"""
compressible-specific boundary conditions. Here, in particular, we
implement an HSE BC in the vertical direction.
Note: the pyro BC routines operate on a single variable at a time, so
some work will necessarily be repeated.
Also note: we may come in here with the aux_data (source terms), so
we'll do a special case for them
"""
import math
import numpy as np
from pyro.compressible import eos
from pyro.util import msg
[docs]
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
"""
# pylint: disable=too-many-nested-blocks
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",
"dens_src", "xmom_src", "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",
"dens_src", "xmom_src", "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 == "ambient":
# we'll assume that the problem setup defines these
# they will not be available for source terms
ambient_rho = ccdata.get_aux("ambient_rho")
ambient_u = ccdata.get_aux("ambient_u")
ambient_v = ccdata.get_aux("ambient_v")
ambient_p = ccdata.get_aux("ambient_p")
if bc_edge == "yrb":
# upper y boundary
# by default, use a zero gradient
v = ccdata.get_var(variable)
for j in range(myg.jhi+1, myg.jhi+myg.ng+1):
v[:, j] = v[:, myg.jhi]
# overwrite with ambient conditions
if variable == "density":
v[:, myg.jhi+1:myg.jhi+myg.ng+1] = ambient_rho
elif variable == "x-momentum":
rhou = ambient_rho * ambient_u
v[:, myg.jhi+1:myg.jhi+myg.ng+1] = rhou
elif variable == "y-momentum":
rhov = ambient_rho * ambient_v
v[:, myg.jhi+1:myg.jhi+myg.ng+1] = rhov
elif variable == "energy":
gamma = ccdata.get_aux("gamma")
ke = 0.5 * ambient_rho * (ambient_u**2 + ambient_v**2)
rhoE = ambient_p / (gamma - 1.0) + ke
v[:, myg.jhi+1:myg.jhi+myg.ng+1] = rhoE
else:
msg.fail("error: ambient BC not supported for xlb, xrb, or ylb")
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(f"error: bc type {bc_name} not supported")
[docs]
def inflow_post_bc(var, g):
# inflow boundary condition with post shock setup
r_l = 8.0
u_l = 7.1447096
v_l = -4.125
p_l = 116.5
if var == "density":
vl = r_l
elif var == "x-momentum":
vl = r_l*u_l
elif var == "y-momentum":
vl = r_l*v_l
elif var == "energy":
vl = p_l/(g - 1.0) + 0.5*r_l*(u_l*u_l + v_l*v_l)
else:
vl = 0.0
return vl
[docs]
def inflow_pre_bc(var, g):
# pre shock setup
r_r = 1.4
u_r = 0.0
v_r = 0.0
p_r = 1.0
if var == "density":
vl = r_r
elif var == "x-momentum":
vl = r_r*u_r
elif var == "y-momentum":
vl = r_r*v_r
elif var == "energy":
vl = p_r/(g - 1.0) + 0.5*r_r*(u_r*u_r + v_r*v_r)
else:
vl = 0.0
return vl
