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 evolve(my_data, dt):
pf = profile.timer("evolve")
pf.begin()
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.rp.get_param("compressible.grav")
myg = my_data.grid
Flux_x, Flux_y = unsplitFluxes(my_data, dt)
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 evolve(my_data, dt):
pf = profile.timer("evolve")
pf.begin()
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.rp.get_param("compressible.grav")
myg = my_data.grid
Flux_x, Flux_y = unsplitFluxes(my_data, dt)
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 unsplitFluxes(my_data, 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 = my_data.grid
rp = my_data.rp
#=========================================================================
# 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(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
#=========================================================================
# x-direction
#=========================================================================
# monotonized central differences in x-direction
pfa = profile.timer("limiting")
pfa.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_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 = rp.get_param("eos.gamma")
V_l = myg.scratch_array(vars.nvar)
V_r = myg.scratch_array(vars.nvar)
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 = 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(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 = 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(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 = rp.get_param("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 = 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")
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 = rp.get_param("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 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
directory).
[runtime parameters] override any of the runtime defaults of
parameters specified in the inputs file. For instance, to turn
off runtime visualization, add:
vis.dovis=0
to the end of the commandline.
"""
msg.bold('pyro ...')
pf = profile.timer("main")
pf.begin()
#-----------------------------------------------------------------------------
# command line arguments / solver setup
#-----------------------------------------------------------------------------
# parse the runtime arguments. We specify a solver (which we import
# locally under the namespace 'solver', the problem name, and the
# input file name
if len(sys.argv) == 1:
print usage
sys.exit(2)
import time
from util import profile
from util import runparams
import os
from util import msg
usage = """
usage:
./pyro [options] <solver name> <problem name> <input file>
"""
msg.bold('pyro ...')
pf = profile.timer("main")
pf.begin()
#-----------------------------------------------------------------------------
# command line arguments / solver setup
#-----------------------------------------------------------------------------
# parse the runtime arguments. We specify a solver (which we import
# locally under the namespace 'solver', the problem name, and the
# input file name
if len(sys.argv) == 1:
print usage
sys.exit(2)
