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scheme.f90
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!===============================================================================
!> \file scheme.f90
!! \brief
!! \b DUMSES-Hybrid:
!! This is scheme subroutines. This file cannot be compiled as is, it needs to
!! be preprocessed with the DUMSES preprocessor to generate call to Riemann
!! solvers.
!! \details
!! Contains primitive(), godunov(), fc_magnetic(), slope(), trace3d(), trace2d()
!! , trace1d(), compflux(), update(), constraint_transport()
!! \author
!! Marc Joos <[email protected]>, Sébastien Fromang, Romain Teyssier,
!! Patrick Hennebelle
!! \copyright
!! Copyrights 2013-2015, CEA.
!! This file is distributed under the CeCILL-A & GNU/GPL licenses, see
!! <http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.html> and
!! <http://www.gnu.org/licenses/>
!! \date
!! \b created: 04-15-2013
!! \b last \b modified: 05-26-2015
!<
!===============================================================================
!> Compute primitive variables
!===============================================================================
subroutine primitive(dt)
use mpi_var
use params
use variables, only: uin, qin, x
use oacc_params
use atmosphere , only : forcing
implicit none
real(dp), intent(in) :: dt
integer :: i, j, k
real(dp) :: eken, emag, eint, dvx, dvy
real(dp) :: smalle, smallp
!$py begin_statement
#if ISO == 1
smalle = one
smallp = smallr*ciso**2
#else
smalle = smallc**2/gamma/(gamma-one)
smallp = smallr*smallc**2/gamma
#endif
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(eken, emag, eint, dvx, dvy)
do k = ku1, ku2
!$acc loop vector(blocky_primitive)
do j = ju1, ju2
!$acc loop vector(blockx_primitive)
do i = iu1, iu2
qin(i,j,k,ir) = max(uin(i,j,k,ir), smallr)
qin(i,j,k,iu) = uin(i,j,k,iu)/uin(i,j,k,ir)
qin(i,j,k,iv) = uin(i,j,k,iv)/uin(i,j,k,ir)
qin(i,j,k,iw) = uin(i,j,k,iw)/uin(i,j,k,ir)
qin(i,j,k,iA) = half*(uin(i,j,k,iA) + uin(i,j,k,iA+3))
qin(i,j,k,iB) = half*(uin(i,j,k,iB) + uin(i,j,k,iB+3))
qin(i,j,k,iC) = half*(uin(i,j,k,iC) + uin(i,j,k,iC+3))
#if ISO == 1
qin(i,j,k,ip) = uin(i,j,k,ir)*ciso**2
#else
eken = half*(qin(i,j,k,iu)**2 + qin(i,j,k,iv)**2 + qin(i,j,k,iw)**2)
emag = half*(qin(i,j,k,iA)**2 + qin(i,j,k,iB)**2 + qin(i,j,k,iC)**2)
eint = (uin(i,j,k,ip) - emag)/uin(i,j,k,ir) - eken
qin(i,j,k,ip) = max((gamma - one)*qin(i,j,k,ir)*eint, smallp)
if(forcing) qin(i,j,k,ip)=half*qin(i,j,k,ir)**2
#endif
! Coriolis force predictor step
#if GEOM == CARTESIAN
if (Omega0 > zero) then
dvx = two*Omega0*qin(i,j,k,iv)
dvy = -half*Omega0*qin(i,j,k,iu)
qin(i,j,k,iu) = qin(i,j,k,iu) + dvx*dt*half
qin(i,j,k,iv) = qin(i,j,k,iv) + dvy*dt*half
endif
#endif
! Remove angular velocity of rotating frame in case of cylindrical geom
#if GEOM == CYLINDRICAL
if (Omega0 > zero) then
qin(i,j,k,iv) = qin(i,j,k,iv) - x(i)*Omega0
endif
#endif
enddo
enddo
enddo
!$OMP END PARALLEL DO
! if ((zposition==nzslice-1).and.(yposition==0).and.(mype==15)) then
! write (*,*) 'Pressure:',mype,qin(1:nx,1,nz,5)
! endif
return
end subroutine primitive
!===============================================================================
!> Godunov scheme subroutine; this is the core routine of the numerical scheme.
!!
!! The main steps are:
!! -# face-centered magnetic field is computed;
!! -# primitive variables are computed;
!! -# slopes at interfaces for hydro variables are computed;
!! -# a half-timestep prediction is performed;
!! -# Riemann fluxes are estimated using a Riemann solver;
!! -# variables are updated using the computed fluxes.
!<
!===============================================================================
subroutine godunov
use params
use variables
implicit none
integer :: i, j, k, idim
!$py begin_statement
!$acc data create(qm, qp, qRT, qRB, qLT, qLB, gravin)
!$acc data create(dq, bfc, dbfc)
!$py start_timing Face-centered magnetic field
call fc_magnetic(bfc)
!$py end_timing Face-centered magnetic field
!$py start_timing Primitive
call primitive(dt)
!$py end_timing Primitive
!$py start_timing Slope
call slope(bfc, dq, dbfc)
!$py end_timing Slope
!$py start_timing Trace
#if NDIM == 3
call trace3d(bfc, dq, dbfc, qm, qp, qRT, qRB, qLT, qLB)
#endif
#if NDIM == 2
call trace2d(bfc, dq, dbfc, qm, qp, qRT, qRB, qLT, qLB)
#endif
#if NDIM == 1
call trace1d(dq, qm, qp)
#endif
!$py end_timing Trace
!$acc end data
!$py start_timing Gravity predictor
if (rhs) then
do idim = 1, ndim
call gravity_predictor(qm(:,:,:,iu:iw,idim), .true., .true., .true.)
call gravity_predictor(qp(:,:,:,iu:iw,idim), .true., .true., .true.)
call gravity_predictor(qRT(:,:,:,iu:iw,idim), .true., .true., .true.)
call gravity_predictor(qRB(:,:,:,iu:iw,idim), .true., .true., .true.)
call gravity_predictor(qLT(:,:,:,iu:iw,idim), .true., .true., .true.)
call gravity_predictor(qLB(:,:,:,iu:iw,idim), .true., .true., .true.)
enddo
endif
!$py end_timing Gravity predictor
!$acc data create(fgodunov, fgodunov_pre, flux)
!$py start_timing Riemann
!$py call_solver riemann (qm, qp, fgodunov, fgodunov_pre)
!$py end_timing Riemann
!$acc data create(emfx, emfy, emfz)
!$py start_timing Riemann magnetic
#if NDIM > 1
!$py call_solver riemann_magnetic (qRT, qRB, qLT, qLB, emfz, 3)
#endif
#if NDIM == 3
!$py call_solver riemann_magnetic (qRT, qLT, qRB, qLB, emfy, 2)
!$py call_solver riemann_magnetic (qRT, qRB, qLT, qLB, emfx, 1)
#endif
!$py end_timing Riemann magnetic
!$py start_timing Flux
call compflux(fgodunov)
!$py end_timing Flux
#if NDIM == 3
if (boundary_type(1) == 'shearingbox') then
!$py start_timing Shearing flux
!$acc update host(dt)
call shearing_flux(time+half*dt)
!$py end_timing Shearing flux
endif
#endif
!$py start_timing Update
call update(fgodunov_pre)
!$py end_timing Update
!$acc end data
!$acc end data
!$acc end data
return
end subroutine godunov
!===============================================================================
!> Compute face-centered magnetic field
!===============================================================================
subroutine fc_magnetic(bfc)
use params
use variables, only: uin
implicit none
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,1:3), intent(out) :: bfc
integer :: i, j, k
!$py begin_statement
! Store face centered magnetic field
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME)
do k = ku1, ku2
do j = ju1, ju2
do i = iu1, iu2+1
if (i <= iu2) then
bfc(i,j,k,1) = uin(i,j,k,iA)
else
bfc(i,j,k,1) = uin(i-1,j,k,iA+3)
endif
end do
end do
end do
!$OMP END PARALLEL DO
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME)
do k = ku1, ku2
do j = ju1, ju2+1
do i = iu1, iu2
if (j <= ju2) then
bfc(i,j,k,2) = uin(i,j,k,iB)
else
bfc(i,j,k,2) = uin(i,j-1,k,iB+3)
endif
end do
end do
end do
!$OMP END PARALLEL DO
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME)
do k = ku1, ku2+1
do j = ju1, ju2
do i = iu1, iu2
if (k <= ku2) then
bfc(i,j,k,3) = uin(i,j,k,iC)
else
bfc(i,j,k,3) = uin(i,j,k-1,iC+3)
endif
end do
end do
end do
!$OMP END PARALLEL DO
return
end subroutine fc_magnetic
!===============================================================================
!> Compute slopes at cell interfaces
!===============================================================================
subroutine slope(bfc, dq, dbfc)
use params
use variables, only: qin,z
use oacc_params
use atmosphere , only: zbuffer
implicit none
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,3),intent(in) :: bfc
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,nvar,ndim),intent(out) :: dq
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,3,ndim),intent(out) :: dbfc
integer :: ilo, ihi, jlo, jhi, klo, khi
integer :: slope_type_loc
real(dp) :: dsgn, dlim, dcen, dlft, drgt, slop
real(dp) :: dfll, dflm, dflr, dfml, dfmm, dfmr, dfrl, dfrm, dfrr, vmin, vmax
real(dp) :: dflll, dflml, dflrl, dfmll, dfmml, dfmrl, dfrll, dfrml, dfrrl
real(dp) :: dfllm, dflmm, dflrm, dfmlm, dfmmm, dfmrm, dfrlm, dfrmm, dfrrm
real(dp) :: dfllr, dflmr, dflrr, dfmlr, dfmmr, dfmrr, dfrlr, dfrmr, dfrrr
real(dp) :: dfx, dfy, dfz, dff
integer :: i, j, k, ivar
! well-balanced scheme variables
real(dp) :: r,p,q0im1,q0ip1,q0kp1,q0km1
!$py begin_statement
ilo=min(1,iu1+1); ihi=max(1,iu2-1)
jlo=min(1,ju1+1); jhi=max(1,ju2-1)
klo=min(1,ku1+1); khi=max(1,ku2-1)
if (slope_type == 0) then
!$OMP PARALLEL WORKSHARE
dq = zero
dbfc = zero
!$OMP END PARALLEL WORKSHARE
return
endif
slope_type_loc = min(slope_type, 2)
#if NDIM == 1
if (slope_type < 3) then
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt) &
!$OMP PRIVATE(slop)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
do ivar = 1, nvar
r=qin(i,j,k,1) ; p=qin(i,j,k,5)
if (ivar==1) call getRhoFaces (r,p,q0ip1,q0im1,gamma,dx)
if (ivar==5) call getPressureFaces(r,p,q0ip1,q0im1,gamma,dx)
if ((ivar/=1).and.(ivar/=5)) then
q0im1=qin(i,j,k,ivar) ; q0ip1=q0im1
endif
dlft = slope_type*(q0im1 - qin(i-1,j,k,ivar))
drgt = slope_type*(qin(i+1,j,k,ivar) - q0ip1 )
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,1) = dsgn*min(dlim, abs(dcen))
end do
end do
enddo
enddo
!$OMP END PARALLEL DO
else
print*, "Unknown slope type!"
stop
endif
#endif
#if NDIM == 2
if (slope_type < 3) then
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt) &
!$OMP PRIVATE(slop)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
do ivar = 1, nvar
! slopes in first coordinate direction
dlft = slope_type*(qin(i ,j,k,ivar) - qin(i-1,j,k,ivar))
drgt = slope_type*(qin(i+1,j,k,ivar) - qin(i ,j,k,ivar))
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,1) = dsgn*min(dlim, abs(dcen))
! slopes in second coordinate direction
dlft = slope_type*(qin(i,j ,k,ivar) - qin(i,j-1,k,ivar))
drgt = slope_type*(qin(i,j+1,k,ivar) - qin(i,j ,k,ivar))
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,2) = dsgn*min(dlim, abs(dcen))
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
else if (slope_type == 3) then
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dfll,dflm,dflr,dfml,dfmm,dfmr)&
!$OMP PRIVATE(dfrl,dfrm,dfrr,vmin,vmax,dfx,dfy,dff,slop,dlim)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
do ivar = 1, nvar
dfll = qin(i-1,j-1,k,ivar) - qin(i,j,k,ivar)
dflm = qin(i-1,j,k,ivar) - qin(i,j,k,ivar)
dflr = qin(i,j-1,k,ivar) - qin(i,j,k,ivar)
dfml = qin(i,j-1,k,ivar) - qin(i,j,k,ivar)
dfmm = qin(i,j,k,ivar) - qin(i,j,k,ivar)
dfmr = qin(i,j+1,k,ivar) - qin(i,j,k,ivar)
dfrl = qin(i+1,j-1,k,ivar) - qin(i,j,k,ivar)
dfrm = qin(i+1,j,k,ivar) - qin(i,j,k,ivar)
dfrr = qin(i+1,j+1,k,ivar) - qin(i,j,k,ivar)
vmin = min(dfll,dflm,dflr,dfml,dfmm,dfmr,dfrl,dfrm,dfrr)
vmax = max(dfll,dflm,dflr,dfml,dfmm,dfmr,dfrl,dfrm,dfrr)
dfx = half*(qin(i+1,j,k,ivar) - qin(i-1,j,k,ivar))
dfy = half*(qin(i,j+1,k,ivar) - qin(i,j-1,k,ivar))
dff = half*(abs(dfx) + abs(dfy))
if (dff > zero) then
slop = min(one, min(abs(vmin), abs(vmax))/dff)
else
slop = one
endif
dlim = slop
dq(i,j,k,ivar,1) = dlim*dfx
dq(i,j,k,ivar,2) = dlim*dfy
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
else
print*, "Unknown slope type!"
stop
endif
! Bx along Y
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt, slop)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi+1
dlft = slope_type_loc*(bfc(i,j ,k,1) - bfc(i,j-1,k,1))
drgt = slope_type_loc*(bfc(i,j+1,k,1) - bfc(i,j ,k,1))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,1,2) = dsgn*min(dlim, abs(dcen))
enddo
enddo
enddo
!$OMP END PARALLEL DO
! By along X
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt, slop)
do k = klo, khi
do j = jlo, jhi+1
do i = ilo, ihi
dlft = slope_type_loc*(bfc(i ,j,k,2) - bfc(i-1,j,k,2))
drgt = slope_type_loc*(bfc(i+1,j,k,2) - bfc(i ,j,k,2))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,2,1) = dsgn*min(dlim,abs(dcen))
enddo
enddo
enddo
!$OMP END PARALLEL DO
#endif
#if NDIM == 3
if (slope_type < 3) then
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt) &
!$OMP PRIVATE(slop)
do k = klo, khi
! if (z(k)<0.9*zmax) then
! slope_type=2
! else
! slope_type=1
! endif
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
do ivar = 1, nvar
! slopes in first coordinate direction
dlft = slope_type*(qin(i ,j,k,ivar) - qin(i-1,j,k,ivar))
drgt = slope_type*(qin(i+1,j,k,ivar) - qin(i ,j,k,ivar))
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,1) = dsgn*min(dlim, abs(dcen))
! slopes in second coordinate direction
dlft = slope_type*(qin(i,j ,k,ivar) - qin(i,j-1,k,ivar))
drgt = slope_type*(qin(i,j+1,k,ivar) - qin(i,j ,k,ivar))
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,2) = dsgn*min(dlim, abs(dcen))
! slopes in third coordinate direction
r=qin(i,j,k,1) ; p=qin(i,j,k,5)
if (ivar==1) call getRhoFaces (r,p,q0kp1,q0km1,gamma,dz)
if (ivar==5) call getPressureFaces(r,p,q0kp1,q0km1,gamma,dz)
if (((ivar/=1).and.(ivar/=5)).or.(z(k)>zbuffer)) then
q0km1=qin(i,j,k,ivar) ; q0kp1=q0km1
endif
dlft = slope_type*(q0km1 - qin(i,j,k-1,ivar))
drgt = slope_type*(qin(i,j,k+1,ivar) - q0kp1 )
dcen = half*(dlft + drgt)/slope_type
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dq(i,j,k,ivar,3) = dsgn*min(dlim, abs(dcen))
end do
end do
end do
end do
!$OMP END PARALLEL DO
else if (slope_type == 3) then
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dflll, dflml, dflrl, dfmll) &
!$OMP PRIVATE(dfmml, dfmrl, dfrll, dfrml, dfrrl, dfllm, dflmm, dflrm) &
!$OMP PRIVATE(dfmlm, dfmmm, dfmrm, dfrlm, dfrmm, dfrrm, dfllr, dflmr) &
!$OMP PRIVATE(dflrr, dfmlr, dfmmr, dfmrr, dfrlr, dfrmr, dfrrr, vmin) &
!$OMP PRIVATE(vmax, dfx, dfy, dfz, dff, slop, dlim)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
do ivar = 1, nvar
r=qin(i,j,k,1) ; p=qin(i,j,k,5)
if (ivar==1) call getRhoFaces (r,p,q0kp1,q0km1,gamma,dz)
if (ivar==5) call getPressureFaces(r,p,q0kp1,q0km1,gamma,dz)
if (((ivar/=1).and.(ivar/=5)).or.(z(k)>zbuffer)) then
q0km1=qin(i,j,k,ivar) ; q0kp1=q0km1
endif
dflll = (qin(i-1,j-1,k-1,ivar) - q0km1)/sqrt(dx**2+dy**2+dz**2)
dflml = (qin(i-1,j ,k-1,ivar) - q0km1)/sqrt(dx**2+dz**2)
dflrl = (qin(i-1,j+1,k-1,ivar) - q0km1)/sqrt(dx**2+dy**2+dz**2)
dfmll = (qin(i ,j-1,k-1,ivar) - q0km1)/sqrt(dy**2+dz**2)
dfmml = (qin(i ,j ,k-1,ivar) - q0km1)/dz
dfmrl = (qin(i ,j+1,k-1,ivar) - q0km1)/sqrt(dy**2+dz**2)
dfrll = (qin(i+1,j-1,k-1,ivar) - q0km1)/sqrt(dx**2+dy**2+dz**2)
dfrml = (qin(i+1,j ,k-1,ivar) - q0km1)/sqrt(dx**2+dz**2)
dfrrl = (qin(i+1,j+1,k-1,ivar) - q0km1)/sqrt(dx**2+dy**2+dz**2)
dfllm = (qin(i-1,j-1,k ,ivar)-qin(i,j,k,ivar))/sqrt(dx**2+dy**2)
dflmm = (qin(i-1,j ,k ,ivar)-qin(i,j,k,ivar))/dx
dflrm = (qin(i-1,j+1,k ,ivar)-qin(i,j,k,ivar))/sqrt(dx**2+dy**2)
dfmlm = (qin(i ,j-1,k ,ivar)-qin(i,j,k,ivar))/dy
dfmmm = (qin(i ,j ,k ,ivar)-qin(i,j,k,ivar))
dfmrm = (qin(i ,j+1,k ,ivar)-qin(i,j,k,ivar))/dy
dfrlm = (qin(i+1,j-1,k ,ivar)-qin(i,j,k,ivar))/sqrt(dx**2+dy**2)
dfrmm = (qin(i+1,j ,k ,ivar)-qin(i,j,k,ivar))/dx
dfrrm = (qin(i+1,j+1,k ,ivar)-qin(i,j,k,ivar))/sqrt(dx**2+dy**2)
dfllr = (qin(i-1,j-1,k+1,ivar)-q0kp1)/sqrt(dx**2+dy**2+dz**2)
dflmr = (qin(i-1,j ,k+1,ivar)-q0kp1)/sqrt(dx**2+dz**2)
dflrr = (qin(i-1,j+1,k+1,ivar)-q0kp1)/sqrt(dx**2+dy**2+dz**2)
dfmlr = (qin(i ,j-1,k+1,ivar)-q0kp1)/sqrt(dy**2+dz**2)
dfmmr = (qin(i ,j ,k+1,ivar)-q0kp1)/dz
dfmrr = (qin(i ,j+1,k+1,ivar)-q0kp1)/sqrt(dy**2+dz**2)
dfrlr = (qin(i+1,j-1,k+1,ivar)-q0kp1)/sqrt(dx**2+dy**2+dz**2)
dfrmr = (qin(i+1,j ,k+1,ivar)-q0kp1)/sqrt(dx**2+dz**2)
dfrrr = (qin(i+1,j+1,k+1,ivar)-q0kp1)/sqrt(dx**2+dy**2+dz**2)
vmin = min(dflll,dflml,dflrl,dfmll,dfmml,dfmrl,dfrll,dfrml &
& ,dfrrl,dfllm,dflmm,dflrm,dfmlm,dfmmm,dfmrm,dfrlm &
& ,dfrmm,dfrrm,dfllr,dflmr,dflrr,dfmlr,dfmmr,dfmrr &
& ,dfrlr,dfrmr,dfrrr)
vmax = max(dflll,dflml,dflrl,dfmll,dfmml,dfmrl,dfrll,dfrml &
& ,dfrrl,dfllm,dflmm,dflrm,dfmlm,dfmmm,dfmrm,dfrlm &
& ,dfrmm,dfrrm,dfllr,dflmr,dflrr,dfmlr,dfmmr,dfmrr &
& ,dfrlr,dfrmr,dfrrr)
dfx = half*(qin(i+1,j,k,ivar) - qin(i-1,j,k,ivar))
dfy = half*(qin(i,j+1,k,ivar) - qin(i,j-1,k,ivar))
r=qin(i,j,k,1) ; p=qin(i,j,k,5)
if (ivar==1) call getRhoFaces (r,p,q0kp1,q0km1,gamma,dz)
if (ivar==5) call getPressureFaces(r,p,q0kp1,q0km1,gamma,dz)
if (((ivar/=1).and.(ivar/=5)).or.(z(k)>zbuffer)) then
q0km1=qin(i,j,k-1,ivar) ; q0kp1=qin(i,j,k+1,ivar)
endif
dfz = half*(q0kp1-q0km1)
dff = half*(abs(dfx) + abs(dfy) + abs(dfz))
if (dff > zero) then
slop = min(one,min(abs(vmin),abs(vmax))/dff)
else
slop = one
endif
dlim = slop
dq(i,j,k,ivar,1) = dlim*dfx
dq(i,j,k,ivar,2) = dlim*dfy
dq(i,j,k,ivar,3) = dlim*dfz
enddo
enddo
enddo
enddo
!$OMP END PARALLEL DO
else
print*, "Unknown slope type!"
stop
endif
! Bx along direction Y and Z
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt, slop)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi+1
! slopes along Y
dlft = slope_type_loc*(bfc(i,j ,k,1) - bfc(i,j-1,k,1))
drgt = slope_type_loc*(bfc(i,j+1,k,1) - bfc(i,j ,k,1))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,1,2) = dsgn*min(dlim, abs(dcen))
! slopes along Z
dlft = slope_type_loc*(bfc(i,j,k ,1) - bfc(i,j,k-1,1))
drgt = slope_type_loc*(bfc(i,j,k+1,1) - bfc(i,j,k ,1))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,1,3) = dsgn*min(dlim, abs(dcen))
end do
end do
end do
!$OMP END PARALLEL DO
! By along direction X and Z
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt, slop)
do k = klo, khi
!$acc loop vector(blocky_slope)
do j = jlo, jhi+1
!$acc loop vector(blockx_slope)
do i = ilo, ihi
! slopes along X
dlft = slope_type_loc*(bfc(i ,j,k,2) - bfc(i-1,j,k,2))
drgt = slope_type_loc*(bfc(i+1,j,k,2) - bfc(i ,j,k,2))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,2,1) = dsgn*min(dlim,abs(dcen))
! slopes along Z
dlft = slope_type_loc*(bfc(i,j,k ,2) - bfc(i,j,k-1,2))
drgt = slope_type_loc*(bfc(i,j,k+1,2) - bfc(i,j,k ,2))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,2,3) = dsgn*min(dlim, abs(dcen))
end do
end do
end do
!$OMP END PARALLEL DO
! Bz along direction X and Y
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(dsgn, dlim, dcen, dlft, drgt, slop)
do k = klo, khi+1
!$acc loop vector(blocky_slope)
do j = jlo, jhi
!$acc loop vector(blockx_slope)
do i = ilo, ihi
! slopes along X
dlft = slope_type_loc*(bfc(i ,j,k,3) - bfc(i-1,j,k,3))
drgt = slope_type_loc*(bfc(i+1,j,k,3) - bfc(i ,j,k,3))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,3,1) = dsgn*min(dlim, abs(dcen))
! slopes along Y
dlft = slope_type_loc*(bfc(i,j ,k,3) - bfc(i,j-1,k,3))
drgt = slope_type_loc*(bfc(i,j+1,k,3) - bfc(i,j ,k,3))
dcen = half*(dlft + drgt)/slope_type_loc
dsgn = sign(one, dcen)
slop = min(abs(dlft), abs(drgt))
dlim = slop
if ((dlft*drgt) <= zero) dlim = zero
dbfc(i,j,k,3,2) = dsgn*min(dlim, abs(dcen))
end do
end do
end do
!$OMP END PARALLEL DO
#endif
return
end subroutine slope
!===============================================================================
#if NDIM == 1
!> Perform a half-timestep prediction
!===============================================================================
subroutine trace1d(dq, qm, qp)
use params
use variables, only: qin, dt, x
use oacc_params
use atmosphere, only: balanced
implicit none
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,nvar,ndim), intent(in) :: dq
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,ndim), intent(out) :: qm
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,ndim), intent(out) :: qp
integer :: i, j, k, l, n
integer :: ilo, ihi, jlo, jhi, klo, khi
real(dp) :: dtdx, xc
real(dp) :: r, u, v, w, p, A, B, C
real(dp) :: drx, dux, dvx, dwx, dpx, dAx, dBx, dCx
real(dp) :: sr0, su0, sv0, sw0, sp0, sA0, sB0, sC0
! local variables for balanced scheme
real(dp) :: rm,rp,pm,pp
!$py begin_statement
ilo = min(1,iu1+1); ihi = max(1,iu2-1)
jlo = min(1,ju1+1); jhi = max(1,ju2-1)
klo = min(1,ku1+1); khi = max(1,ku2-1)
su0 = zero; sv0 = zero; sw0 = zero
dtdx = dt/dx
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(xc, r, u, v, w, p, A, B, C, drx) &
!$OMP PRIVATE(dux, dvx, dwx, dpx, dAx, dBx, dCx, sr0, su0, sv0, sw0, sp0) &
!$OMP PRIVATE(sA0, sB0, sC0)
do k = klo, khi
!$acc loop vector(blocky_trace)
do j = jlo, jhi
!$acc loop vector(blockx_trace)
do i = ilo, ihi
xc = x(i)
! Cell centered values
r = qin(i,j,k,ir)
u = qin(i,j,k,iu)
v = qin(i,j,k,iv)
w = qin(i,j,k,iw)
p = qin(i,j,k,ip)
A = qin(i,j,k,iA)
B = qin(i,j,k,iB)
C = qin(i,j,k,iC)
! TVD slopes in X direction
drx = half*dq(i,j,k,ir,1)
dux = half*dq(i,j,k,iu,1)
dvx = half*dq(i,j,k,iv,1)
dwx = half*dq(i,j,k,iw,1)
dpx = half*dq(i,j,k,ip,1)
dBx = half*dq(i,j,k,iB,1)
dCx = half*dq(i,j,k,iC,1)
! Source terms (including transverse derivatives)
#if GEOM == CARTESIAN
sr0 = -u*drx - r*dux ; sr0 = sr0*dtdx
su0 = -u*dux - (dpx + B*dBx + C*dCx)/r; su0 = su0*dtdx
sv0 = -u*dvx + (A*dBx)/r ; sv0 = sv0*dtdx
sw0 = -u*dwx + (A*dCx)/r ; sw0 = sw0*dtdx
sp0 = -u*dpx - gamma*p*dux ; sp0 = sp0*dtdx
sB0 = -u*dBx + A*dvx - B*dux ; sB0 = sB0*dtdx
sC0 = -u*dCx + A*dwx - C*dux ; sC0 = sC0*dtdx
#endif
#if GEOM == CYLINDRICAL
! Note that A=0 by definition in this case
sr0 = -u*drx - r*dux
sr0 = sr0*dtdx - r*u/xc*half*dt
su0 = -u*dux - (dpx + B*dBx + C*dCx)/r
su0 = su0*dtdx + (v*v - B*B/r)/xc*half*dt
sv0 = -u*dvx
sv0 = sv0*dtdx - u*v/xc*half*dt
sw0 = -u*dwx
sw0 = sw0*dtdx
sp0 = -u*dpx - gamma*p*dux
sp0 = sp0*dtdx - gamma*p*u/xc*half*dt
sB0 = -u*dBx - B*dux
sB0 = sB0*dtdx
sC0 = -u*dCx - C*dux
sC0 = sC0*dtdx - u*C/xc*half*dt
#endif
#if GEOM == SPHERICAL
! Note that theta=pi/2 is assumed
sr0 = -u*drx - r*dux
sr0 = sr0*dtdx - two*r*u
su0 = -u*dux - (dpx + B*dBx + C*dCx)/r
su0 = su0*dtdx + (v*v + w*w - B*B/r - C*C/r)/xc*half*dt
sv0 = -u*dvx + (A*dBx)/r
sv0 = sv0*dtdx - (u*v - A*B/r)/xc*half*dt
sw0 = -u*dwx + (A*dCx)/r
sw0 = sw0*dtdx - (u*w - A*C/r)/xc*half*dt
sp0 = -u*dpx - gamma*p*dux
sp0 = sp0*dtdx - two*gamma*p*u/xc*half*dt
sB0 = -u*dBx + A*dvx - B*dux
sB0 = sB0*dtdx - (u*B - v*A)/xc*half*dt
sC0 = -u*dCx + A*dwx - C*dux
sC0 = sC0*dtdx - (w*A - u*C)/xc*half*dt
#endif
if (balanced) then
call getRhoFaces (r,p,rm,rp,gamma,dx/2.d0)
call getPressureFaces(r,p,pm,pp,gamma,dx/2.d0)
endif
!Update in time the primitive variables
if (.not.(balanced)) then
rm = r + sr0 ; rp = r + sr0
pm = p + sp0 ; pp = p + sp0
else
rm = rm + sr0 ; rp = rp + sr0
pm = pm + sp0 ; pp = pp + sp0
endif
! Cell-centered predicted states
r = r + sr0
u = u + su0
v = v + sv0
w = w + sw0
p = p + sp0
B = B + sB0
C = C + sC0
#if GEOM == CARTESIAN
if (Omega0 > zero) then
sC0 = sc0 - 1.5d0*Omega0*A*dtdx
endif
#endif
! Right state at left interface
qp(i,j,k,ir,1) = rp - drx
qp(i,j,k,iu,1) = u - dux
qp(i,j,k,iv,1) = v - dvx
qp(i,j,k,iw,1) = w - dwx
qp(i,j,k,ip,1) = pp - dpx
qp(i,j,k,iA,1) = A
qp(i,j,k,iB,1) = B - dBx
qp(i,j,k,iC,1) = C - dCx
qp(i,j,k,ir,1) = max(smallr, qp(i,j,k,ir,1))
! Left state at right interface
qm(i,j,k,ir,1) = rm + drx
qm(i,j,k,iu,1) = u + dux
qm(i,j,k,iv,1) = v + dvx
qm(i,j,k,iw,1) = w + dwx
qm(i,j,k,ip,1) = pm + dpx
qm(i,j,k,iA,1) = A
qm(i,j,k,iB,1) = B + dBx
qm(i,j,k,iC,1) = C + dCx
qm(i,j,k,ir,1) = max(smallr, qm(i,j,k,ir,1))
enddo
enddo
enddo
!$OMP END PARALLEL DO
return
end subroutine trace1d
#endif
!===============================================================================
#if NDIM == 2
!> Perform a half-timestep prediction
!===============================================================================
subroutine trace2d(bfc, dq, dbfc, qm, qp, qRT, qRB, qLT, qLB)
use params
use variables, only: qin, dt, x, y, Ez
use oacc_params
implicit none
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,3), intent(in) :: bfc
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,nvar,ndim), intent(in) :: dq
real(dp), dimension(iu1:iu2+1,ju1:ju2+1,ku1:ku2+1,3,ndim), intent(in) :: dbfc
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,ndim), intent(out) :: qm
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,ndim), intent(out) :: qp
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,3), intent(out) :: qRT
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,3), intent(out) :: qRB
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,3), intent(out) :: qLT
real(dp), dimension(iu1:iu2,ju1:ju2,ku1:ku2,nvar,3), intent(out) :: qLB
integer :: i, j, k, l
integer :: ilo, ihi, jlo, jhi, klo, khi
real(dp) :: dtdx, dtdy, xc, xL, xR, yL, yR, sinxc, sinxL, sinxR, cotanxc
real(dp) :: smallp, shear
real(dp) :: r, u, v, w, p, A, B, C
real(dp) :: ELL, ELR, ERL, ERR
real(dp) :: drx, dux, dvx, dwx, dpx, dAx, dBx, dCx
real(dp) :: dry, duy, dvy, dwy, dpy, dAy, dBy, dCy
real(dp) :: sr0, su0, sv0, sw0, sp0, sA0, sB0, sC0
real(dp) :: AL, AR, BL, BR
real(dp) :: dALy, dARy
real(dp) :: dBLx, dBRx
real(dp) :: sAL0, sAR0, sBL0, sBR0
!$py begin_statement
smallp = smallr*smallc**2/gamma
ilo = min(1,iu1+1); ihi = max(1,iu2-1)
jlo = min(1,ju1+1); jhi = max(1,ju2-1)
klo = min(1,ku1+1); khi = max(1,ku2-1)
dtdx = dt/dx
dtdy = dt/dy
!$acc data pcreate(Ez)
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(u, v, A, B)
do k = klo, ku2
!$acc loop vector(blocky_trace)
do j = jlo, ju2
!$acc loop vector(blockx_trace)
do i = ilo, iu2
u = 0.25*(qin(i-1,j-1,k,iu) + qin(i-1,j,k,iu) + qin(i,j-1,k,iu) &
& + qin(i,j,k,iu))
v = 0.25*(qin(i-1,j-1,k,iv) + qin(i-1,j,k,iv) + qin(i,j-1,k,iv) &
& + qin(i,j,k,iv))
A = 0.5*(bfc(i,j-1,k,1) + bfc(i,j,k,1))
B = 0.5*(bfc(i-1,j,k,2) + bfc(i,j,k,2))
Ez(i,j,k) = u*B - v*A
end do
end do
end do
!$OMP END PARALLEL DO
!$acc kernels loop
!$OMP PARALLEL DO SCHEDULE(RUNTIME) PRIVATE(xL, xR, xc, yL, yR, sinxc, sinxL)&
!$OMP PRIVATE(sinxR, cotanxc, r, u, v, w, p, A, B, C, ELL, ELR, ERL, ERR) &
!$OMP PRIVATE(drx, dux, dvx, dwx, dpx, dAx, dBx, dCx, dry, duy, dvy, dwy) &
!$OMP PRIVATE(dpy, dAy, dBy, dCy, sr0, su0, sv0, sw0, sp0, sA0, sB0, sC0, AL)&
!$OMP PRIVATE(AR, BL, BR, dALy, dARy, dBLx, dBRx, sAL0, sAR0, sBL0, sBR0)
do k = klo, khi
!$acc loop vector(blocky_trace)
do j = jlo, jhi
#if GEOM == SPHERICAL
yL = half*(y(j-1) + y(j))
yR = half*(y(j+1) + y(j))
sinxc = sin(y(j))
sinxL = sin(yL)
sinxR = sin(yR)
cotanxc = cos(y(j))/sinxc
#endif
!$acc loop vector(blockx_trace)
do i = ilo, ihi
xL = half*(x(i-1)+x(i))
xR = half*(x(i+1)+x(i))
xc = x(i)
! Cell centered values
r = qin(i,j,k,ir)
u = qin(i,j,k,iu)
v = qin(i,j,k,iv)
w = qin(i,j,k,iw)
p = qin(i,j,k,ip)
A = qin(i,j,k,iA)
B = qin(i,j,k,iB)
C = qin(i,j,k,iC)
! Face centered variables
AL = bfc(i ,j ,k,1)
AR = bfc(i+1,j ,k,1)
BL = bfc(i ,j ,k,2)
BR = bfc(i ,j+1,k,2)
! Electric field
ELL = Ez(i ,j ,k)
ELR = Ez(i ,j+1,k)
ERL = Ez(i+1,j ,k)
ERR = Ez(i+1,j+1,k)
! Cell centered TVD slopes in X direction
drx = half*dq(i,j,k,ir,1)
dux = half*dq(i,j,k,iu,1)
dvx = half*dq(i,j,k,iv,1)
dwx = half*dq(i,j,k,iw,1)
dCx = half*dq(i,j,k,iC,1)
dpx = half*dq(i,j,k,ip,1)
dBx = half*dq(i,j,k,iB,1)
! Cell centered TVD slopes in Y direction
dry = half*dq(i,j,k,ir,2)
duy = half*dq(i,j,k,iu,2)
dvy = half*dq(i,j,k,iv,2)
dwy = half*dq(i,j,k,iw,2)
dCy = half*dq(i,j,k,iC,2)
dpy = half*dq(i,j,k,ip,2)
dAy = half*dq(i,j,k,iA,2)
! Face centered TVD slopes in transverse direction
dALy = half*dbfc(i ,j ,k,1,2)
dARy = half*dbfc(i+1,j ,k,1,2)