d):
print(my_data.__class__)
msg.fail("ERROR: patch invalid in sedov.py")
# get the density, momenta, and energy as separate variables
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
# initialize the components, remember, that ener here is rho*eint
# + 0.5*rho*v**2, where eint is the specific internal energy
# (erg/g)
dens[:, :] = 1.0
xmom[:, :] = 0.0
ymom[:, :] = 0.0
rho_1 = rp.get_param("kh.rho_1")
v_1 = rp.get_param("kh.v_1")
rho_2 = rp.get_param("kh.rho_2")
v_2 = rp.get_param("kh.v_2")
gamma = rp.get_param("eos.gamma")
xmin = rp.get_param("mesh.xmin")
xmax = rp.get_param("mesh.xmax")
ymin = rp.get_param("mesh.ymin")
ymax = rp.get_param("mesh.ymax")
yctr = 0.5 * (ymin + ymax)
L_x = xmax - xmin
myg = my_data.grid
idx_l = myg.y2d < yctr + 0.01 * np.sin(10.0 * np.pi * myg.x2d / L_x)
idx_h = myg.y2d >= yctr + 0.01 * np.sin(10.0 * np.pi * myg.x2d / L_x)
# lower half
dens[idx_l] = rho_1
xmom[idx_l] = rho_1 * v_1
ymom[idx_l] = 0.0
# upper half
dens[idx_h] = rho_2
xmom[idx_h] = rho_2 * v_2
ymom[idx_h] = 0.0
#p = 1.0
p = 6.9E06 * np.ones(np.shape(dens))
#ener[:,:] = p/(gamma - 1.0) + 0.5*(xmom[:,:]**2 + ymom[:,:]**2)/dens[:,:]
ener[:, :] = eos.rhoe(
dens[:, :], p) + 0.5 * (xmom[:, :]**2 + ymom[:, :]**2) / dens[:, :]
keyboard()
def fluxes(my_data, rp, vars, solid, tc):
"""
unsplitFluxes returns the fluxes through the x and y interfaces by
doing an unsplit reconstruction of the interface values and then
solving the Riemann problem through all the interfaces at once
currently we assume a gamma-law EOS
Parameters
----------
my_data : CellCenterData2d object
The data object containing the grid and advective scalar that
we are advecting.
rp : RuntimeParameters object
The runtime parameters for the simulation
vars : Variables object
The Variables object that tells us which indices refer to which
variables
tc : TimerCollection object
The timers we are using to profile
Returns
-------
out : ndarray, ndarray
The fluxes on the x- and y-interfaces
"""
tm_flux = tc.timer("unsplitFluxes")
tm_flux.begin()
myg = my_data.grid
gamma = rp.get_param("eos.gamma")
#=========================================================================
# compute the primitive variables
#=========================================================================
# Q = (rho, u, v, p)
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
r = dens
# get the velocities
u = xmom / dens
v = ymom / dens
# get the pressure
e = (ener - 0.5 * (xmom**2 + ymom**2) / dens) / dens
p = eos.pres(gamma, dens, e)
smallp = 1.e-10
p = p.clip(smallp) # apply a floor to the pressure
#=========================================================================
# compute the flattening coefficients
#=========================================================================
# there is a single flattening coefficient (xi) for all directions
use_flattening = rp.get_param("compressible.use_flattening")
if use_flattening:
delta = rp.get_param("compressible.delta")
z0 = rp.get_param("compressible.z0")
z1 = rp.get_param("compressible.z1")
xi_x = reconstruction_f.flatten(1, p, u, myg.qx, myg.qy, myg.ng,
smallp, delta, z0, z1)
xi_y = reconstruction_f.flatten(2, p, v, myg.qx, myg.qy, myg.ng,
smallp, delta, z0, z1)
xi = reconstruction_f.flatten_multid(xi_x, xi_y, p, myg.qx, myg.qy,
myg.ng)
else:
xi = 1.0
# monotonized central differences in x-direction
tm_limit = tc.timer("limiting")
tm_limit.begin()
limiter = rp.get_param("compressible.limiter")
if limiter == 0:
limitFunc = reconstruction_f.nolimit
elif limiter == 1:
limitFunc = reconstruction_f.limit2
else:
limitFunc = reconstruction_f.limit4
_ldelta_rx = xi * limitFunc(1, r, myg.qx, myg.qy, myg.ng)
_ldelta_ux = xi * limitFunc(1, u, myg.qx, myg.qy, myg.ng)
_ldelta_vx = xi * limitFunc(1, v, myg.qx, myg.qy, myg.ng)
_ldelta_px = xi * limitFunc(1, p, myg.qx, myg.qy, myg.ng)
# wrap these in ArrayIndexer objects
ldelta_rx = ai.ArrayIndexer(d=_ldelta_rx, grid=myg)
ldelta_ux = ai.ArrayIndexer(d=_ldelta_ux, grid=myg)
ldelta_vx = ai.ArrayIndexer(d=_ldelta_vx, grid=myg)
ldelta_px = ai.ArrayIndexer(d=_ldelta_px, grid=myg)
# monotonized central differences in y-direction
_ldelta_ry = xi * limitFunc(2, r, myg.qx, myg.qy, myg.ng)
_ldelta_uy = xi * limitFunc(2, u, myg.qx, myg.qy, myg.ng)
_ldelta_vy = xi * limitFunc(2, v, myg.qx, myg.qy, myg.ng)
_ldelta_py = xi * limitFunc(2, p, myg.qx, myg.qy, myg.ng)
ldelta_ry = ai.ArrayIndexer(d=_ldelta_ry, grid=myg)
ldelta_uy = ai.ArrayIndexer(d=_ldelta_uy, grid=myg)
ldelta_vy = ai.ArrayIndexer(d=_ldelta_vy, grid=myg)
ldelta_py = ai.ArrayIndexer(d=_ldelta_py, grid=myg)
tm_limit.end()
#=========================================================================
# x-direction
#=========================================================================
# left and right primitive variable states
tm_states = tc.timer("interfaceStates")
tm_states.begin()
V_l = myg.scratch_array(vars.nvar)
V_r = myg.scratch_array(vars.nvar)
V_l.ip(1, n=vars.irho, buf=2)[:, :] = r.v(buf=2) + 0.5 * ldelta_rx.v(buf=2)
V_r.v(n=vars.irho, buf=2)[:, :] = r.v(buf=2) - 0.5 * ldelta_rx.v(buf=2)
V_l.ip(1, n=vars.iu, buf=2)[:, :] = u.v(buf=2) + 0.5 * ldelta_ux.v(buf=2)
V_r.v(n=vars.iu, buf=2)[:, :] = u.v(buf=2) - 0.5 * ldelta_ux.v(buf=2)
V_l.ip(1, n=vars.iv, buf=2)[:, :] = v.v(buf=2) + 0.5 * ldelta_vx.v(buf=2)
V_r.v(n=vars.iv, buf=2)[:, :] = v.v(buf=2) - 0.5 * ldelta_vx.v(buf=2)
V_l.ip(1, n=vars.ip, buf=2)[:, :] = p.v(buf=2) + 0.5 * ldelta_px.v(buf=2)
V_r.v(n=vars.ip, buf=2)[:, :] = p.v(buf=2) - 0.5 * ldelta_px.v(buf=2)
tm_states.end()
# transform interface states back into conserved variables
U_xl = myg.scratch_array(vars.nvar)
U_xr = myg.scratch_array(vars.nvar)
U_xl[:, :, vars.idens] = V_l[:, :, vars.irho]
U_xl[:, :, vars.ixmom] = V_l[:, :, vars.irho] * V_l[:, :, vars.iu]
U_xl[:, :, vars.iymom] = V_l[:, :, vars.irho] * V_l[:, :, vars.iv]
U_xl[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_xr[:, :, vars.idens] = V_r[:, :, vars.irho]
U_xr[:, :, vars.ixmom] = V_r[:, :, vars.irho] * V_r[:, :, vars.iu]
U_xr[:, :, vars.iymom] = V_r[:, :, vars.irho] * V_r[:, :, vars.iv]
U_xr[:,:,vars.iener] = eos.rhoe(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# y-direction
#=========================================================================
# left and right primitive variable states
tm_states.begin()
V_l.jp(1, n=vars.irho, buf=2)[:, :] = r.v(buf=2) + 0.5 * ldelta_ry.v(buf=2)
V_r.v(n=vars.irho, buf=2)[:, :] = r.v(buf=2) - 0.5 * ldelta_ry.v(buf=2)
V_l.jp(1, n=vars.iu, buf=2)[:, :] = u.v(buf=2) + 0.5 * ldelta_uy.v(buf=2)
V_r.v(n=vars.iu, buf=2)[:, :] = u.v(buf=2) - 0.5 * ldelta_uy.v(buf=2)
V_l.jp(1, n=vars.iv, buf=2)[:, :] = v.v(buf=2) + 0.5 * ldelta_vy.v(buf=2)
V_r.v(n=vars.iv, buf=2)[:, :] = v.v(buf=2) - 0.5 * ldelta_vy.v(buf=2)
V_l.jp(1, n=vars.ip, buf=2)[:, :] = p.v(buf=2) + 0.5 * ldelta_py.v(buf=2)
V_r.v(n=vars.ip, buf=2)[:, :] = p.v(buf=2) - 0.5 * ldelta_py.v(buf=2)
tm_states.end()
# transform interface states back into conserved variables
U_yl = myg.scratch_array(vars.nvar)
U_yr = myg.scratch_array(vars.nvar)
U_yl[:, :, vars.idens] = V_l[:, :, vars.irho]
U_yl[:, :, vars.ixmom] = V_l[:, :, vars.irho] * V_l[:, :, vars.iu]
U_yl[:, :, vars.iymom] = V_l[:, :, vars.irho] * V_l[:, :, vars.iv]
U_yl[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_yr[:, :, vars.idens] = V_r[:, :, vars.irho]
U_yr[:, :, vars.ixmom] = V_r[:, :, vars.irho] * V_r[:, :, vars.iu]
U_yr[:, :, vars.iymom] = V_r[:, :, vars.irho] * V_r[:, :, vars.iv]
U_yr[:,:,vars.iener] = eos.rhoe(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# construct the fluxes normal to the interfaces
#=========================================================================
tm_riem = tc.timer("Riemann")
tm_riem.begin()
riemann = rp.get_param("compressible.riemann")
if riemann == "HLLC":
riemannFunc = interface_f.riemann_hllc
elif riemann == "CGF":
riemannFunc = interface_f.riemann_cgf
else:
msg.fail("ERROR: Riemann solver undefined")
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng, vars.nvar, vars.idens,
vars.ixmom, vars.iymom, vars.iener, solid.xl, solid.xr,
gamma, U_xl, U_xr)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng, vars.nvar, vars.idens,
vars.ixmom, vars.iymom, vars.iener, solid.yl, solid.yr,
gamma, U_yl, U_yr)
F_x = ai.ArrayIndexer(d=_fx, grid=myg)
F_y = ai.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = rp.get_param("compressible.cvisc")
_ax, _ay = interface_f.artificial_viscosity(myg.qx, myg.qy, myg.ng, myg.dx,
myg.dy, cvisc, u, v)
avisco_x = ai.ArrayIndexer(d=_ax, grid=myg)
avisco_y = ai.ArrayIndexer(d=_ay, grid=myg)
b = (2, 1)
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
F_x.v(buf=b, n=vars.idens)[:,:] += \
avisco_x.v(buf=b)*(dens.ip(-1, buf=b) - dens.v(buf=b))
F_x.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_x.v(buf=b)*(xmom.ip(-1, buf=b) - xmom.v(buf=b))
F_x.v(buf=b, n=vars.iymom)[:,:] += \
avisco_x.v(buf=b)*(ymom.ip(-1, buf=b) - ymom.v(buf=b))
F_x.v(buf=b, n=vars.iener)[:,:] += \
avisco_x.v(buf=b)*(ener.ip(-1, buf=b) - ener.v(buf=b))
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y.v(buf=b, n=vars.idens)[:,:] += \
avisco_y.v(buf=b)*(dens.jp(-1, buf=b) - dens.v(buf=b))
F_y.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_y.v(buf=b)*(xmom.jp(-1, buf=b) - xmom.v(buf=b))
F_y.v(buf=b, n=vars.iymom)[:,:] += \
avisco_y.v(buf=b)*(ymom.jp(-1, buf=b) - ymom.v(buf=b))
F_y.v(buf=b, n=vars.iener)[:,:] += \
avisco_y.v(buf=b)*(ener.jp(-1, buf=b) - ener.v(buf=b))
tm_flux.end()
return F_x, F_y
def user(bc_name, bc_edge, variable, ccdata):
"""
A hydrostatic boundary. This integrates the equation of HSE into
the ghost cells to get the pressure and density under the assumption
that the specific internal energy is constant.
Upon exit, the ghost cells for the input variable will be set
Parameters
----------
bc_name : {'hse'}
The descriptive name for the boundary condition -- this allows
for pyro to have multiple types of user-supplied boundary
conditions. For this module, it needs to be 'hse'.
bc_edge : {'ylb', 'yrb'}
The boundary to update: ylb = lower y boundary; yrb = upper y
boundary.
variable : {'density', 'x-momentum', 'y-momentum', 'energy'}
The variable whose ghost cells we are filling
ccdata : CellCenterData2d object
The data object
"""
myg = ccdata.grid
if bc_name == "hse":
if bc_edge == "ylb":
# lower y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable in ["density", "x-momentum", "y-momentum", "ymom_src", "E_src", "fuel", "ash"]:
v = ccdata.get_var(variable)
j = myg.jlo-1
while j >= 0:
v[:, j] = v[:, myg.jlo]
j -= 1
elif variable == "energy":
dens = ccdata.get_var("density")
xmom = ccdata.get_var("x-momentum")
ymom = ccdata.get_var("y-momentum")
ener = ccdata.get_var("energy")
grav = ccdata.get_aux("grav")
gamma = ccdata.get_aux("gamma")
dens_base = dens[:, myg.jlo]
ke_base = 0.5*(xmom[:, myg.jlo]**2 + ymom[:, myg.jlo]**2) / \
dens[:, myg.jlo]
eint_base = (ener[:, myg.jlo] - ke_base)/dens[:, myg.jlo]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
j = myg.jlo-1
while j >= 0:
pres_below = pres_base - grav*dens_base*myg.dy
rhoe = eos.rhoe(gamma, pres_below)
ener[:, j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
raise NotImplementedError("variable not defined")
elif bc_edge == "yrb":
# upper y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable in ["density", "x-momentum", "y-momentum", "ymom_src", "E_src", "fuel", "ash"]:
v = ccdata.get_var(variable)
for j in range(myg.jhi+1, myg.jhi+myg.ng+1):
v[:, j] = v[:, myg.jhi]
elif variable == "energy":
dens = ccdata.get_var("density")
xmom = ccdata.get_var("x-momentum")
ymom = ccdata.get_var("y-momentum")
ener = ccdata.get_var("energy")
grav = ccdata.get_aux("grav")
gamma = ccdata.get_aux("gamma")
dens_base = dens[:, myg.jhi]
ke_base = 0.5*(xmom[:, myg.jhi]**2 + ymom[:, myg.jhi]**2) / \
dens[:, myg.jhi]
eint_base = (ener[:, myg.jhi] - ke_base)/dens[:, myg.jhi]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
for j in range(myg.jhi+1, myg.jhi+myg.ng+1):
pres_above = pres_base + grav*dens_base*myg.dy
rhoe = eos.rhoe(gamma, pres_above)
ener[:, j] = rhoe + ke_base
pres_base = pres_above.copy()
else:
raise NotImplementedError("variable not defined")
else:
msg.fail("error: hse BC not supported for xlb or xrb")
elif bc_name == "ramp":
# Boundary conditions for double Mach reflection problem
gamma = ccdata.get_aux("gamma")
if bc_edge == "xlb":
# lower x boundary
# inflow condition with post shock setup
v = ccdata.get_var(variable)
i = myg.ilo - 1
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
val = inflow_post_bc(variable, gamma)
while i >= 0:
v[i, :] = val
i = i - 1
else:
v[:, :] = 0.0 # no source term
elif bc_edge == "ylb":
# lower y boundary
# for x > 1./6., reflective boundary
# for x < 1./6., inflow with post shock setup
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
v = ccdata.get_var(variable)
j = myg.jlo - 1
jj = 0
while j >= 0:
xcen_l = myg.x < 1.0/6.0
xcen_r = myg.x >= 1.0/6.0
v[xcen_l, j] = inflow_post_bc(variable, gamma)
if variable == "y-momentum":
v[xcen_r, j] = -1.0*v[xcen_r, myg.jlo+jj]
else:
v[xcen_r, j] = v[xcen_r, myg.jlo+jj]
j = j - 1
jj = jj + 1
else:
v = ccdata.get_var(variable)
v[:, :] = 0.0 # no source term
elif bc_edge == "yrb":
# upper y boundary
# time-dependent boundary, the shockfront moves with a 10 mach velocity forming an angle
# to the x-axis of 30 degrees clockwise.
# x coordinate of the grid is used to judge whether the cell belongs to pure post shock area,
# the pure pre shock area or the mixed area.
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
v = ccdata.get_var(variable)
for j in range(myg.jhi+1, myg.jhi+myg.ng+1):
shockfront_up = 1.0/6.0 + (myg.y[j] + 0.5*myg.dy*math.sqrt(3))/math.tan(math.pi/3.0) \
+ (10.0/math.sin(math.pi/3.0))*ccdata.t
shockfront_down = 1.0/6.0 + (myg.y[j] - 0.5*myg.dy*math.sqrt(3))/math.tan(math.pi/3.0) \
+ (10.0/math.sin(math.pi/3.0))*ccdata.t
shockfront = np.array([shockfront_down, shockfront_up])
for i in range(myg.ihi+myg.ng+1):
v[i, j] = 0.0
cx_down = myg.x[i] - 0.5*myg.dx*math.sqrt(3)
cx_up = myg.x[i] + 0.5*myg.dx*math.sqrt(3)
cx = np.array([cx_down, cx_up])
for sf in shockfront:
for x in cx:
if x < sf:
v[i, j] = v[i, j] + 0.25*inflow_post_bc(variable, gamma)
else:
v[i, j] = v[i, j] + 0.25*inflow_pre_bc(variable, gamma)
else:
v = ccdata.get_var(variable)
v[:, :] = 0.0 # no source term
else:
msg.fail("error: bc type %s not supported" % (bc_name))
def user(bc_name, bc_edge, variable, ccdata):
"""
A hydrostatic boundary. This integrates the equation of HSE into
the ghost cells to get the pressure and density under the assumption
that the specific internal energy is constant.
Upon exit, the ghost cells for the input variable will be set
Parameters
----------
bc_name : {'hse'}
The descriptive name for the boundary condition -- this allows
for pyro to have multiple types of user-supplied boundary
conditions. For this module, it needs to be 'hse'.
bc_edge : {'ylb', 'yrb'}
The boundary to update: ylb = lower y boundary; yrb = upper y
boundary.
variable : {'density', 'x-momentum', 'y-momentum', 'energy'}
The variable whose ghost cells we are filling
ccdata : CellCenterData2d object
The data object
"""
myg = ccdata.grid
if bc_name == "hse":
if bc_edge == "ylb":
# lower y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable in [
"density", "x-momentum", "y-momentum", "ymom_src", "E_src",
"fuel", "ash"
]:
v = ccdata.get_var(variable)
j = myg.jlo - 1
while j >= 0:
v[:, j] = v[:, myg.jlo]
j -= 1
elif variable == "energy":
dens = ccdata.get_var("density")
xmom = ccdata.get_var("x-momentum")
ymom = ccdata.get_var("y-momentum")
ener = ccdata.get_var("energy")
grav = ccdata.get_aux("grav")
gamma = ccdata.get_aux("gamma")
dens_base = dens[:, myg.jlo]
ke_base = 0.5*(xmom[:, myg.jlo]**2 + ymom[:, myg.jlo]**2) / \
dens[:, myg.jlo]
eint_base = (ener[:, myg.jlo] - ke_base) / dens[:, myg.jlo]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
j = myg.jlo - 1
while j >= 0:
pres_below = pres_base - grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_below)
ener[:, j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
raise NotImplementedError("variable not defined")
elif bc_edge == "yrb":
# upper y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable in [
"density", "x-momentum", "y-momentum", "ymom_src", "E_src",
"fuel", "ash"
]:
v = ccdata.get_var(variable)
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
v[:, j] = v[:, myg.jhi]
elif variable == "energy":
dens = ccdata.get_var("density")
xmom = ccdata.get_var("x-momentum")
ymom = ccdata.get_var("y-momentum")
ener = ccdata.get_var("energy")
grav = ccdata.get_aux("grav")
gamma = ccdata.get_aux("gamma")
dens_base = dens[:, myg.jhi]
ke_base = 0.5*(xmom[:, myg.jhi]**2 + ymom[:, myg.jhi]**2) / \
dens[:, myg.jhi]
eint_base = (ener[:, myg.jhi] - ke_base) / dens[:, myg.jhi]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
pres_above = pres_base + grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_above)
ener[:, j] = rhoe + ke_base
pres_base = pres_above.copy()
else:
raise NotImplementedError("variable not defined")
else:
msg.fail("error: hse BC not supported for xlb or xrb")
elif bc_name == "ramp":
# Boundary conditions for double Mach reflection problem
gamma = ccdata.get_aux("gamma")
if bc_edge == "xlb":
# lower x boundary
# inflow condition with post shock setup
v = ccdata.get_var(variable)
i = myg.ilo - 1
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
val = inflow_post_bc(variable, gamma)
while i >= 0:
v[i, :] = val
i = i - 1
else:
v[:, :] = 0.0 # no source term
elif bc_edge == "ylb":
# lower y boundary
# for x > 1./6., reflective boundary
# for x < 1./6., inflow with post shock setup
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
v = ccdata.get_var(variable)
j = myg.jlo - 1
jj = 0
while j >= 0:
xcen_l = myg.x < 1.0 / 6.0
xcen_r = myg.x >= 1.0 / 6.0
v[xcen_l, j] = inflow_post_bc(variable, gamma)
if variable == "y-momentum":
v[xcen_r, j] = -1.0 * v[xcen_r, myg.jlo + jj]
else:
v[xcen_r, j] = v[xcen_r, myg.jlo + jj]
j = j - 1
jj = jj + 1
else:
v = ccdata.get_var(variable)
v[:, :] = 0.0 # no source term
elif bc_edge == "yrb":
# upper y boundary
# time-dependent boundary, the shockfront moves with a 10 mach velocity forming an angle
# to the x-axis of 30 degrees clockwise.
# x coordinate of the grid is used to judge whether the cell belongs to pure post shock area,
# the pure pre shock area or the mixed area.
if variable in ["density", "x-momentum", "y-momentum", "energy"]:
v = ccdata.get_var(variable)
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
shockfront_up = 1.0/6.0 + (myg.y[j] + 0.5*myg.dy*math.sqrt(3))/math.tan(math.pi/3.0) \
+ (10.0/math.sin(math.pi/3.0))*ccdata.t
shockfront_down = 1.0/6.0 + (myg.y[j] - 0.5*myg.dy*math.sqrt(3))/math.tan(math.pi/3.0) \
+ (10.0/math.sin(math.pi/3.0))*ccdata.t
shockfront = np.array([shockfront_down, shockfront_up])
for i in range(myg.ihi + myg.ng + 1):
v[i, j] = 0.0
cx_down = myg.x[i] - 0.5 * myg.dx * math.sqrt(3)
cx_up = myg.x[i] + 0.5 * myg.dx * math.sqrt(3)
cx = np.array([cx_down, cx_up])
for sf in shockfront:
for x in cx:
if x < sf:
v[i, j] = v[i, j] + 0.25 * inflow_post_bc(
variable, gamma)
else:
v[i, j] = v[i, j] + 0.25 * inflow_pre_bc(
variable, gamma)
else:
v = ccdata.get_var(variable)
v[:, :] = 0.0 # no source term
else:
msg.fail("error: bc type %s not supported" % (bc_name))
def user(bc_name, bc_edge, variable, my_data):
"""
A hydrostatic boundary. This integrates the equation of HSE into
the ghost cells to get the pressure and density under the assumption
that the specific internal energy is constant.
Upon exit, the ghost cells for the input variable will be set
Parameters
----------
bc_name : {'hse'}
The descriptive name for the boundary condition -- this allows
for pyro to have multiple types of user-supplied boundary
conditions. For this module, it needs to be 'hse'.
bc_edge : {'ylb', 'yrb'}
The boundary to update: ylb = lower y boundary; yrb = upper y
boundary.
variable : {'density', 'x-momentum', 'y-momentum', 'energy'}
The variable whose ghost cells we are filling
my_data : CellCenterData2d object
The data object
"""
dens = my_data.get_var("density")
xmom = my_data.get_var("x-momentum")
ymom = my_data.get_var("y-momentum")
ener = my_data.get_var("energy")
grav = my_data.get_aux("grav")
gamma = my_data.get_aux("gamma")
myg = my_data.grid
if bc_name == "hse":
if bc_edge == "ylb":
# lower y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable == "density":
j = myg.jlo - 1
while j >= 0:
dens.d[:, j] = dens.d[:, myg.jlo]
j -= 1
elif variable == "x-momentum":
j = myg.jlo - 1
while j >= 0:
xmom.d[:, j] = xmom.d[:, myg.jlo]
j -= 1
elif variable == "y-momentum":
j = myg.jlo - 1
while j >= 0:
ymom.d[:, j] = ymom.d[:, myg.jlo]
j -= 1
elif variable == "energy":
dens_base = dens.d[:, myg.jlo]
ke_base = 0.5*(xmom.d[:,myg.jlo]**2 + ymom.d[:,myg.jlo]**2) / \
dens.d[:,myg.jlo]
eint_base = (ener.d[:, myg.jlo] - ke_base) / dens.d[:, myg.jlo]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
j = myg.jlo - 1
while (j >= 0):
pres_below = pres_base - grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_below)
ener.d[:, j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
msg.fail("error: variable not defined")
elif bc_edge == "yrb":
# upper y boundary
# we will take the density to be constant, the velocity to
# be outflow, and the pressure to be in HSE
if variable == "density":
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
dens.d[:, j] = dens.d[:, myg.jhi]
elif variable == "x-momentum":
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
xmom.d[:, j] = xmom.d[:, myg.jhi]
elif variable == "y-momentum":
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
ymom.d[:, j] = ymom.d[:, myg.jhi]
elif variable == "energy":
dens_base = dens.d[:, myg.jhi]
ke_base = 0.5*(xmom.d[:,myg.jhi]**2 + ymom.d[:,myg.jhi]**2) / \
dens.d[:,myg.jhi]
eint_base = (ener.d[:, myg.jhi] - ke_base) / dens.d[:, myg.jhi]
pres_base = eos.pres(gamma, dens_base, eint_base)
# we are assuming that the density is constant in this
# formulation of HSE, so the pressure comes simply from
# differencing the HSE equation
for j in range(myg.jhi + 1, myg.jhi + myg.ng + 1):
pres_above = pres_base + grav * dens_base * myg.dy
rhoe = eos.rhoe(gamma, pres_above)
ener.d[:, j] = rhoe + ke_base
pres_base = pres_above.copy()
else:
msg.fail("error: variable not defined")
else:
msg.fail("error: hse BC not supported for xlb or xrb")
else:
msg.fail("error: bc type %s not supported" % (bc_name))