def timestep(myData):
"""
compute the CFL timestep for the current patch.
"""
cfl = runparams.getParam("driver.cfl")
# get the variables we need
dens = myData.getVarPtr("density")
xmom = myData.getVarPtr("x-momentum")
ymom = myData.getVarPtr("y-momentum")
ener = myData.getVarPtr("energy")
# we need to compute the pressure
u = xmom / dens
v = ymom / dens
e = (ener - 0.5 * dens * (u * u + v * v)) / dens
p = eos.pres(dens, e)
# compute the sounds speed
gamma = runparams.getParam("eos.gamma")
cs = numpy.sqrt(gamma * p / dens)
# the timestep is min(dx/(|u| + cs), dy/(|v| + cs))
xtmp = myData.grid.dx / (abs(u) + cs)
ytmp = myData.grid.dy / (abs(v) + cs)
dt = cfl * min(xtmp.min(), ytmp.min())
return dt
def evolve(myData, dt):
pf = profile.timer("evolve")
pf.begin()
dens = myData.getVarPtr("density")
xmom = myData.getVarPtr("x-momentum")
ymom = myData.getVarPtr("y-momentum")
ener = myData.getVarPtr("energy")
grav = runparams.getParam("compressible.grav")
myg = myData.grid
(Flux_x, Flux_y) = unsplitFluxes(myData, dt)
#Flux_x = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
#Flux_y = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
old_dens = dens.copy()
old_ymom = ymom.copy()
# conservative update
dtdx = dt/myg.dx
dtdy = dt/myg.dy
dens[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] += \
dtdx*(Flux_x[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.idens] - \
Flux_x[myg.ilo+1:myg.ihi+2,myg.jlo :myg.jhi+1,vars.idens]) + \
dtdy*(Flux_y[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.idens] - \
Flux_y[myg.ilo :myg.ihi+1,myg.jlo+1:myg.jhi+2,vars.idens])
xmom[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] += \
dtdx*(Flux_x[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.ixmom] - \
Flux_x[myg.ilo+1:myg.ihi+2,myg.jlo :myg.jhi+1,vars.ixmom]) + \
dtdy*(Flux_y[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.ixmom] - \
Flux_y[myg.ilo :myg.ihi+1,myg.jlo+1:myg.jhi+2,vars.ixmom])
ymom[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] += \
dtdx*(Flux_x[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.iymom] - \
Flux_x[myg.ilo+1:myg.ihi+2,myg.jlo :myg.jhi+1,vars.iymom]) + \
dtdy*(Flux_y[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.iymom] - \
Flux_y[myg.ilo :myg.ihi+1,myg.jlo+1:myg.jhi+2,vars.iymom])
ener[myg.ilo:myg.ihi+1,myg.jlo:myg.jhi+1] += \
dtdx*(Flux_x[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.iener] - \
Flux_x[myg.ilo+1:myg.ihi+2,myg.jlo :myg.jhi+1,vars.iener]) + \
dtdy*(Flux_y[myg.ilo :myg.ihi+1,myg.jlo :myg.jhi+1,vars.iener] - \
Flux_y[myg.ilo :myg.ihi+1,myg.jlo+1:myg.jhi+2,vars.iener])
# gravitational source terms
ymom += 0.5*dt*(dens + old_dens)*grav
ener += 0.5*dt*(ymom + old_ymom)*grav
pf.end()
def rhoe(pres):
""" given the pressure, return (rho * e) """
gamma = runparams.getParam("eos.gamma")
rhoe = pres / (gamma - 1.0)
return rhoe
def rhoe(pres):
""" given the pressure, return (rho * e) """
gamma = runparams.getParam("eos.gamma")
rhoe = pres/(gamma - 1.0)
return rhoe
def pres(dens, eint):
""" given the density and the specific internal energy, return the
pressure """
gamma = runparams.getParam("eos.gamma")
p = dens*eint*(gamma - 1.0)
return p
def dens(pres, eint):
""" given the pressure and the specific internal energy, return
the density """
gamma = runparams.getParam("eos.gamma")
dens = pres/(eint*(gamma - 1.0))
return dens
def pres(dens, eint):
""" given the density and the specific internal energy, return the
pressure """
gamma = runparams.getParam("eos.gamma")
p = dens * eint * (gamma - 1.0)
return p
def dens(pres, eint):
""" given the pressure and the specific internal energy, return
the density """
gamma = runparams.getParam("eos.gamma")
dens = pres / (eint * (gamma - 1.0))
return dens
def timestep(myData):
"""
compute the CFL timestep for the current patch.
"""
cfl = runparams.getParam("driver.cfl")
# get the variables we need
dens = myData.getVarPtr("density")
xmom = myData.getVarPtr("x-momentum")
ymom = myData.getVarPtr("y-momentum")
ener = myData.getVarPtr("energy")
# we need to compute the pressure
u = xmom/dens
v = ymom/dens
e = (ener - 0.5*dens*(u*u + v*v))/dens
p = eos.pres(dens, e)
# compute the sounds speed
gamma = runparams.getParam("eos.gamma")
cs = numpy.sqrt(gamma*p/dens)
# the timestep is min(dx/(|u| + cs), dy/(|v| + cs))
xtmp = myData.grid.dx/(abs(u) + cs)
ytmp = myData.grid.dy/(abs(v) + cs)
dt = cfl*min(xtmp.min(), ytmp.min())
return dt
def initData(myPatch):
""" initialize the sod problem """
msg.bold("initializing the sod problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in sod.py"
print myPatch.__class__
sys.exit()
# get the sod parameters
dens_left = runparams.getParam("sod.dens_left")
dens_right = runparams.getParam("sod.dens_right")
u_left = runparams.getParam("sod.u_left")
u_right = runparams.getParam("sod.u_right")
p_left = runparams.getParam("sod.p_left")
p_right = runparams.getParam("sod.p_right")
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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 = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
gamma = runparams.getParam("eos.gamma")
direction = runparams.getParam("sod.direction")
xctr = 0.5*(xmin + xmax)
yctr = 0.5*(ymin + ymax)
myg = myPatch.grid
# 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 pressue 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.
if direction == "x":
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if myg.x[i] <= xctr:
dens[i,j] = dens_left
xmom[i,j] = dens_left*u_left
ymom[i,j] = 0.0
ener[i,j] = p_left/(gamma - 1.0) + 0.5*xmom[i,j]*u_left
else:
dens[i,j] = dens_right
xmom[i,j] = dens_right*u_right
ymom[i,j] = 0.0
ener[i,j] = p_right/(gamma - 1.0) + 0.5*xmom[i,j]*u_right
j += 1
i += 1
else:
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if myg.y[j] <= yctr:
dens[i,j] = dens_left
xmom[i,j] = 0.0
ymom[i,j] = dens_left*u_left
ener[i,j] = p_left/(gamma - 1.0) + 0.5*ymom[i,j]*u_left
else:
dens[i,j] = dens_right
xmom[i,j] = 0.0
ymom[i,j] = dens_right*u_right
ener[i,j] = p_right/(gamma - 1.0) + 0.5*ymom[i,j]*u_right
j += 1
i += 1
def initData(myPatch):
""" initialize the Rayleigh-Taylor instability problem """
msg.bold("initializing the Rayleigh-Taylor instability problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in raytay.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("energy")
# get the other input parameters for the problem
gamma = runparams.getParam("eos.gamma")
grav = runparams.getParam("compressible.grav")
dens_up = runparams.getParam("raytay.dens_up")
dens_down = runparams.getParam("raytay.dens_down")
A = runparams.getParam("raytay.pert_amplitude_factor")
p0 = runparams.getParam("raytay.pressure_bottom")
sigma = runparams.getParam("raytay.sigma")
# get the grid parameters
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
yctr = 0.5*(ymin + ymax)
# initialize the components, remember, that ener here is
# rho*eint + 0.5*rho*v**2, where eint is the specific
# internal energy (erg/g)
xmom[:,:] = 0.0
ymom[:,:] = 0.0
dens[:,:] = 0.0
Lx = xmax - xmin
# set the density and energy to be stratified in the y-direction
myg = myPatch.grid
j = myg.jlo
while j <= myg.jhi:
if myg.y[j] < yctr :
dens[:,j] = dens_down
pres = dens_down*grav*myg.y[j] + p0
ener[:,j] = pres/(gamma - 1.0) #+ 0.5*(xmom[:,j]**2 + ymom[:,j]**2)/dens_down
else:
dens[:,j] = dens_up
pres = p0 + dens_down*grav*yctr + dens_up*grav*(myg.y[j] - yctr)
ener[:,j] = pres/(gamma - 1.0) #+ 0.5*(xmom[:,j]**2 + ymom[:,j]**2)/dens_up
j += 1
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
v_pert = A*numpy.sin(2.0*numpy.pi*myg.x[i]/Lx)*numpy.exp( - (( myg.y[j]-yctr)/sigma)**2 )
# momentum
ymom[i,j] = dens[i,j]*v_pert
# internal energy
ener[i,j] += 0.5*(xmom[i,j]**2 - ymom[i,j]**2)/dens[i,j]
j += 1
i += 1
def initData(myPatch):
""" initialize the quadrant problem """
msg.bold("initializing the quadrant problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in quad.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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 = runparams.getParam("quadrant.rho1")
u1 = runparams.getParam("quadrant.u1")
v1 = runparams.getParam("quadrant.v1")
p1 = runparams.getParam("quadrant.p1")
r2 = runparams.getParam("quadrant.rho2")
u2 = runparams.getParam("quadrant.u2")
v2 = runparams.getParam("quadrant.v2")
p2 = runparams.getParam("quadrant.p2")
r3 = runparams.getParam("quadrant.rho3")
u3 = runparams.getParam("quadrant.u3")
v3 = runparams.getParam("quadrant.v3")
p3 = runparams.getParam("quadrant.p3")
r4 = runparams.getParam("quadrant.rho4")
u4 = runparams.getParam("quadrant.u4")
v4 = runparams.getParam("quadrant.v4")
p4 = runparams.getParam("quadrant.p4")
cx = runparams.getParam("quadrant.cx")
cy = runparams.getParam("quadrant.cy")
gamma = runparams.getParam("eos.gamma")
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
# 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 pressue 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 = myPatch.grid
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if (myg.x[i] >= cx and myg.y[j] >= cy):
# quadrant 1
dens[i, j] = r1
xmom[i, j] = r1 * u1
ymom[i, j] = r1 * v1
ener[i,
j] = p1 / (gamma - 1.0) + 0.5 * r1 * (u1 * u1 + v1 * v1)
elif (myg.x[i] < cx and myg.y[j] >= cy):
# quadrant 2
dens[i, j] = r2
xmom[i, j] = r2 * u2
ymom[i, j] = r2 * v2
ener[i,
j] = p2 / (gamma - 1.0) + 0.5 * r2 * (u2 * u2 + v2 * v2)
elif (myg.x[i] < cx and myg.y[j] < cy):
# quadrant 3
dens[i, j] = r3
xmom[i, j] = r3 * u3
ymom[i, j] = r3 * v3
ener[i,
j] = p3 / (gamma - 1.0) + 0.5 * r3 * (u3 * u3 + v3 * v3)
elif (myg.x[i] >= cx and myg.y[j] < cy):
# quadrant 4
dens[i, j] = r4
xmom[i, j] = r4 * u4
ymom[i, j] = r4 * v4
ener[i,
j] = p4 / (gamma - 1.0) + 0.5 * r4 * (u4 * u4 + v4 * v4)
j += 1
i += 1
def initData(myPatch):
""" initialize the sod problem """
msg.bold("initializing the sod problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in sod.py"
print myPatch.__class__
sys.exit()
# get the sod parameters
dens_left = runparams.getParam("sod.dens_left")
dens_right = runparams.getParam("sod.dens_right")
u_left = runparams.getParam("sod.u_left")
u_right = runparams.getParam("sod.u_right")
p_left = runparams.getParam("sod.p_left")
p_right = runparams.getParam("sod.p_right")
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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 = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
gamma = runparams.getParam("eos.gamma")
direction = runparams.getParam("sod.direction")
xctr = 0.5 * (xmin + xmax)
yctr = 0.5 * (ymin + ymax)
myg = myPatch.grid
# 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 pressue 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.
if direction == "x":
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if myg.x[i] <= xctr:
dens[i, j] = dens_left
xmom[i, j] = dens_left * u_left
ymom[i, j] = 0.0
ener[
i,
j] = p_left / (gamma - 1.0) + 0.5 * xmom[i, j] * u_left
else:
dens[i, j] = dens_right
xmom[i, j] = dens_right * u_right
ymom[i, j] = 0.0
ener[i,
j] = p_right / (gamma - 1.0) + 0.5 * xmom[i,
j] * u_right
j += 1
i += 1
else:
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if myg.y[j] <= yctr:
dens[i, j] = dens_left
xmom[i, j] = 0.0
ymom[i, j] = dens_left * u_left
ener[
i,
j] = p_left / (gamma - 1.0) + 0.5 * ymom[i, j] * u_left
else:
dens[i, j] = dens_right
xmom[i, j] = 0.0
ymom[i, j] = dens_right * u_right
ener[i,
j] = p_right / (gamma - 1.0) + 0.5 * ymom[i,
j] * u_right
j += 1
i += 1
def initData(myPatch):
""" initialize the bubble problem """
msg.bold("initializing the bubble problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in bubble.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("energy")
gamma = runparams.getParam("eos.gamma")
grav = runparams.getParam("compressible.grav")
scale_height = runparams.getParam("bubble.scale_height")
dens_base = runparams.getParam("bubble.dens_base")
dens_cutoff = runparams.getParam("bubble.dens_cutoff")
x_pert = runparams.getParam("bubble.x_pert")
y_pert = runparams.getParam("bubble.y_pert")
r_pert = runparams.getParam("bubble.r_pert")
pert_amplitude_factor = runparams.getParam("bubble.pert_amplitude_factor")
# initialize the components, remember, that ener here is
# rho*eint + 0.5*rho*v**2, where eint is the specific
# internal energy (erg/g)
xmom[:,:] = 0.0
ymom[:,:] = 0.0
dens[:,:] = dens_cutoff
# set the density to be stratified in the y-direction
myg = myPatch.grid
j = myg.jlo
while j <= myg.jhi:
dens[:,j] = max(dens_base*numpy.exp(-myg.y[j]/scale_height),
dens_cutoff)
j += 1
cs2 = scale_height*abs(grav)
# set the energy (P = cs2*dens)
ener[:,:] = cs2*dens[:,:]/(gamma - 1.0) + \
0.5*(xmom[:,:]**2 + ymom[:,:]**2)/dens[:,:]
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
r = numpy.sqrt((myg.x[i] - x_pert)**2 + (myg.y[j] - y_pert)**2)
if (r <= r_pert):
# boost the specific internal energy, keeping the pressure
# constant, by dropping the density
eint = (ener[i,j] -
0.5*(xmom[i,j]**2 - ymom[i,j]**2)/dens[i,j])/dens[i,j]
pres = dens[i,j]*eint*(gamma - 1.0)
eint = eint*pert_amplitude_factor
dens[i,j] = pres/(eint*(gamma - 1.0))
ener[i,j] = dens[i,j]*eint + \
0.5*(xmom[i,j]**2 + ymom[i,j]**2)/dens[i,j]
j += 1
i += 1
def initialize():
"""
initialize the grid and variables for compressible flow
"""
import vars
# setup the grid
nx = runparams.getParam("mesh.nx")
ny = runparams.getParam("mesh.ny")
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
myGrid = patch.grid2d(nx, ny, xmin=xmin, xmax=xmax, ymin=ymin, ymax=ymax, ng=4)
# create the variables
myData = patch.ccData2d(myGrid)
# first figure out the boundary conditions. Note: the action
# can depend on the variable (for reflecting BCs)
xlb_type = runparams.getParam("mesh.xlboundary")
xrb_type = runparams.getParam("mesh.xrboundary")
ylb_type = runparams.getParam("mesh.ylboundary")
yrb_type = runparams.getParam("mesh.yrboundary")
bcObj = patch.bcObject(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type)
# density and energy
myData.registerVar("density", bcObj)
myData.registerVar("energy", bcObj)
# for velocity, if we are reflecting, we need odd reflection
# in the normal direction.
# x-momentum -- if we are reflecting in x, then we need to
# reflect odd
bcObj_xodd = patch.bcObject(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type, oddReflectDir="x")
myData.registerVar("x-momentum", bcObj_xodd)
# y-momentum -- if we are reflecting in y, then we need to
# reflect odd
bcObj_yodd = patch.bcObject(xlb=xlb_type, xrb=xrb_type, ylb=ylb_type, yrb=yrb_type, oddReflectDir="y")
myData.registerVar("y-momentum", bcObj_yodd)
# store the EOS gamma as an auxillary quantity so we can have a
# self-contained object stored in output files to make plots
gamma = runparams.getParam("eos.gamma")
myData.setAux("gamma", gamma)
myData.create()
vars.idens = myData.vars.index("density")
vars.ixmom = myData.vars.index("x-momentum")
vars.iymom = myData.vars.index("y-momentum")
vars.iener = myData.vars.index("energy")
print myData
return myGrid, myData
# initialize the data
exec 'from ' + solverName + '.problems import *'
exec problemName + '.initData(myData)'
#-----------------------------------------------------------------------------
# pre-evolve
#-----------------------------------------------------------------------------
solver.preevolve(myData)
#-----------------------------------------------------------------------------
# evolve
#-----------------------------------------------------------------------------
tmax = runparams.getParam("driver.tmax")
max_steps = runparams.getParam("driver.max_steps")
init_tstep_factor = runparams.getParam("driver.init_tstep_factor")
max_dt_change = runparams.getParam("driver.max_dt_change")
fix_dt = runparams.getParam("driver.fix_dt")
pylab.ion()
n = 0
myData.t = 0.0
# output the 0th data
basename = runparams.getParam("io.basename")
myData.write(basename + "%4.4d" % (n))
def initData(myPatch):
""" initialize the sedov problem """
msg.bold("initializing the sedov problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in sedov.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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
E_sedov = 1.0
r_init = runparams.getParam("sedov.r_init")
gamma = runparams.getParam("eos.gamma")
pi = 3.14159
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
xctr = 0.5*(xmin + xmax)
yctr = 0.5*(ymin + ymax)
# initialize the pressure by putting the explosion energy into a
# volume of constant pressure. Then compute the energy in a zone
# from this.
nsub = 4
i = myPatch.grid.ilo
while i <= myPatch.grid.ihi:
j = myPatch.grid.jlo
while j <= myPatch.grid.jhi:
dist = numpy.sqrt((myPatch.grid.x[i] - xctr)**2 +
(myPatch.grid.y[j] - yctr)**2)
if (dist < 2.0*r_init):
pzone = 0.0
ii = 0
while ii < nsub:
jj = 0
while jj < nsub:
xsub = myPatch.grid.xl[i] + (myPatch.grid.dx/nsub)*(ii + 0.5)
ysub = myPatch.grid.yl[j] + (myPatch.grid.dy/nsub)*(jj + 0.5)
dist = numpy.sqrt((xsub - xctr)**2 + \
(ysub - yctr)**2)
if dist <= r_init:
p = (gamma - 1.0)*E_sedov/(pi*r_init*r_init)
else:
p = 1.e-5
pzone += p
jj += 1
ii += 1
p = pzone/(nsub*nsub)
else:
p = 1.e-5
ener[i,j] = p/(gamma - 1.0)
j += 1
i += 1
def initialize():
"""
initialize the grid and variables for compressible flow
"""
import vars
# setup the grid
nx = runparams.getParam("mesh.nx")
ny = runparams.getParam("mesh.ny")
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
myGrid = patch.grid2d(nx,
ny,
xmin=xmin,
xmax=xmax,
ymin=ymin,
ymax=ymax,
ng=4)
# create the variables
myData = patch.ccData2d(myGrid)
# first figure out the boundary conditions. Note: the action
# can depend on the variable (for reflecting BCs)
xlb_type = runparams.getParam("mesh.xlboundary")
xrb_type = runparams.getParam("mesh.xrboundary")
ylb_type = runparams.getParam("mesh.ylboundary")
yrb_type = runparams.getParam("mesh.yrboundary")
bcObj = patch.bcObject(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type)
# density and energy
myData.registerVar("density", bcObj)
myData.registerVar("energy", bcObj)
# for velocity, if we are reflecting, we need odd reflection
# in the normal direction.
# x-momentum -- if we are reflecting in x, then we need to
# reflect odd
bcObj_xodd = patch.bcObject(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
oddReflectDir="x")
myData.registerVar("x-momentum", bcObj_xodd)
# y-momentum -- if we are reflecting in y, then we need to
# reflect odd
bcObj_yodd = patch.bcObject(xlb=xlb_type,
xrb=xrb_type,
ylb=ylb_type,
yrb=yrb_type,
oddReflectDir="y")
myData.registerVar("y-momentum", bcObj_yodd)
# store the EOS gamma as an auxillary quantity so we can have a
# self-contained object stored in output files to make plots
gamma = runparams.getParam("eos.gamma")
myData.setAux("gamma", gamma)
myData.create()
vars.idens = myData.vars.index("density")
vars.ixmom = myData.vars.index("x-momentum")
vars.iymom = myData.vars.index("y-momentum")
vars.iener = myData.vars.index("energy")
print myData
return myGrid, myData
def initData(myPatch):
""" initialize the sedov problem """
msg.bold("initializing the sedov problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in sedov.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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
E_sedov = 1.0
r_init = runparams.getParam("sedov.r_init")
gamma = runparams.getParam("eos.gamma")
pi = 3.14159
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
xctr = 0.5 * (xmin + xmax)
yctr = 0.5 * (ymin + ymax)
# initialize the pressure by putting the explosion energy into a
# volume of constant pressure. Then compute the energy in a zone
# from this.
nsub = 4
i = myPatch.grid.ilo
while i <= myPatch.grid.ihi:
j = myPatch.grid.jlo
while j <= myPatch.grid.jhi:
dist = numpy.sqrt((myPatch.grid.x[i] - xctr)**2 +
(myPatch.grid.y[j] - yctr)**2)
if (dist < 2.0 * r_init):
pzone = 0.0
ii = 0
while ii < nsub:
jj = 0
while jj < nsub:
xsub = myPatch.grid.xl[i] + (myPatch.grid.dx /
nsub) * (ii + 0.5)
ysub = myPatch.grid.yl[j] + (myPatch.grid.dy /
nsub) * (jj + 0.5)
dist = numpy.sqrt((xsub - xctr)**2 + \
(ysub - yctr)**2)
if dist <= r_init:
p = (gamma - 1.0) * E_sedov / (pi * r_init *
r_init)
else:
p = 1.e-5
pzone += p
jj += 1
ii += 1
p = pzone / (nsub * nsub)
else:
p = 1.e-5
ener[i, j] = p / (gamma - 1.0)
j += 1
i += 1
def initData(myPatch):
""" initialize the quadrant problem """
msg.bold("initializing the quadrant problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in quad.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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 = runparams.getParam("quadrant.rho1")
u1 = runparams.getParam("quadrant.u1")
v1 = runparams.getParam("quadrant.v1")
p1 = runparams.getParam("quadrant.p1")
r2 = runparams.getParam("quadrant.rho2")
u2 = runparams.getParam("quadrant.u2")
v2 = runparams.getParam("quadrant.v2")
p2 = runparams.getParam("quadrant.p2")
r3 = runparams.getParam("quadrant.rho3")
u3 = runparams.getParam("quadrant.u3")
v3 = runparams.getParam("quadrant.v3")
p3 = runparams.getParam("quadrant.p3")
r4 = runparams.getParam("quadrant.rho4")
u4 = runparams.getParam("quadrant.u4")
v4 = runparams.getParam("quadrant.v4")
p4 = runparams.getParam("quadrant.p4")
cx = runparams.getParam("quadrant.cx")
cy = runparams.getParam("quadrant.cy")
gamma = runparams.getParam("eos.gamma")
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
# 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 pressue 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 = myPatch.grid
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
if (myg.x[i] >= cx and myg.y[j] >= cy):
# quadrant 1
dens[i,j] = r1
xmom[i,j] = r1*u1
ymom[i,j] = r1*v1
ener[i,j] = p1/(gamma - 1.0) + 0.5*r1*(u1*u1 + v1*v1)
elif (myg.x[i] < cx and myg.y[j] >= cy):
# quadrant 2
dens[i,j] = r2
xmom[i,j] = r2*u2
ymom[i,j] = r2*v2
ener[i,j] = p2/(gamma - 1.0) + 0.5*r2*(u2*u2 + v2*v2)
elif (myg.x[i] < cx and myg.y[j] < cy):
# quadrant 3
dens[i,j] = r3
xmom[i,j] = r3*u3
ymom[i,j] = r3*v3
ener[i,j] = p3/(gamma - 1.0) + 0.5*r3*(u3*u3 + v3*v3)
elif (myg.x[i] >= cx and myg.y[j] < cy):
# quadrant 4
dens[i,j] = r4
xmom[i,j] = r4*u4
ymom[i,j] = r4*v4
ener[i,j] = p4/(gamma - 1.0) + 0.5*r4*(u4*u4 + v4*v4)
j += 1
i += 1
def initData(myPatch):
""" initialize the bubble problem """
msg.bold("initializing the bubble problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in bubble.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("energy")
gamma = runparams.getParam("eos.gamma")
grav = runparams.getParam("compressible.grav")
scale_height = runparams.getParam("bubble.scale_height")
dens_base = runparams.getParam("bubble.dens_base")
dens_cutoff = runparams.getParam("bubble.dens_cutoff")
x_pert = runparams.getParam("bubble.x_pert")
y_pert = runparams.getParam("bubble.y_pert")
r_pert = runparams.getParam("bubble.r_pert")
pert_amplitude_factor = runparams.getParam("bubble.pert_amplitude_factor")
# initialize the components, remember, that ener here is
# rho*eint + 0.5*rho*v**2, where eint is the specific
# internal energy (erg/g)
xmom[:, :] = 0.0
ymom[:, :] = 0.0
dens[:, :] = dens_cutoff
# set the density to be stratified in the y-direction
myg = myPatch.grid
j = myg.jlo
while j <= myg.jhi:
dens[:, j] = max(dens_base * numpy.exp(-myg.y[j] / scale_height),
dens_cutoff)
j += 1
cs2 = scale_height * abs(grav)
# set the energy (P = cs2*dens)
ener[:,:] = cs2*dens[:,:]/(gamma - 1.0) + \
0.5*(xmom[:,:]**2 + ymom[:,:]**2)/dens[:,:]
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
r = numpy.sqrt((myg.x[i] - x_pert)**2 + (myg.y[j] - y_pert)**2)
if (r <= r_pert):
# boost the specific internal energy, keeping the pressure
# constant, by dropping the density
eint = (ener[i, j] - 0.5 *
(xmom[i, j]**2 - ymom[i, j]**2) / dens[i, j]) / dens[i,
j]
pres = dens[i, j] * eint * (gamma - 1.0)
eint = eint * pert_amplitude_factor
dens[i, j] = pres / (eint * (gamma - 1.0))
ener[i,j] = dens[i,j]*eint + \
0.5*(xmom[i,j]**2 + ymom[i,j]**2)/dens[i,j]
j += 1
i += 1
def unsplitFluxes(myData, 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
grav is the gravitational acceleration in the y-direction
"""
pf = profile.timer("unsplitFluxes")
pf.begin()
myg = myData.grid
#=========================================================================
# compute the primitive variables
#=========================================================================
# Q = (rho, u, v, p)
dens = myData.getVarPtr("density")
xmom = myData.getVarPtr("x-momentum")
ymom = myData.getVarPtr("y-momentum")
ener = myData.getVarPtr("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(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 = runparams.getParam("compressible.use_flattening")
if (use_flattening):
smallp = 1.e-10
delta = runparams.getParam("compressible.delta")
z0 = runparams.getParam("compressible.z0")
z1 = runparams.getParam("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
#=========================================================================
# x-direction
#=========================================================================
# monotonized central differences in x-direction
pfa = profile.timer("limiting")
pfa.begin()
limiter = runparams.getParam("compressible.limiter")
if (limiter == 0):
limitFunc = reconstruction_f.nolimit
elif (limiter == 1):
limitFunc = reconstruction_f.limit2
else:
limitFunc = reconstruction_f.limit4
ldelta_r = xi*limitFunc(1, r, myg.qx, myg.qy, myg.ng)
ldelta_u = xi*limitFunc(1, u, myg.qx, myg.qy, myg.ng)
ldelta_v = xi*limitFunc(1, v, myg.qx, myg.qy, myg.ng)
ldelta_p = xi*limitFunc(1, p, myg.qx, myg.qy, myg.ng)
pfa.end()
# left and right primitive variable states
pfb = profile.timer("interfaceStates")
pfb.begin()
gamma = runparams.getParam("eos.gamma")
V_l = numpy.zeros((myg.qx, myg.qy, vars.nvar), dtype=numpy.float64)
V_r = numpy.zeros((myg.qx, myg.qy, vars.nvar), dtype=numpy.float64)
(V_l, V_r) = interface_f.states(1, myg.qx, myg.qy, myg.ng, myg.dx, dt,
vars.nvar,
gamma,
r, u, v, p,
ldelta_r, ldelta_u, ldelta_v, ldelta_p)
pfb.end()
# transform interface states back into conserved variables
U_xl = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
U_xr = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
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(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(V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# y-direction
#=========================================================================
# monotonized central differences in y-direction
pfa.begin()
ldelta_r = xi*limitFunc(2, r, myg.qx, myg.qy, myg.ng)
ldelta_u = xi*limitFunc(2, u, myg.qx, myg.qy, myg.ng)
ldelta_v = xi*limitFunc(2, v, myg.qx, myg.qy, myg.ng)
ldelta_p = xi*limitFunc(2, p, myg.qx, myg.qy, myg.ng)
pfa.end()
# left and right primitive variable states
pfb.begin()
(V_l, V_r) = interface_f.states(2, myg.qx, myg.qy, myg.ng, myg.dy, dt,
vars.nvar,
gamma,
r, u, v, p,
ldelta_r, ldelta_u, ldelta_v, ldelta_p)
pfb.end()
# transform interface states back into conserved variables
U_yl = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
U_yr = numpy.zeros((myg.qx, myg.qy, myData.nvar), dtype=numpy.float64)
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(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(V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# apply source terms
#=========================================================================
grav = runparams.getParam("compressible.grav")
# ymom_xl[i,j] += 0.5*dt*dens[i-1,j]*grav
U_xl[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iymom] += \
0.5*dt*dens[myg.ilo-2:myg.ihi+1,myg.jlo-1:myg.jhi+2]*grav
U_xl[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iener] += \
0.5*dt*ymom[myg.ilo-2:myg.ihi+1,myg.jlo-1:myg.jhi+2]*grav
# ymom_xr[i,j] += 0.5*dt*dens[i,j]*grav
U_xr[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iymom] += \
0.5*dt*dens[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2]*grav
U_xr[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iener] += \
0.5*dt*ymom[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2]*grav
# ymom_yl[i,j] += 0.5*dt*dens[i,j-1]*grav
U_yl[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iymom] += \
0.5*dt*dens[myg.ilo-1:myg.ihi+2,myg.jlo-2:myg.jhi+1]*grav
U_yl[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iener] += \
0.5*dt*ymom[myg.ilo-1:myg.ihi+2,myg.jlo-2:myg.jhi+1]*grav
# ymom_yr[i,j] += 0.5*dt*dens[i,j]*grav
U_yr[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iymom] += \
0.5*dt*dens[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2]*grav
U_yr[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2,vars.iener] += \
0.5*dt*ymom[myg.ilo-1:myg.ihi+2,myg.jlo-1:myg.jhi+2]*grav
#=========================================================================
# compute transverse fluxes
#=========================================================================
pfc = profile.timer("riemann")
pfc.begin()
riemann = runparams.getParam("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")
F_x = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
gamma, U_xl, U_xr)
F_y = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
gamma, U_yl, U_yr)
pfc.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
"""
pfd = profile.timer("transverse flux addition")
pfd.begin()
# 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[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:] += \
- 0.5*dt/myg.dy * (F_y[myg.ilo-3:myg.ihi+1,myg.jlo-1:myg.jhi+3,:] - \
F_y[myg.ilo-3:myg.ihi+1,myg.jlo-2:myg.jhi+2,:])
# U_xr[i,j,:] = U_xr[i,j,:] - 0.5*dt/dy * (F_y[i,j+1,:] - F_y[i,j,:])
U_xr[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:] += \
- 0.5*dt/myg.dy * (F_y[myg.ilo-2:myg.ihi+2,myg.jlo-1:myg.jhi+3,:] - \
F_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:])
# 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[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:] += \
- 0.5*dt/myg.dx * (F_x[myg.ilo-1:myg.ihi+3,myg.jlo-3:myg.jhi+1,:] - \
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-3:myg.jhi+1,:])
# U_yr[i,j,:] = U_yr[i,j,:] - 0.5*dt/dx * (F_x[i+1,j,:] - F_x[i,j,:])
U_yr[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:] += \
- 0.5*dt/myg.dx * (F_x[myg.ilo-1:myg.ihi+3,myg.jlo-2:myg.jhi+2,:] - \
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,:])
pfd.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
pfc.begin()
F_x = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
gamma, U_xl, U_xr)
F_y = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
gamma, U_yl, U_yr)
pfc.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = runparams.getParam("compressible.cvisc")
(avisco_x, avisco_y) = interface_f.artificial_viscosity( \
myg.qx, myg.qy, myg.ng, myg.dx, myg.dy, \
cvisc, u, v)
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.idens] += \
avisco_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(dens[myg.ilo-3:myg.ihi+1,myg.jlo-2:myg.jhi+2] - \
dens[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.ixmom] += \
avisco_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(xmom[myg.ilo-3:myg.ihi+1,myg.jlo-2:myg.jhi+2] - \
xmom[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.iymom] += \
avisco_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(ymom[myg.ilo-3:myg.ihi+1,myg.jlo-2:myg.jhi+2] - \
ymom[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.iener] += \
avisco_x[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(ener[myg.ilo-3:myg.ihi+1,myg.jlo-2:myg.jhi+2] - \
ener[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.idens] += \
avisco_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(dens[myg.ilo-2:myg.ihi+2,myg.jlo-3:myg.jhi+1] - \
dens[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.ixmom] += \
avisco_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(xmom[myg.ilo-2:myg.ihi+2,myg.jlo-3:myg.jhi+1] - \
xmom[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.iymom] += \
avisco_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(ymom[myg.ilo-2:myg.ihi+2,myg.jlo-3:myg.jhi+1] - \
ymom[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
F_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2,vars.iener] += \
avisco_y[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2]* \
(ener[myg.ilo-2:myg.ihi+2,myg.jlo-3:myg.jhi+1] - \
ener[myg.ilo-2:myg.ihi+2,myg.jlo-2:myg.jhi+2])
pf.end()
return F_x, F_y
def initData(myPatch):
""" initialize the Rayleigh-Taylor instability problem """
msg.bold("initializing the Rayleigh-Taylor instability problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print "ERROR: patch invalid in raytay.py"
print myPatch.__class__
sys.exit()
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("energy")
# get the other input parameters for the problem
gamma = runparams.getParam("eos.gamma")
grav = runparams.getParam("compressible.grav")
dens_up = runparams.getParam("raytay.dens_up")
dens_down = runparams.getParam("raytay.dens_down")
A = runparams.getParam("raytay.pert_amplitude_factor")
p0 = runparams.getParam("raytay.pressure_bottom")
sigma = runparams.getParam("raytay.sigma")
# get the grid parameters
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
yctr = 0.5 * (ymin + ymax)
# initialize the components, remember, that ener here is
# rho*eint + 0.5*rho*v**2, where eint is the specific
# internal energy (erg/g)
xmom[:, :] = 0.0
ymom[:, :] = 0.0
dens[:, :] = 0.0
Lx = xmax - xmin
# set the density and energy to be stratified in the y-direction
myg = myPatch.grid
j = myg.jlo
while j <= myg.jhi:
if myg.y[j] < yctr:
dens[:, j] = dens_down
pres = dens_down * grav * myg.y[j] + p0
ener[:, j] = pres / (
gamma - 1.0) #+ 0.5*(xmom[:,j]**2 + ymom[:,j]**2)/dens_down
else:
dens[:, j] = dens_up
pres = p0 + dens_down * grav * yctr + dens_up * grav * (myg.y[j] -
yctr)
ener[:, j] = pres / (
gamma - 1.0) #+ 0.5*(xmom[:,j]**2 + ymom[:,j]**2)/dens_up
j += 1
i = myg.ilo
while i <= myg.ihi:
j = myg.jlo
while j <= myg.jhi:
v_pert = A * numpy.sin(
2.0 * numpy.pi * myg.x[i] / Lx) * numpy.exp(-(
(myg.y[j] - yctr) / sigma)**2)
# momentum
ymom[i, j] = dens[i, j] * v_pert
# internal energy
ener[i, j] += 0.5 * (xmom[i, j]**2 - ymom[i, j]**2) / dens[i, j]
j += 1
i += 1
def initData(myPatch):
""" initialize the Kelvin-Helmholtz problem """
msg.bold("initializing the sedov problem...")
# make sure that we are passed a valid patch object
if not isinstance(myPatch, patch.ccData2d):
print myPatch.__class__
msg.fail("ERROR: patch invalid in sedov.py")
# get the density, momenta, and energy as separate variables
dens = myPatch.getVarPtr("density")
xmom = myPatch.getVarPtr("x-momentum")
ymom = myPatch.getVarPtr("y-momentum")
ener = myPatch.getVarPtr("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
E_sedov = 1.0
rho_1 = runparams.getParam("kh.rho_1")
v_1 = runparams.getParam("kh.v_1")
rho_2 = runparams.getParam("kh.rho_2")
v_2 = runparams.getParam("kh.v_2")
gamma = runparams.getParam("eos.gamma")
xmin = runparams.getParam("mesh.xmin")
xmax = runparams.getParam("mesh.xmax")
ymin = runparams.getParam("mesh.ymin")
ymax = runparams.getParam("mesh.ymax")
xctr = 0.5*(xmin + xmax)
yctr = 0.5*(ymin + ymax)
L_x = xmax - xmin
# initialize the pressure by putting the explosion energy into a
# volume of constant pressure. Then compute the energy in a zone
# from this.
nsub = 4
i = myPatch.grid.ilo
while i <= myPatch.grid.ihi:
j = myPatch.grid.jlo
while j <= myPatch.grid.jhi:
if myPatch.grid.y[j] < yctr + 0.01*math.sin(10.0*math.pi*myPatch.grid.x[i]/L_x):
# lower half
dens[i,j] = rho_1
xmom[i,j] = rho_1*v_1
ymom[i,j] = 0.0
else:
# upper half
dens[i,j] = rho_2
xmom[i,j] = rho_2*v_2
ymom[i,j] = 0.0
p = 1.0
ener[i,j] = p/(gamma - 1.0) + 0.5*(xmom[i,j]**2 + ymom[i,j]**2)/dens[i,j]
j += 1
i += 1