def unsplitFluxes(my_data, my_aux, rp, vars, solid, tc, 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
The runtime parameter grav is assumed to be the gravitational
acceleration in the y-direction
Parameters
----------
my_data : CellCenterData2d object
The data object containing the grid and advective scalar that
we are advecting.
rp : RuntimeParameters object
The runtime parameters for the simulation
vars : Variables object
The Variables object that tells us which indices refer to which
variables
tc : TimerCollection object
The timers we are using to profile
dt : float
The timestep we are advancing through.
Returns
-------
out : ndarray, ndarray
The fluxes on the x- and y-interfaces
"""
tm_flux = tc.timer("unsplitFluxes")
tm_flux.begin()
myg = my_data.grid
gamma = rp.get_param("eos.gamma")
#=========================================================================
# 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(gamma, dens, e)
smallp = 1.e-10
p.d = p.d.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.d, u.d, myg.qx, myg.qy, myg.ng, smallp, delta, z0, z1)
xi_y = reconstruction_f.flatten(2, p.d, v.d, myg.qx, myg.qy, myg.ng, smallp, delta, z0, z1)
xi = reconstruction_f.flatten_multid(xi_x, xi_y, p.d, myg.qx, myg.qy, myg.ng)
else:
xi = 1.0
# monotonized central differences in x-direction
tm_limit = tc.timer("limiting")
tm_limit.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_rx = xi*limitFunc(1, r.d, myg.qx, myg.qy, myg.ng)
ldelta_ux = xi*limitFunc(1, u.d, myg.qx, myg.qy, myg.ng)
ldelta_vx = xi*limitFunc(1, v.d, myg.qx, myg.qy, myg.ng)
ldelta_px = xi*limitFunc(1, p.d, myg.qx, myg.qy, myg.ng)
# monotonized central differences in y-direction
ldelta_ry = xi*limitFunc(2, r.d, myg.qx, myg.qy, myg.ng)
ldelta_uy = xi*limitFunc(2, u.d, myg.qx, myg.qy, myg.ng)
ldelta_vy = xi*limitFunc(2, v.d, myg.qx, myg.qy, myg.ng)
ldelta_py = xi*limitFunc(2, p.d, myg.qx, myg.qy, myg.ng)
tm_limit.end()
#=========================================================================
# x-direction
#=========================================================================
# left and right primitive variable states
tm_states = tc.timer("interfaceStates")
tm_states.begin()
V_l, V_r = interface_f.states(1, myg.qx, myg.qy, myg.ng, myg.dx, dt,
vars.nvar,
gamma,
r.d, u.d, v.d, p.d,
ldelta_rx, ldelta_ux, ldelta_vx, ldelta_px)
tm_states.end()
# transform interface states back into conserved variables
U_xl = myg.scratch_array(vars.nvar)
U_xr = myg.scratch_array(vars.nvar)
U_xl.d[:,:,vars.idens] = V_l[:,:,vars.irho]
U_xl.d[:,:,vars.ixmom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iu]
U_xl.d[:,:,vars.iymom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iv]
U_xl.d[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_xr.d[:,:,vars.idens] = V_r[:,:,vars.irho]
U_xr.d[:,:,vars.ixmom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iu]
U_xr.d[:,:,vars.iymom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iv]
U_xr.d[:,:,vars.iener] = eos.rhoe(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# y-direction
#=========================================================================
# left and right primitive variable states
tm_states.begin()
V_l, V_r = interface_f.states(2, myg.qx, myg.qy, myg.ng, myg.dy, dt,
vars.nvar,
gamma,
r.d, u.d, v.d, p.d,
ldelta_ry, ldelta_uy, ldelta_vy, ldelta_py)
tm_states.end()
# transform interface states back into conserved variables
U_yl = myg.scratch_array(vars.nvar)
U_yr = myg.scratch_array(vars.nvar)
U_yl.d[:,:,vars.idens] = V_l[:,:,vars.irho]
U_yl.d[:,:,vars.ixmom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iu]
U_yl.d[:,:,vars.iymom] = V_l[:,:,vars.irho]*V_l[:,:,vars.iv]
U_yl.d[:,:,vars.iener] = eos.rhoe(gamma, V_l[:,:,vars.ip]) + \
0.5*V_l[:,:,vars.irho]*(V_l[:,:,vars.iu]**2 + V_l[:,:,vars.iv]**2)
U_yr.d[:,:,vars.idens] = V_r[:,:,vars.irho]
U_yr.d[:,:,vars.ixmom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iu]
U_yr.d[:,:,vars.iymom] = V_r[:,:,vars.irho]*V_r[:,:,vars.iv]
U_yr.d[:,:,vars.iener] = eos.rhoe(gamma, 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_src = my_aux.get_var("ymom_src")
ymom_src.v()[:,:] = dens.v()*grav
my_aux.fill_BC("ymom_src")
E_src = my_aux.get_var("E_src")
E_src.v()[:,:] = ymom.v()*grav
my_aux.fill_BC("E_src")
# ymom_xl[i,j] += 0.5*dt*dens[i-1,j]*grav
U_xl.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.ip(-1, buf=1)
U_xl.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.ip(-1, buf=1)
# ymom_xr[i,j] += 0.5*dt*dens[i,j]*grav
U_xr.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.v(buf=1)
U_xr.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.v(buf=1)
# ymom_yl[i,j] += 0.5*dt*dens[i,j-1]*grav
U_yl.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.jp(-1, buf=1)
U_yl.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.jp(-1, buf=1)
# ymom_yr[i,j] += 0.5*dt*dens[i,j]*grav
U_yr.v(buf=1, n=vars.iymom)[:,:] += 0.5*dt*ymom_src.v(buf=1)
U_yr.v(buf=1, n=vars.iener)[:,:] += 0.5*dt*E_src.v(buf=1)
#=========================================================================
# compute transverse fluxes
#=========================================================================
tm_riem = tc.timer("riemann")
tm_riem.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")
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.xl, solid.xr,
gamma, U_xl.d, U_xr.d)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.yl, solid.yr,
gamma, U_yl.d, U_yr.d)
F_x = patch.ArrayIndexer(d=_fx, grid=myg)
F_y = patch.ArrayIndexer(d=_fy, grid=myg)
tm_riem.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
"""
tm_transverse = tc.timer("transverse flux addition")
tm_transverse.begin()
dtdx = dt/myg.dx
dtdy = dt/myg.dy
b = (2,1)
for n in range(vars.nvar):
# 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.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.ip_jp(-1, 1, buf=b, n=n) - F_y.ip(-1, buf=b, n=n))
# U_xr[i,j,:] = U_xr[i,j,:] - 0.5*dt/dy * (F_y[i,j+1,:] - F_y[i,j,:])
U_xr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.jp(1, buf=b, n=n) - F_y.v(buf=b, n=n))
# 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.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip_jp(1, -1, buf=b, n=n) - F_x.jp(-1, buf=b, n=n))
# U_yr[i,j,:] = U_yr[i,j,:] - 0.5*dt/dx * (F_x[i+1,j,:] - F_x[i,j,:])
U_yr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip(1, buf=b, n=n) - F_x.v(buf=b, n=n))
tm_transverse.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
tm_riem.begin()
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.xl, solid.xr,
gamma, U_xl.d, U_xr.d)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng,
vars.nvar, vars.idens, vars.ixmom, vars.iymom, vars.iener,
solid.yl, solid.yr,
gamma, U_yl.d, U_yr.d)
F_x = patch.ArrayIndexer(d=_fx, grid=myg)
F_y = patch.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = rp.get_param("compressible.cvisc")
_ax, _ay = interface_f.artificial_viscosity(
myg.qx, myg.qy, myg.ng, myg.dx, myg.dy,
cvisc, u.d, v.d)
avisco_x = patch.ArrayIndexer(d=_ax, grid=myg)
avisco_y = patch.ArrayIndexer(d=_ay, grid=myg)
b = (2,1)
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
F_x.v(buf=b, n=vars.idens)[:,:] += \
avisco_x.v(buf=b)*(dens.ip(-1, buf=b) - dens.v(buf=b))
F_x.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_x.v(buf=b)*(xmom.ip(-1, buf=b) - xmom.v(buf=b))
F_x.v(buf=b, n=vars.iymom)[:,:] += \
avisco_x.v(buf=b)*(ymom.ip(-1, buf=b) - ymom.v(buf=b))
F_x.v(buf=b, n=vars.iener)[:,:] += \
avisco_x.v(buf=b)*(ener.ip(-1, buf=b) - ener.v(buf=b))
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y.v(buf=b, n=vars.idens)[:,:] += \
avisco_y.v(buf=b)*(dens.jp(-1, buf=b) - dens.v(buf=b))
F_y.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_y.v(buf=b)*(xmom.jp(-1, buf=b) - xmom.v(buf=b))
F_y.v(buf=b, n=vars.iymom)[:,:] += \
avisco_y.v(buf=b)*(ymom.jp(-1, buf=b) - ymom.v(buf=b))
F_y.v(buf=b, n=vars.iener)[:,:] += \
avisco_y.v(buf=b)*(ener.jp(-1, buf=b) - ener.v(buf=b))
tm_flux.end()
return F_x, F_y
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 fluxes(my_data, rp, vars, solid, tc):
"""
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
Parameters
----------
my_data : CellCenterData2d object
The data object containing the grid and advective scalar that
we are advecting.
rp : RuntimeParameters object
The runtime parameters for the simulation
vars : Variables object
The Variables object that tells us which indices refer to which
variables
tc : TimerCollection object
The timers we are using to profile
Returns
-------
out : ndarray, ndarray
The fluxes on the x- and y-interfaces
"""
tm_flux = tc.timer("unsplitFluxes")
tm_flux.begin()
myg = my_data.grid
gamma = rp.get_param("eos.gamma")
#=========================================================================
# 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(gamma, 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
# monotonized central differences in x-direction
tm_limit = tc.timer("limiting")
tm_limit.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_rx = xi * limitFunc(1, r, myg.qx, myg.qy, myg.ng)
_ldelta_ux = xi * limitFunc(1, u, myg.qx, myg.qy, myg.ng)
_ldelta_vx = xi * limitFunc(1, v, myg.qx, myg.qy, myg.ng)
_ldelta_px = xi * limitFunc(1, p, myg.qx, myg.qy, myg.ng)
# wrap these in ArrayIndexer objects
ldelta_rx = ai.ArrayIndexer(d=_ldelta_rx, grid=myg)
ldelta_ux = ai.ArrayIndexer(d=_ldelta_ux, grid=myg)
ldelta_vx = ai.ArrayIndexer(d=_ldelta_vx, grid=myg)
ldelta_px = ai.ArrayIndexer(d=_ldelta_px, grid=myg)
# monotonized central differences in y-direction
_ldelta_ry = xi * limitFunc(2, r, myg.qx, myg.qy, myg.ng)
_ldelta_uy = xi * limitFunc(2, u, myg.qx, myg.qy, myg.ng)
_ldelta_vy = xi * limitFunc(2, v, myg.qx, myg.qy, myg.ng)
_ldelta_py = xi * limitFunc(2, p, myg.qx, myg.qy, myg.ng)
ldelta_ry = ai.ArrayIndexer(d=_ldelta_ry, grid=myg)
ldelta_uy = ai.ArrayIndexer(d=_ldelta_uy, grid=myg)
ldelta_vy = ai.ArrayIndexer(d=_ldelta_vy, grid=myg)
ldelta_py = ai.ArrayIndexer(d=_ldelta_py, grid=myg)
tm_limit.end()
#=========================================================================
# x-direction
#=========================================================================
# left and right primitive variable states
tm_states = tc.timer("interfaceStates")
tm_states.begin()
V_l = myg.scratch_array(vars.nvar)
V_r = myg.scratch_array(vars.nvar)
V_l.ip(1, n=vars.irho, buf=2)[:, :] = r.v(buf=2) + 0.5 * ldelta_rx.v(buf=2)
V_r.v(n=vars.irho, buf=2)[:, :] = r.v(buf=2) - 0.5 * ldelta_rx.v(buf=2)
V_l.ip(1, n=vars.iu, buf=2)[:, :] = u.v(buf=2) + 0.5 * ldelta_ux.v(buf=2)
V_r.v(n=vars.iu, buf=2)[:, :] = u.v(buf=2) - 0.5 * ldelta_ux.v(buf=2)
V_l.ip(1, n=vars.iv, buf=2)[:, :] = v.v(buf=2) + 0.5 * ldelta_vx.v(buf=2)
V_r.v(n=vars.iv, buf=2)[:, :] = v.v(buf=2) - 0.5 * ldelta_vx.v(buf=2)
V_l.ip(1, n=vars.ip, buf=2)[:, :] = p.v(buf=2) + 0.5 * ldelta_px.v(buf=2)
V_r.v(n=vars.ip, buf=2)[:, :] = p.v(buf=2) - 0.5 * ldelta_px.v(buf=2)
tm_states.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(gamma, 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(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# y-direction
#=========================================================================
# left and right primitive variable states
tm_states.begin()
V_l.jp(1, n=vars.irho, buf=2)[:, :] = r.v(buf=2) + 0.5 * ldelta_ry.v(buf=2)
V_r.v(n=vars.irho, buf=2)[:, :] = r.v(buf=2) - 0.5 * ldelta_ry.v(buf=2)
V_l.jp(1, n=vars.iu, buf=2)[:, :] = u.v(buf=2) + 0.5 * ldelta_uy.v(buf=2)
V_r.v(n=vars.iu, buf=2)[:, :] = u.v(buf=2) - 0.5 * ldelta_uy.v(buf=2)
V_l.jp(1, n=vars.iv, buf=2)[:, :] = v.v(buf=2) + 0.5 * ldelta_vy.v(buf=2)
V_r.v(n=vars.iv, buf=2)[:, :] = v.v(buf=2) - 0.5 * ldelta_vy.v(buf=2)
V_l.jp(1, n=vars.ip, buf=2)[:, :] = p.v(buf=2) + 0.5 * ldelta_py.v(buf=2)
V_r.v(n=vars.ip, buf=2)[:, :] = p.v(buf=2) - 0.5 * ldelta_py.v(buf=2)
tm_states.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(gamma, 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(gamma, V_r[:,:,vars.ip]) + \
0.5*V_r[:,:,vars.irho]*(V_r[:,:,vars.iu]**2 + V_r[:,:,vars.iv]**2)
#=========================================================================
# construct the fluxes normal to the interfaces
#=========================================================================
tm_riem = tc.timer("Riemann")
tm_riem.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")
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng, vars.nvar, vars.idens,
vars.ixmom, vars.iymom, vars.iener, solid.xl, solid.xr,
gamma, U_xl, U_xr)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng, vars.nvar, vars.idens,
vars.ixmom, vars.iymom, vars.iener, solid.yl, solid.yr,
gamma, U_yl, U_yr)
F_x = ai.ArrayIndexer(d=_fx, grid=myg)
F_y = ai.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = rp.get_param("compressible.cvisc")
_ax, _ay = interface_f.artificial_viscosity(myg.qx, myg.qy, myg.ng, myg.dx,
myg.dy, cvisc, u, v)
avisco_x = ai.ArrayIndexer(d=_ax, grid=myg)
avisco_y = ai.ArrayIndexer(d=_ay, grid=myg)
b = (2, 1)
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
F_x.v(buf=b, n=vars.idens)[:,:] += \
avisco_x.v(buf=b)*(dens.ip(-1, buf=b) - dens.v(buf=b))
F_x.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_x.v(buf=b)*(xmom.ip(-1, buf=b) - xmom.v(buf=b))
F_x.v(buf=b, n=vars.iymom)[:,:] += \
avisco_x.v(buf=b)*(ymom.ip(-1, buf=b) - ymom.v(buf=b))
F_x.v(buf=b, n=vars.iener)[:,:] += \
avisco_x.v(buf=b)*(ener.ip(-1, buf=b) - ener.v(buf=b))
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y.v(buf=b, n=vars.idens)[:,:] += \
avisco_y.v(buf=b)*(dens.jp(-1, buf=b) - dens.v(buf=b))
F_y.v(buf=b, n=vars.ixmom)[:,:] += \
avisco_y.v(buf=b)*(xmom.jp(-1, buf=b) - xmom.v(buf=b))
F_y.v(buf=b, n=vars.iymom)[:,:] += \
avisco_y.v(buf=b)*(ymom.jp(-1, buf=b) - ymom.v(buf=b))
F_y.v(buf=b, n=vars.iener)[:,:] += \
avisco_y.v(buf=b)*(ener.jp(-1, buf=b) - ener.v(buf=b))
tm_flux.end()
return F_x, F_y
def unsplit_fluxes(my_data, my_aux, rp, ivars, solid, tc, 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
The runtime parameter grav is assumed to be the gravitational
acceleration in the y-direction
Parameters
----------
my_data : CellCenterData2d object
The data object containing the grid and advective scalar that
we are advecting.
rp : RuntimeParameters object
The runtime parameters for the simulation
vars : Variables object
The Variables object that tells us which indices refer to which
variables
tc : TimerCollection object
The timers we are using to profile
dt : float
The timestep we are advancing through.
Returns
-------
out : ndarray, ndarray
The fluxes on the x- and y-interfaces
"""
tm_flux = tc.timer("unsplitFluxes")
tm_flux.begin()
myg = my_data.grid
gamma = rp.get_param("eos.gamma")
#=========================================================================
# 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, u, v, p, re = my_data.get_var("primitive")
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
# monotonized central differences in x-direction
tm_limit = tc.timer("limiting")
tm_limit.begin()
limiter = rp.get_param("compressible.limiter")
ldelta_rx = xi * reconstruction.limit(r, myg, 1, limiter)
ldelta_ux = xi * reconstruction.limit(u, myg, 1, limiter)
ldelta_vx = xi * reconstruction.limit(v, myg, 1, limiter)
ldelta_px = xi * reconstruction.limit(p, myg, 1, limiter)
ldelta_rex = xi * reconstruction.limit(re, myg, 1, limiter)
# monotonized central differences in y-direction
ldelta_ry = xi * reconstruction.limit(r, myg, 2, limiter)
ldelta_uy = xi * reconstruction.limit(u, myg, 2, limiter)
ldelta_vy = xi * reconstruction.limit(v, myg, 2, limiter)
ldelta_py = xi * reconstruction.limit(p, myg, 2, limiter)
ldelta_rey = xi * reconstruction.limit(re, myg, 2, limiter)
tm_limit.end()
gamcl = 1.4 * np.ones((136, 18), order='F')
gamcr = gamcl
#=========================================================================
# x-direction
#=========================================================================
# left and right primitive variable states
tm_states = tc.timer("interfaceStates")
tm_states.begin()
# r = np.array(r, order = 'F')
# u = np.array(u, order = 'F')
# v = np.array(v, order = 'F')
# p = np.array(p, order = 'F')
# re = np.array(re, order = 'F')
# ldelta_rx = np.array(ldelta_rx, order = 'F')
# ldelta_ux = np.array(ldelta_ux, order = 'F')
# ldelta_vx = np.array(ldelta_vx, order = 'F')
# ldelta_px = np.array(ldelta_px, order = 'F')
# ldelta_rex = np.array(ldelta_rex, order = 'F')
# myg.ng = 5
# ivars.nvar = 5
# V_l, V_r = interface_f.states(1, myg.qx, myg.qy, myg.ng, myg.dx, dt,
# ivars.nvar,
# gamma,
# r, u, v, p, re,
# ldelta_rx, ldelta_ux, ldelta_vx, ldelta_px, ldelta_rex)
# myg.ng = 4
# ivars.nvar = 4
V_l, V_r = interface_f.states(1, myg.qx, myg.qy, myg.ng, myg.dx, dt,
ivars.nvar, gamma, r, u, v, p, ldelta_rx,
ldelta_ux, ldelta_vx, ldelta_px)
# keyboard()
tm_states.end()
# transform interface states back into conserved variables
U_xl = comp.prim_to_cons(V_l, gamma, ivars, myg)
U_xr = comp.prim_to_cons(V_r, gamma, ivars, myg)
#=========================================================================
# y-direction
#=========================================================================
# left and right primitive variable states
tm_states.begin()
# V_l, V_r = interface_f.states(2, myg.qx, myg.qy, myg.ng, myg.dy, dt,
# ivars.nvar,
# gamma,
# r, u, v, p, re,
# ldelta_ry, ldelta_uy, ldelta_vy, ldelta_py, ldelta_rey)
V_l, V_r = interface_f.states(2, myg.qx, myg.qy, myg.ng, myg.dx, dt,
ivars.nvar, gamma, r, u, v, p, ldelta_rx,
ldelta_ux, ldelta_vx, ldelta_px)
tm_states.end()
# transform interface states back into conserved variables
U_yl = comp.prim_to_cons(V_l, gamma, ivars, myg)
U_yr = comp.prim_to_cons(V_r, gamma, ivars, myg)
#myg.ng = 4
#=========================================================================
# apply source terms
#=========================================================================
grav = rp.get_param("compressible.grav")
ymom_src = my_aux.get_var("ymom_src")
ymom_src.v()[:, :] = dens.v() * grav
my_aux.fill_BC("ymom_src")
E_src = my_aux.get_var("E_src")
E_src.v()[:, :] = ymom.v() * grav
my_aux.fill_BC("E_src")
# ymom_xl[i,j] += 0.5*dt*dens[i-1,j]*grav
U_xl.v(buf=1, n=ivars.iymom)[:, :] += 0.5 * dt * ymom_src.ip(-1, buf=1)
U_xl.v(buf=1, n=ivars.iener)[:, :] += 0.5 * dt * E_src.ip(-1, buf=1)
# ymom_xr[i,j] += 0.5*dt*dens[i,j]*grav
U_xr.v(buf=1, n=ivars.iymom)[:, :] += 0.5 * dt * ymom_src.v(buf=1)
U_xr.v(buf=1, n=ivars.iener)[:, :] += 0.5 * dt * E_src.v(buf=1)
# ymom_yl[i,j] += 0.5*dt*dens[i,j-1]*grav
U_yl.v(buf=1, n=ivars.iymom)[:, :] += 0.5 * dt * ymom_src.jp(-1, buf=1)
U_yl.v(buf=1, n=ivars.iener)[:, :] += 0.5 * dt * E_src.jp(-1, buf=1)
# ymom_yr[i,j] += 0.5*dt*dens[i,j]*grav
U_yr.v(buf=1, n=ivars.iymom)[:, :] += 0.5 * dt * ymom_src.v(buf=1)
U_yr.v(buf=1, n=ivars.iener)[:, :] += 0.5 * dt * E_src.v(buf=1)
#=========================================================================
# compute transverse fluxes
#=========================================================================
tm_riem = tc.timer("riemann")
tm_riem.begin()
riemann = rp.get_param("compressible.riemann")
riemann = "CGF"
if riemann == "HLLC":
riemannFunc = interface_f.riemann_hllc
elif riemann == "CGF":
riemannFunc = interface_f.riemann_cgf
else:
msg.fail("ERROR: Riemann solver undefined")
#myg.ng = 5
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng, ivars.nvar, ivars.idens,
ivars.ixmom, ivars.iymom, ivars.iener, solid.xl,
solid.xr, gamma, U_xl, U_xr)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng, ivars.nvar, ivars.idens,
ivars.ixmom, ivars.iymom, ivars.iener, solid.yl,
solid.yr, gamma, U_yl, U_yr)
F_x = ai.ArrayIndexer(d=_fx, grid=myg)
F_y = ai.ArrayIndexer(d=_fy, grid=myg)
tm_riem.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
"""
tm_transverse = tc.timer("transverse flux addition")
tm_transverse.begin()
dtdx = dt / myg.dx
dtdy = dt / myg.dy
b = (2, 1)
for n in range(ivars.nvar):
# 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.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.ip_jp(-1, 1, buf=b, n=n) - F_y.ip(-1, buf=b, n=n))
# U_xr[i,j,:] = U_xr[i,j,:] - 0.5*dt/dy * (F_y[i,j+1,:] - F_y[i,j,:])
U_xr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdy*(F_y.jp(1, buf=b, n=n) - F_y.v(buf=b, n=n))
# 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.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip_jp(1, -1, buf=b, n=n) - F_x.jp(-1, buf=b, n=n))
# U_yr[i,j,:] = U_yr[i,j,:] - 0.5*dt/dx * (F_x[i+1,j,:] - F_x[i,j,:])
U_yr.v(buf=b, n=n)[:,:] += \
- 0.5*dtdx*(F_x.ip(1, buf=b, n=n) - F_x.v(buf=b, n=n))
tm_transverse.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
tm_riem.begin()
_fx = riemannFunc(1, myg.qx, myg.qy, myg.ng, ivars.nvar, ivars.idens,
ivars.ixmom, ivars.iymom, ivars.iener, solid.xl,
solid.xr, gamma, U_xl, U_xr)
_fy = riemannFunc(2, myg.qx, myg.qy, myg.ng, ivars.nvar, ivars.idens,
ivars.ixmom, ivars.iymom, ivars.iener, solid.yl,
solid.yr, gamma, U_yl, U_yr)
F_x = ai.ArrayIndexer(d=_fx, grid=myg)
F_y = ai.ArrayIndexer(d=_fy, grid=myg)
tm_riem.end()
#=========================================================================
# apply artificial viscosity
#=========================================================================
cvisc = rp.get_param("compressible.cvisc")
# myg.ng = 4
# ivars.nvar = 4
_ax, _ay = interface_f.artificial_viscosity(myg.qx, myg.qy, myg.ng, myg.dx,
myg.dy, cvisc, u, v)
avisco_x = ai.ArrayIndexer(d=_ax, grid=myg)
avisco_y = ai.ArrayIndexer(d=_ay, grid=myg)
b = (2, 1)
for n in range(ivars.nvar):
# F_x = F_x + avisco_x * (U(i-1,j) - U(i,j))
var = my_data.get_var_by_index(n)
F_x.v(buf=b, n=n)[:,:] += \
avisco_x.v(buf=b)*(var.ip(-1, buf=b) - var.v(buf=b))
# F_y = F_y + avisco_y * (U(i,j-1) - U(i,j))
F_y.v(buf=b, n=n)[:,:] += \
avisco_y.v(buf=b)*(var.jp(-1, buf=b) - var.v(buf=b))
tm_flux.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