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m_rhsvar.f90
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m_rhsvar.f90
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Module that assigns values used in m_rhs
!
! Last update: January 24, 2010
! Author: Keita Ando
! Department of Mechanical Engineering
! Division of Engineering and Applied Science
! California Institute of Technology, Pasadena CA 91125
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
MODULE m_rhsvar
USE mpi_setup
USE m_globalvar
USE m_misc
IMPLICIT NONE
! for direction 1 to be solved
INTEGER :: Nbeg
INTEGER :: Nend
INTEGER :: Nroe
INTEGER :: N1
INTEGER :: dir1
! index matrix
INTEGER, DIMENSION(:,:), POINTER :: ip
! grid spacing
REAL(KIND(0.D0)), DIMENSION(:), POINTER :: ds
! WENO coefficients
! smoothness indicators
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: betaw0
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: betaw1
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: betaw2
! ideal weights
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: dwenor
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: dwenol
! polynomials
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyr0
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyr1
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyr2
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyl0
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyl1
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: polyl2
! WENO3
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: w3beta
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: w3dr
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: w3dl
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: w3polyr
REAL(KIND(0.D0)), DIMENSION(:,:), POINTER :: w3polyl
! velocity in x direction
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE, TARGET :: xvel
! velocity in direction 1 to be solved
REAL(KIND(0.D0)), DIMENSION(:), POINTER :: vel1
! physical quantities for cells
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: pres
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: sound
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: nbub
! "L" & "R" quantities
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: lpres
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: rpres
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: lvel
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: rvel
! characteristic speeds for cells
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: charsp
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: charsproe
! bubble dynamics variables for cells
! bub(1,:): R, bub(2,:): \dot{R}, bub(3,:): p_b, bub(4,:): m_v
TYPE(coordinate), DIMENSION(:,:), ALLOCATABLE :: bub
! BCs
TYPE(bc) :: bound
! used for nonreflective BCs
REAL(KIND(0.D0)) :: oneside
REAL(KIND(0.D0)), DIMENSION(:), POINTER :: onesidebeg
REAL(KIND(0.D0)), DIMENSION(:), POINTER :: onesideend
! conserved variables
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: qval
! numerical flux at cell edges
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: nfx
! numerical source flux in momentum equation at cell edges
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: nsfx
! cell-edge velocity
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: velhf
! flux used in subroutines for nonreflective BCs
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: fxtmp
! rhs for each cell
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rhsfx
! sources for each cell
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rhsrc
! quantities for WENO
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: inweno
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: lweno
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rweno
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: lflux
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rflux
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: lqval
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rqval
TYPE(wenochar), DIMENSION(:), ALLOCATABLE :: linw
TYPE(wenochar), DIMENSION(:), ALLOCATABLE :: rinw
! for characteristic decomposition
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: v_out
! left & right eigenvectors at cell edges
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rr
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: ll
! HLLC
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: sr
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: sl
REAL(KIND(0.D0)), DIMENSION(:), ALLOCATABLE :: sstar
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: lqstar
TYPE(coordinate), DIMENSION(:), ALLOCATABLE :: rqstar
CONTAINS
!========================================================================
SUBROUTINE s_start_rhsvar
INTEGER :: n
INTEGER :: iv
INTEGER :: ir
INTEGER :: ib
INTEGER :: ieig
INTEGER :: istart
INTEGER :: istop
! pointers for direction to be solved
N1 = Nx
bound = xbound
ip => ix
ds => dxs
! for WENO coefficients
betaw0 => betax0
betaw1 => betax1
betaw2 => betax2
dwenor => dwxr
dwenol => dwxl
polyr0 => polyrx0
polyr1 => polyrx1
polyr2 => polyrx2
polyl0 => polylx0
polyl1 => polylx1
polyl2 => polylx2
onesidebeg => onesidebegx
onesideend => onesideendx
w3beta => w3betax
w3dr => w3drx
w3dl => w3dlx
w3polyr => w3polyrx
w3polyl => w3polylx
dir1 = 2
IF ( bound%beg=='reflect'.AND.mpi_rank==0 ) THEN
istart = 1 - wenonum
Nbeg = 0
ELSE
istart = 1
Nbeg = 1
END IF
IF ( bound%end=='reflect'.AND.mpi_rank==mpi_size-1 ) THEN
istop = N1 + wenonum
Nend = N1 + 1
Nroe = N1 - 1
ELSE
istop = N1
Nend = N1
Nroe = N1
END IF
! velocity
ALLOCATE( xvel(1:N1) )
vel1 => xvel
! cell-averaged quantities
ALLOCATE( pres(1:N1) )
ALLOCATE( sound(1:N1) )
ALLOCATE( nbub(1:N1) )
! "L" & "R" quantities
ALLOCATE( lpres(Nbeg:N1) )
ALLOCATE( rpres(1:Nend) )
ALLOCATE( lvel(Nbeg:N1) )
ALLOCATE( rvel(1:Nend) )
! HLLC wavespeeds
ALLOCATE( sl(Nbeg:N1) )
ALLOCATE( sr(Nbeg:N1) )
ALLOCATE( sstar(Nbeg:N1) )
! numerical source flux in momentum equation
ALLOCATE( nsfx(0:N1) )
! cell-edge velocity
ALLOCATE( velhf(0:N1) )
ALLOCATE( charsp(Nv),charsproe(Nv) )
ALLOCATE( qval(Nv) )
ALLOCATE( nfx(Nv) )
ALLOCATE( fxtmp(Nv) )
ALLOCATE( rhsfx(Nv) )
ALLOCATE( rhsrc(Nv) )
ALLOCATE( inweno(Nv) )
ALLOCATE( lweno(Nv) )
ALLOCATE( rweno(Nv) )
ALLOCATE( lflux(Nv) )
ALLOCATE( rflux(Nv) )
ALLOCATE( lqval(Nv) )
ALLOCATE( rqval(Nv) )
ALLOCATE( linw(Nv) )
ALLOCATE( rinw(Nv) )
ALLOCATE( v_out(Nv) )
ALLOCATE( lqstar(Nv) )
ALLOCATE( rqstar(Nv) )
DO iv = 1,Nv
! numerical flux at cell edges
ALLOCATE( nfx(iv)%f(Nbeg:N1) )
! RHS for cells
ALLOCATE( rhsfx(iv)%f(1:N1) )
ALLOCATE( rhsrc(iv)%f(1:N1) )
ALLOCATE( qval(iv)%f(1:N1) )
ALLOCATE( fxtmp(iv)%f(1:N1) )
ALLOCATE( inweno(iv)%f(istart:istop) )
! note that lweno is "R" state
ALLOCATE( lweno(iv)%f(1:N1) )
! note that rweno is "L" state
ALLOCATE( rweno(iv)%f(1:N1) )
! eigenvalues for cells
ALLOCATE( charsp(iv)%f(1:N1) )
! Roe-averaged eigenvalues at cell edges
ALLOCATE( charsproe(iv)%f(Nbeg:N1) )
DO n = -wenonum,wenonum
ALLOCATE( linw(iv)%w(n)%f(1:N1) )
ALLOCATE( rinw(iv)%w(n)%f(1:N1) )
END DO
! used for local characteristic decomposition
ALLOCATE( v_out(iv)%f(1:N1) )
! lqval is "L" state <== rweno
ALLOCATE( lqval(iv)%f(Nbeg:N1) )
! rqval is "R" state <== lweno
ALLOCATE( rqval(iv)%f(1:Nend) )
! lflux "L" state, rflux "R" state
ALLOCATE( lflux(iv)%f(Nbeg:N1) )
ALLOCATE( rflux(iv)%f(1:Nend) )
ALLOCATE( lqstar(iv)%f(Nbeg:N1) )
ALLOCATE( rqstar(iv)%f(Nbeg:N1) )
END DO
ALLOCATE( bub(Nb,NR0) )
DO ib = 1,Nb
DO ir = 1,NR0
! bubble dynamics variables
ALLOCATE( bub(ib,ir)%f(1:N1) )
END DO
END DO
! right (rr) & left (ll) eigenvectors
ALLOCATE( rr(Neig) )
ALLOCATE( ll(Neig) )
DO ieig = 1,Neig
ALLOCATE( rr(ieig)%f(Nbeg:N1) )
ALLOCATE( ll(ieig)%f(Nbeg:N1) )
END DO
END SUBROUTINE s_start_rhsvar
!========================================================================
SUBROUTINE s_compvar
INTEGER :: i
INTEGER :: ir
INTEGER :: ib
INTEGER :: iv
REAL(KIND(0.D0)) :: plpB
REAL(KIND(0.D0)) :: vf1
REAL(KIND(0.D0)), DIMENSION(NR0) :: nRtmp
! velocity
xvel = qval(2)%f/qval(1)%f
DO i = 1,N1
DO ir = 1,NR0
nRtmp(ir) = qval(ibub(1,ir))%f(i)
END DO
CALL s_comp_n( qval(Nveul)%f(i),nRtmp,nbub(i) )
DO ir = 1,NR0
! bubble-dynamic variables
DO ib = 1,Nb
bub(ib,ir)%f(i) = qval(ibub(ib,ir))%f(i)/nbub(i)
END DO
END DO
! averaged liquid pressure
vf1 = 1.D0 - qval(Nveul)%f(i)
plpB = ( pl0+B_tait )*( qval(1)%f(i)/vf1 )**n_tait
pres(i) = plpB - B_tait
! \tilde{c}_l
sound(i) = DSQRT( n_tait*plpB/vf1/qval(1)%f(i) )
END DO
! characteristic speeds (eigenvalues) used for nonreflective BCs
charsp(1)%f = vel1 - sound
charsp(2)%f = vel1 + sound
DO iv = Nveul,Nv
charsp(iv)%f = vel1
END DO
END SUBROUTINE s_compvar
!========================================================================
SUBROUTINE s_roeaverage
INTEGER :: i
INTEGER :: iv
INTEGER :: ir
INTEGER :: ib
REAL(KIND(0.D0)) :: rhoroe
REAL(KIND(0.D0)) :: ratio
REAL(KIND(0.D0)) :: denom
REAL(KIND(0.D0)) :: umroe
REAL(KIND(0.D0)) :: vfroe
REAL(KIND(0.D0)) :: vfroe1
REAL(KIND(0.D0)) :: nbubroe
REAL(KIND(0.D0)) :: plpBroe
REAL(KIND(0.D0)) :: cmroe
DO i = 1,Nroe
!!! Euler part !!!
! Roe averages
rhoroe = DSQRT( qval(1)%f(i)*qval(1)%f(ip(i,1)) )
ratio = DSQRT( qval(1)%f(ip(i,1))/qval(1)%f(i) )
denom = 1.D0 + ratio
umroe = ( vel1(i)+ratio*vel1(ip(i,1)) )/denom
DO iv = Nveul,Nv
charsproe(iv)%f(i) = umroe
END DO
vfroe = ( ratio*qval(Nveul)%f(i)+qval(Nveul)%f(ip(i,1)) )/denom
vfroe1 = 1.D0 - vfroe
plpBroe = ( pl0+B_tait )*( rhoroe/vfroe1 )**n_tait
cmroe = DSQRT( n_tait*plpBroe/vfroe1/rhoroe )
charsproe(1)%f(i) = umroe - cmroe
charsproe(2)%f(i) = umroe + cmroe
! right eigenvectors at i+1/2
rr(1)%f(i) = rhoroe
rr(2)%f(i) = rhoroe*charsproe(1)%f(i)
rr(3)%f(i) = rhoroe*charsproe(2)%f(i)
rr(4)%f(i) = rhoroe*umroe
rr(5)%f(i) = vfroe
! left eigenvectors at i+1/2
ll(2)%f(i) = 0.5D0/rhoroe/cmroe
ll(1)%f(i) = ( umroe+vfroe1*cmroe )*ll(2)%f(i)
ll(3)%f(i) = ( -umroe+vfroe1*cmroe )*ll(2)%f(i)
ll(4)%f(i) = vfroe/rhoroe
ll(5)%f(i) = vfroe1/rhoroe
!!! bubble-dynamic part !!!
DO ib = 1,Nb
DO ir = 1,NR0
! Roe averages
nbubroe = ( ratio*qval(ibub(ib,ir))%f(i) &
+ qval(ibub(ib,ir))%f(ip(i,1)) )/denom
! right eigenvectors at i+1/2
rr(ieig(ib,ir))%f(i) = nbubroe
! left eigenvectors at i+1/2
ll(ieig(ib,ir))%f(i) = nbubroe
END DO
END DO
END DO
!!! reflective BCs !!!
! for left boundary (i=0), moving wall BC incoporated
IF ( bound%beg=='reflect'.AND.mpi_rank==0 ) THEN
!!! Euler part !!!
! Roe averages
rhoroe = qval(1)%f(1)
umroe = uwall ! wall velocity
DO iv = Nveul,Nv
charsproe(iv)%f(0) = umroe
END DO
vfroe = qval(Nveul)%f(1)
vfroe1 = 1.D0 - vfroe
plpBroe = ( pl0+B_tait )*( rhoroe/vfroe1 )**n_tait
cmroe = DSQRT( n_tait*plpBroe/vfroe1/rhoroe )
charsproe(1)%f(0) = umroe - cmroe
charsproe(2)%f(0) = umroe + cmroe
! right eigenvectors at 1/2
rr(1)%f(0) = rhoroe
rr(2)%f(0) = rhoroe*charsproe(1)%f(0)
rr(3)%f(0) = rhoroe*charsproe(2)%f(0)
rr(4)%f(0) = rhoroe*umroe
rr(5)%f(0) = vfroe
! left eigenvectors at 1/2
ll(2)%f(0) = 0.5D0/rhoroe/cmroe
ll(1)%f(0) = ( umroe+vfroe1*cmroe )*ll(2)%f(0)
ll(3)%f(0) = ( -umroe+vfroe1*cmroe )*ll(2)%f(0)
ll(4)%f(0) = vfroe/rhoroe
ll(5)%f(0) = vfroe1/rhoroe
!!! bubble-dynamic part !!!
DO ib = 1,Nb
DO ir = 1,NR0
! right eigenvectors at 1/2
rr(ieig(ib,ir))%f(0) = qval(ibub(ib,ir))%f(1)
! left eigenvectors at 1/2
ll(ieig(ib,ir))%f(0) = qval(ibub(ib,ir))%f(1)
END DO
END DO
END IF
! for right boundary (i=N1)
IF ( bound%end=='reflect'.AND.mpi_rank==mpi_size-1 ) THEN
!!! Euler part !!!
! Roe averages
rhoroe = qval(1)%f(N1)
umroe = 0.D0
DO iv = Nveul,Nv
charsproe(iv)%f(N1) = umroe
END DO
vfroe = qval(Nveul)%f(N1)
vfroe1 = 1.D0 - vfroe
plpBroe = ( pl0+B_tait )*( rhoroe/vfroe1 )**n_tait
cmroe = DSQRT( n_tait*plpBroe/vfroe1/rhoroe )
charsproe(1)%f(N1) = umroe - cmroe
charsproe(2)%f(N1) = umroe + cmroe
! right eigenvectors at N1+1/2
rr(1)%f(N1) = rhoroe
rr(2)%f(N1) = rhoroe*charsproe(1)%f(N1)
rr(3)%f(N1) = rhoroe*charsproe(2)%f(N1)
rr(4)%f(N1) = rhoroe*umroe
rr(5)%f(N1) = vfroe
! left eigenvectors at N1+1/2
ll(2)%f(N1) = 0.5D0/rhoroe/cmroe
ll(1)%f(N1) = ( umroe+vfroe1*cmroe )*ll(2)%f(N1)
ll(3)%f(N1) = ( -umroe+vfroe1*cmroe )*ll(2)%f(N1)
ll(4)%f(N1) = vfroe/rhoroe
ll(5)%f(N1) = vfroe1/rhoroe
!!! bubble-dynamic part !!!
DO ib = 1,Nb
DO ir = 1,NR0
! right eigenvectors at N1+1/2
rr(ieig(ib,ir))%f(N1) = qval(ibub(ib,ir))%f(N1)
! left eigenvectors at N1+1/2
ll(ieig(ib,ir))%f(N1) = qval(ibub(ib,ir))%f(N1)
END DO
END DO
END IF
END SUBROUTINE s_roeaverage
!========================================================================
SUBROUTINE s_multiply_rr( v_in,st,lr )
INTEGER, INTENT(IN) :: st ! 0
INTEGER, INTENT(IN) :: lr ! -1, 0 (left or right celledge)
TYPE(coordinate), DIMENSION(Nv), INTENT(IN) :: v_in
INTEGER :: i
INTEGER :: ir
INTEGER :: ib
DO i = 1,N1
v_out(1)%f(i) = rr(1)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
+ rr(1)%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ rr(1)%f(ip(i,lr))*v_in(Nveul)%f(ip(i,st))
v_out(dir1)%f(i) = rr(2)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
+ rr(3)%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ rr(4)%f(ip(i,lr))*v_in(Nveul)%f(ip(i,st))
v_out(Nveul)%f(i) = rr(5)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
+ rr(5)%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ ( rr(5)%f(ip(i,lr))-1.D0 ) &
* v_in(Nveul)%f(ip(i,st))
DO ib = 1,Nb
DO ir = 1,NR0
v_out(ibub(ib,ir))%f(i) = &
rr(ieig(ib,ir))%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
+ rr(ieig(ib,ir))%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ v_in(ibub(ib,ir))%f(ip(i,st))
END DO
END DO
END DO
END SUBROUTINE s_multiply_rr
!========================================================================
SUBROUTINE s_multiply_ll( v_in,st,lr )
INTEGER, INTENT(IN) :: st ! -2, -1, 0, 1, 2 (five stencils for WENO5)
INTEGER, INTENT(IN) :: lr ! -1, 0 (left or right celledge)
TYPE(coordinate), DIMENSION(Nv), INTENT(IN) :: v_in
INTEGER :: i
INTEGER :: ir
INTEGER :: ib
REAL(KIND(0.D0)) :: tmp
DO i = 1,N1
v_out(1)%f(i) = ll(1)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
- ll(2)%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ 0.5D0*v_in(Nveul)%f(ip(i,st))
v_out(dir1)%f(i) = ll(3)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
+ ll(2)%f(ip(i,lr))*v_in(dir1)%f(ip(i,st)) &
+ 0.5D0*v_in(Nveul)%f(ip(i,st))
v_out(Nveul)%f(i) = ll(4)%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
- v_in(Nveul)%f(ip(i,st))
tmp = ll(5)%f(ip(i,lr))
DO ib = 1,Nb
DO ir = 1,NR0
v_out(ibub(ib,ir))%f(i) = &
- tmp*ll(ieig(ib,ir))%f(ip(i,lr))*v_in(1)%f(ip(i,st)) &
- ll(ieig(ib,ir))%f(ip(i,lr))*v_in(Nveul)%f(ip(i,st)) &
+ v_in(ibub(ib,ir))%f(ip(i,st))
END DO
END DO
END DO
END SUBROUTINE s_multiply_ll
!========================================================================
SUBROUTINE s_celledgevalue
! creates celledge values used in HLLC
INTEGER :: i
INTEGER :: iv
INTEGER :: ir
REAL(KIND(0.D0)) :: vf1
! conserved variables
DO iv = 1,Nv
DO i = 1,N1
lqval(iv)%f(i) = rweno(iv)%f(i) ! "L" state
rqval(iv)%f(i) = lweno(iv)%f(i) ! "R" state
END DO
END DO
IF ( bound%beg=='reflect'.AND.mpi_rank==0 ) THEN
! moving wall BC incorporated
lqval(1)%f(0) = lweno(1)%f(1)
lqval(dir1)%f(0) = 2.D0*uwall - lweno(dir1)%f(1)
DO iv = Nveul,Nv
lqval(iv)%f(0) = lweno(iv)%f(1)
END DO
END IF
IF ( bound%end=='reflect'.AND.mpi_rank==mpi_size-1 ) THEN
rqval(1)%f(N1+1) = rweno(1)%f(N1)
rqval(dir1)%f(N1+1) = -rweno(dir1)%f(N1)
DO iv = Nveul,Nv
rqval(iv)%f(N1+1) = rweno(iv)%f(N1)
END DO
END IF
! velocity, pressure & flux
DO i = Nbeg,N1
lvel(i) = lqval(dir1)%f(i)/lqval(1)%f(i)
vf1 = 1.D0 - lqval(Nveul)%f(i)
lpres(i) = ( pl0+B_tait )*( lqval(1)%f(i)/vf1 )**n_tait - B_tait
lflux(1)%f(i) = lqval(dir1)%f(i)
lflux(dir1)%f(i) = lqval(dir1)%f(i)*lvel(i) + lpres(i)
DO iv = Nveul,Nv
lflux(iv)%f(i) = lqval(iv)%f(i)*lvel(i)
END DO
END DO
DO i = 1,Nend
rvel(i) = rqval(dir1)%f(i)/rqval(1)%f(i)
vf1 = 1.D0 - rqval(Nveul)%f(i)
rpres(i) = ( pl0+B_tait )*( rqval(1)%f(i)/vf1 )**n_tait - B_tait
rflux(1)%f(i) = rqval(dir1)%f(i)
rflux(dir1)%f(i) = rqval(dir1)%f(i)*rvel(i) + rpres(i)
DO iv = Nveul,Nv
rflux(iv)%f(i) = rqval(iv)%f(i)*rvel(i)
END DO
END DO
END SUBROUTINE s_celledgevalue
!========================================================================
SUBROUTINE s_hllwavespeed
INTEGER :: i
REAL(KIND(0.D0)) :: soundsqr
REAL(KIND(0.D0)) :: soundsql
REAL(KIND(0.D0)) :: tmpl, tmpr
REAL(KIND(0.D0)) :: lp, lrho, lu, lvf ! "L" state
REAL(KIND(0.D0)) :: rp, rrho, ru, rvf ! "R" state
DO i = Nbeg,N1
rp = rpres(ip(i,1))
lp = lpres(i)
ru = rvel(ip(i,1))
lu = lvel(i)
rrho = rqval(1)%f(ip(i,1))
lrho = lqval(1)%f(i)
rvf = rqval(Nveul)%f(ip(i,1))
lvf = lqval(Nveul)%f(i)
soundsqr = n_tait*( rp+B_tait )/( 1.D0-rvf )/rrho
soundsql = n_tait*( lp+B_tait )/( 1.D0-lvf )/lrho
sr(i) = MAX( charsproe(2)%f(i),ru+DSQRT(soundsqr) )
sl(i) = MIN( charsproe(1)%f(i),lu-DSQRT(soundsql) )
! middle wavespeed
tmpl = sl(i) - lu
tmpr = sr(i) - ru
sstar(i) = ( rp-lp-rqval(dir1)%f(ip(i,1))*tmpr &
+ lqval(dir1)%f(i)*tmpl )/( lrho*tmpl-rrho*tmpr )
END DO
END SUBROUTINE s_hllwavespeed
!========================================================================
SUBROUTINE s_stop_rhsvar
DEALLOCATE( xvel )
NULLIFY( ip )
NULLIFY( ds )
NULLIFY( betaw0 )
NULLIFY( betaw1 )
NULLIFY( betaw2 )
NULLIFY( dwenor )
NULLIFY( dwenol )
NULLIFY( polyr0 )
NULLIFY( polyr1 )
NULLIFY( polyr2 )
NULLIFY( polyl0 )
NULLIFY( polyl1 )
NULLIFY( polyl2 )
NULLIFY( w3beta )
NULLIFY( w3dr )
NULLIFY( w3dl )
NULLIFY( w3polyr )
NULLIFY( w3polyl )
NULLIFY( vel1 )
NULLIFY( onesidebeg )
NULLIFY( onesideend )
DEALLOCATE( pres )
DEALLOCATE( sound )
DEALLOCATE( nbub )
DEALLOCATE( lpres )
DEALLOCATE( rpres )
DEALLOCATE( lvel )
DEALLOCATE( rvel )
DEALLOCATE( sl )
DEALLOCATE( sr )
DEALLOCATE( sstar )
DEALLOCATE( nsfx )
DEALLOCATE( velhf )
DEALLOCATE( nfx )
DEALLOCATE( rhsfx )
DEALLOCATE( rhsrc )
DEALLOCATE( fxtmp )
DEALLOCATE( qval )
DEALLOCATE( lflux )
DEALLOCATE( rflux )
DEALLOCATE( inweno )
DEALLOCATE( lweno )
DEALLOCATE( rweno )
DEALLOCATE( charsp )
DEALLOCATE( charsproe )
DEALLOCATE( linw )
DEALLOCATE( rinw )
DEALLOCATE( v_out )
DEALLOCATE( lqval )
DEALLOCATE( rqval )
DEALLOCATE( lqstar )
DEALLOCATE( rqstar )
DEALLOCATE( bub )
DEALLOCATE( rr )
DEALLOCATE( ll )
END SUBROUTINE s_stop_rhsvar
!========================================================================
END MODULE m_rhsvar