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
def user(bcName, bcEdge, variable, my_data):
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
if (bcName == "hse"):
if (bcEdge == "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(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(pres_below)
ener[:, j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
msg.fail("error: variable not defined")
elif (bcEdge == "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(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(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" % (bcName))
def user(bcName, bcEdge, variable, my_data):
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
if (bcName == "hse"):
if (bcEdge == "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(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(pres_below)
ener[:,j] = rhoe + ke_base
pres_base = pres_below.copy()
j -= 1
else:
msg.fail("error: variable not defined")
elif (bcEdge == "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(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(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" % (bcName) )