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)