Source code for pyro.compressible_rk.problems.quad
"""The quadrant problem from Shulz-Rinne et al. 1993; Lax and Lui 1998.
Four different states are initialized in the quadrants of the domain, driving
shocks and other hydrodynamic waves at the interfaces. This can be used to
test the symmetry of the solver.
"""
import numpy as np
from pyro.util import msg
DEFAULT_INPUTS = "inputs.quad"
# these defaults seem to be equivalent to Configuration 3 from
# Shulz-Rinne et al. SIAM J. Sci. Comput., 14, 6, 1394-1414, 1993
#
# Also, with the numbers written out, this is Configuration 3 from
# Lax and Liu, SIAM J. Sci. Comput., 19, 2, 319-340, 1998
#
# See also LeVeque JCP 131, 327-353, 1997
PROBLEM_PARAMS = {"quadrant.rho1": 1.5, # quadrant 1 initial density
"quadrant.u1": 0.0, # quadrant 1 initial x-velocity
"quadrant.v1": 0.0, # quadrant 1 initial y-velocity
"quadrant.p1": 1.5, # quadrant 1 initial pressure
"quadrant.rho2": 0.532258064516129, # quadrant 2 initial density
"quadrant.u2": 1.206045378311055, # quadrant 2 initial x-velocity
"quadrant.v2": 0.0, # quadrant 2 initial y-velocity
"quadrant.p2": 0.3, # quadrant 2 initial pressure
"quadrant.rho3": 0.137992831541219, # quadrant 3 initial density
"quadrant.u3": 1.206045378311055, # quadrant 3 initial x-velocity
"quadrant.v3": 1.206045378311055, # quadrant 3 initial y-velocity
"quadrant.p3": 0.029032258064516, # quadrant 3 initial pressure
"quadrant.rho4": 0.532258064516129, # quadrant 4 initial density
"quadrant.u4": 0.0, # quadrant 4 initial x-velocity
"quadrant.v4": 1.206045378311055, # quadrant 4 initial y-velocity
"quadrant.p4": 0.3, # quadrant 4 initial pressure
"quadrant.cx": 0.5, # corner x position
"quadrant.cy": 0.5} # corner y position
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def init_data(my_data, rp):
""" initialize the quadrant problem """
if rp.get_param("driver.verbose"):
msg.bold("initializing the quadrant problem...")
# 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)
r1 = rp.get_param("quadrant.rho1")
u1 = rp.get_param("quadrant.u1")
v1 = rp.get_param("quadrant.v1")
p1 = rp.get_param("quadrant.p1")
r2 = rp.get_param("quadrant.rho2")
u2 = rp.get_param("quadrant.u2")
v2 = rp.get_param("quadrant.v2")
p2 = rp.get_param("quadrant.p2")
r3 = rp.get_param("quadrant.rho3")
u3 = rp.get_param("quadrant.u3")
v3 = rp.get_param("quadrant.v3")
p3 = rp.get_param("quadrant.p3")
r4 = rp.get_param("quadrant.rho4")
u4 = rp.get_param("quadrant.u4")
v4 = rp.get_param("quadrant.v4")
p4 = rp.get_param("quadrant.p4")
cx = rp.get_param("quadrant.cx")
cy = rp.get_param("quadrant.cy")
gamma = rp.get_param("eos.gamma")
# there is probably an easier way to do this, but for now, we
# will just do an explicit loop. Also, we really want to set
# the pressure and get the internal energy from that, and then
# compute the total energy (which is what we store). For now
# we will just fake this
myg = my_data.grid
iq1 = np.logical_and(myg.x2d >= cx, myg.y2d >= cy)
iq2 = np.logical_and(myg.x2d < cx, myg.y2d >= cy)
iq3 = np.logical_and(myg.x2d < cx, myg.y2d < cy)
iq4 = np.logical_and(myg.x2d >= cx, myg.y2d < cy)
# quadrant 1
dens[iq1] = r1
xmom[iq1] = r1*u1
ymom[iq1] = r1*v1
ener[iq1] = p1/(gamma - 1.0) + 0.5*r1*(u1*u1 + v1*v1)
# quadrant 2
dens[iq2] = r2
xmom[iq2] = r2*u2
ymom[iq2] = r2*v2
ener[iq2] = p2/(gamma - 1.0) + 0.5*r2*(u2*u2 + v2*v2)
# quadrant 3
dens[iq3] = r3
xmom[iq3] = r3*u3
ymom[iq3] = r3*v3
ener[iq3] = p3/(gamma - 1.0) + 0.5*r3*(u3*u3 + v3*v3)
# quadrant 4
dens[iq4] = r4
xmom[iq4] = r4*u4
ymom[iq4] = r4*v4
ener[iq4] = p4/(gamma - 1.0) + 0.5*r4*(u4*u4 + v4*v4)
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def finalize():
""" print out any information to the user at the end of the run """
