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wwm_nums1d.F90
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#include "wwm_functions.h"
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE COMPUTE_ADVECTION1D_QUICKEST_A()
USE DATAPOOL
IMPLICIT NONE
INTEGER :: ISTEP
INTEGER :: IS, ID, IT
INTEGER :: INC
REAL(rkind) :: CFL, REST, DT41A, DX
REAL(rkind) :: ACQ(0:MNP+1), CAXQ(0:MNP+1)
ACQ = ZERO
CAXQ = ZERO
INC = 1
ISTEP = 0
DX = XP(4)-XP(3)
!todo IS ID ordering
DO IS = 1, NUMSIG
DO ID = 1, NUMDIR
ACQ(1:MNP) = AC2(IS,ID,:)
CAXQ(1:MNP) = CG(IS,:)*COSTH(ID)+CURTXY(:,1)
IF (LVAR1D) THEN
CFL = MAXVAL ( ABS(CAXQ) * DT4A / MINVAL(DX2) )
ELSE
CFL = MAXVAL ( ABS(CAXQ) * DT4A / DX )
END IF
REST = ABS(MOD(CFL,ONE))
IF (CFL .LT. THR) THEN
ISTEP = 0
ELSE
IF (CFL .LT. 1.0) THEN
ISTEP = 1
ELSE
IF (REST .LT. THR) THEN
ISTEP = INT(CFL)
ELSE
ISTEP = INT(CFL) + 1
END IF
END IF
END IF
DT41A = DT4A/ISTEP
CAXQ = MAX(ZERO,CAXQ)
DO IT = 1, ISTEP
IF (LVAR1D) THEN
IF (LWBSET) THEN
CAXQ(0) = CAXQ(1)
ACQ(0) = WBAC(IS,ID,1)
CAXQ(MNP+1) = CAXQ(MNP)
ACQ(MNP+1) = ACQ(MNP)
ELSE
CAXQ(0) = CAXQ(0)
ACQ(0) = ACQ(1)
CAXQ(MNP+1) = CAXQ(MNP)
ACQ(MNP+1) = ACQ(MNP)
END IF
CALL QUICKEST_VAR_ADV(MNP,ACQ,CAXQ,DT41A,DX1,DX2)
ELSE
IF (LWBSET) THEN
CAXQ(0) = CAXQ(1)
ACQ(0) = WBAC(IS,ID,1)
CAXQ(MNP+1) = CAXQ(MNP)
ACQ(MNP+1) = ACQ(MNP)
ELSE
CAXQ(0) = CAXQ(1)
ACQ(0) = ZERO
CAXQ(MNP+1) = CAXQ(MNP)
ACQ(MNP+1) = ACQ(MNP)
END IF
CALL QUICKEST_ADV(MNP,INC,ACQ,CAXQ,DT41A,DX)
END IF
END DO
AC2(IS,ID,:) = ACQ(1:MNP)
END DO
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE QUICKEST_ADV( MX, INC, Q, CS, DT, DX )
USE DATAPOOL, ONLY : RKIND, ZERO, ONE
IMPLICIT NONE
INTEGER, INTENT(IN) :: MX
INTEGER, INTENT(IN) :: INC
REAL(rkind), INTENT(INOUT) :: Q(0:MX+1)
REAL(rkind), INTENT(INOUT) :: CS(0:MX+1)
REAL(rkind), INTENT(IN) :: DT, DX
REAL(rkind) :: CFLL(0:MX+1), FLA(0:MX+1)
INTEGER :: IXY, IXYC, IXYU, IXYD
REAL(rkind) :: CFL
REAL(rkind) :: DQ, DQNZ, QCN, QBN, QBR, QB
REAL(rkind) :: CFAC
DO IXY = 0, MX+1
CFLL(IXY) = CS(IXY) * DT / DX
END DO
!
! Fluxes for central points (Fi,+)
!
DO IXY = 1, MX - 1
CFL = 0.5_rkind * ( CFLL(IXY) + CFLL(IXY+INC) )
IXYC = IXY - INC * INT( MIN( ZERO, SIGN(1.1_rkind,CFL) ) )
QB = 0.5_rkind*((1.0-CFL)*Q(IXY+INC)+(1.0+CFL)*Q(IXY))-(1.0-CFL**2.0)/6.0*(Q(IXYC-INC)-2.0*Q(IXYC)+Q(IXYC+INC))
IXYU = IXYC - INC * INT( SIGN(1.1_rkind,CFL) )
IXYD = 2*IXYC - IXYU
DQ = Q(IXYD) - Q(IXYU) ! DEL = Qd - Qu
DQNZ = SIGN( MAX(10E-15_rkind, ABS(DQ)), DQ )
QCN = ( Q(IXYC) - Q(IXYU) ) / DQNZ ! ~Qc = ( Qc - Qu ) / DEL
QCN = MIN( 1.1_rkind, MAX( -0.1_rkind, QCN ) ) ! -0.1 < ~Qc < 1.1_rkind
QBN = MAX( (QB - Q(IXYU)) / DQNZ, QCN ) ! ~Qf = ( Qf - Qu ) / DEL
QBN = MIN( QBN, ONE, QCN/MAX( 1.0E-10_rkind, ABS(CFL) ) )
QBR = Q(IXYU) + QBN * DQ ! Qf = ~Qf * DEL + Qu
CFAC = MyREAL( INT(2.0*ABS(QCN-0.5_rkind)) ) ! if 0 < ~Qc < 1, then CFAC = 1.0, Qf = Qc
QB = (ONE - CFAC) * QBR + CFAC * Q(IXYC)
FLA(IXY) = CFL * QB
END DO
!
! Fluxes for points with boundary above
!
IXY = 0
CFL = CFLL(IXY)
IXYC = IXY - INC * INT(MIN(ZERO, SIGN(1.1_rkind,CFL) ) )
FLA(IXY) = CFL * Q(IXY)
!
! Fluxes for points with boundary below
!
IXY = MX
CFL = CFLL(IXY+INC)
IXYC = IXY - INC * INT(MIN(ZERO, SIGN(1.1_rkind,CFL) ) )
FLA(IXY) = CFL * Q(IXY)
DO IXY = 1, MX
Q(IXY) = MAX(ZERO,Q(IXY) + FLA(IXY-INC) - FLA(IXY))
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE QUICKEST_VAR_ADV(MX, Q, CS, DT, DX1, DX2)
USE DATAPOOL, ONLY : RKIND, ZERO, ONE
IMPLICIT NONE
INTEGER, INTENT(IN) :: MX
REAL(rkind), INTENT(IN) :: DT
REAL(rkind), INTENT(INOUT) :: Q(0:MX+1)
REAL(rkind), INTENT(IN) :: CS(0:MX+1), DX1(0:MX+1), DX2(0:MX+1)
REAL(rkind) :: FLA(0:MX+1)
INTEGER :: IXY, IXYC, IXYU, IXYD
REAL(rkind) :: CSM, CFL
REAL(rkind) :: DQ, DQNZ, QCN, QBN, QBR, QB
REAL(rkind) :: CFAC
DO IXY = 1, MX-1
CSM = 0.5_rkind * ( CS(IXY) + CS(IXY+1) )
CFL = DT * CSM / DX2(IXY)
IXYC = IXY - 1 * INT(MIN(ZERO , SIGN(1.1_rkind,CFL) ) )
QB = 0.5_rkind *((ONE-CFL)*Q(IXY+1)+(1.+CFL)*Q(IXY)) - DX2(IXY)**2/DX1(IXYC) * (1.-CFL**2) / 6. * &
& ( (Q(IXYC+1)-Q(IXYC))/DX2(IXYC)-(Q(IXYC)-Q(IXYC-1))/DX2(IXYC-1) )
IXYU = IXYC - 1 * INT ( SIGN (1.1_rkind,CFL) )
IXYD = 2*IXYC - IXYU
DQ = Q(IXYD) - Q(IXYU)
DQNZ = SIGN ( MAX(10E-10_rkind,ABS(DQ)) , DQ )
QCN = ( Q(IXYC) - Q(IXYU) ) / DQNZ
QCN = MIN ( 1.1_rkind, MAX ( -0.1_rkind , QCN ) )
QBN = MAX ( (QB-Q(IXYU))/DQNZ , QCN )
QBN = MIN ( QBN , ONE , QCN/MAX(10E-10_rkind,ABS(CFL)) )
QBR = Q(IXYU) + QBN*DQ
CFAC = MyREAL ( INT( 2. * ABS(QCN-0.5_rkind) ) )
QB = (ONE-CFAC)*QBR + CFAC*Q(IXYC)
FLA(IXY) = CSM * QB
END DO
IXY = 0
IXYC = IXY - 1 * INT( MIN(ZERO, SIGN(1.1_rkind,CS(IXY)) ) )
FLA(IXY) = MIN(ZERO,CS(IXY)) * Q(IXYC)
!
IXY = MX
IXYC = IXY - 1 * INT( MIN(ZERO, SIGN(1.1_rkind,CS(IXY)) ) )
FLA(IXY) = MAX(ZERO,CS(IXY)) * Q(IXYC)
DO IXY = 1, MX
Q(IXY) = MAX(ZERO, Q(IXY) - ( FLA(IXY)-FLA(IXY-1) ) * DT/DX1(IXY))
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE QUICKEST_DIR(MX, LCIRD, Q, CS, DT, DX)
USE DATAPOOL, ONLY : RKIND, ZERO, ONE
IMPLICIT NONE
INTEGER, INTENT(IN) :: MX
LOGICAL, INTENT(IN) :: LCIRD
REAL(rkind), INTENT(INOUT) :: Q(0:MX+1), CS(0:MX+1)
REAL(rkind), INTENT(IN) :: DT, DX
REAL(rkind) :: CFLL(0:MX+1), FLA(0:MX+1)
INTEGER :: IXY, IXYC, IXYU, IXYD, INC
REAL(rkind) :: CFL
REAL(rkind) :: DQ, DQNZ, QCN, QBN, QBR, QB
REAL(rkind) :: CFAC
INC = 1
CS(0) = CS(MX)
CS(MX+1) = CS(1)
Q(0) = Q(MX)
Q(MX+1) = Q(1)
DO IXY = 0, MX+1
CFLL(IXY) = CS(IXY) * DT / DX
END DO
!
! Fluxes for central points (Fi,+)
!
DO IXY = 1, MX - 1
CFL = 0.5_rkind * ( CFLL(IXY) + CFLL(IXY+INC) )
IXYC = IXY - INC * INT(MIN(ZERO, SIGN(1.1_rkind,CFL) ) )
QB = 0.5_rkind*((1.0-CFL)*Q(IXY+INC)+(1.0+CFL)*Q(IXY))-(1.0-CFL**2.0)/6.0*(Q(IXYC-INC)-2.0*Q(IXYC)+Q(IXYC+INC))
IXYU = IXYC - INC * INT( SIGN(1.1_rkind,CFL) )
IXYD = 2*IXYC - IXYU
DQ = Q(IXYD) - Q(IXYU) ! DEL = Qd - Qu
DQNZ = SIGN( MAX(10E-15_rkind, ABS(DQ)), DQ )
QCN = ( Q(IXYC) - Q(IXYU) ) / DQNZ ! ~Qc = ( Qc - Qu ) / DEL
QCN = MIN( 1.1_rkind, MAX( -0.1_rkind, QCN ) ) ! -0.1 < ~Qc < 1.1_rkind
QBN = MAX( (QB - Q(IXYU)) / DQNZ, QCN ) ! ~Qf = ( Qf - Qu ) / DEL
QBN = MIN( QBN, ONE, QCN/MAX( 1.0E-10_rkind, ABS(CFL) ) )
QBR = Q(IXYU) + QBN * DQ ! Qf = ~Qf * DEL + Qu
CFAC = MyREAL( INT(2.0*ABS(QCN-0.5_rkind)) ) ! if 0 < ~Qc < 1, then CFAC = 1.0, Qf = Qc
QB = (1.0 - CFAC) * QBR + CFAC * Q(IXYC)
FLA(IXY) = CFL * QB
END DO
!
! Fluxes for points with boundary above
!
IXY = 0
CFL = CFLL(IXY)
IXYC = IXY - INC * INT( MIN(ZERO, SIGN(1.1_rkind,CFL) ) )
FLA(IXY) = CFL * Q(IXYC)
! Fluxes for points with boundary below
!
IXY = MX
CFL = CFLL(MX)
IXYC = IXY - INC * INT( MIN(ZERO, SIGN(1.1_rkind,CFL) ) )
FLA(IXY) = CFL * Q(IXYC)
!
! check this !
IF (LCIRD) THEN
FLA(0) = FLA(MX)
ELSE
FLA(0) = ZERO
FLA(MX) = ZERO
END IF
!
! Propagation
!
DO IXY = 1, MX
Q(IXY) = MAX(ZERO,Q(IXY) + FLA(IXY-INC) - FLA(IXY))
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************
SUBROUTINE QUICKEST_FREQ(MX, Q, CS, DT, DX1, DX2)
USE DATAPOOL, ONLY : RKIND, ZERO, ONE
IMPLICIT NONE
INTEGER, INTENT(IN) :: MX
REAL(rkind), INTENT(IN) :: DT
REAL(rkind), INTENT(INOUT) :: Q(0:MX+1)
REAL(rkind), INTENT(IN) :: CS(0:MX+1)
REAL(rkind), INTENT(IN) :: DX1(0:MX+1), DX2(0:MX+1)
REAL(rkind) :: FLA(0:MX+1)
INTEGER :: IXY, IXYC, IXYU, IXYD
REAL(rkind) :: CSM, CFL
REAL(rkind) :: DQ, DQNZ, QCN, QBN, QBR, QB
REAL(rkind) :: CFAC
!
! Fluxes for central points (Fi,+)
!
DO IXY = 1, MX-1
CSM = 0.5_rkind * ( CS(IXY) + CS(IXY+1) )
CFL = DT * CSM / DX2(IXY)
IXYC = IXY - 1 * INT(MIN(ZERO , SIGN(1.1_rkind,CFL) ) )
QB = 0.5_rkind *((1.-CFL)*Q(IXY+1)+(1.+CFL)*Q(IXY)) - &
& DX2(IXY)**2/DX1(IXYC) * (1.-CFL**2) / 6. * &
& ( (Q(IXYC+1)-Q(IXYC))/DX2(IXYC)-(Q(IXYC)-Q(IXYC-1))/DX2(IXYC-1) )
IXYU = IXYC - 1 * INT ( SIGN (1.1_rkind,CFL) )
IXYD = 2*IXYC - IXYU
DQ = Q(IXYD) - Q(IXYU)
DQNZ = SIGN ( MAX(1.E-15_rkind,ABS(DQ)) , DQ )
QCN = ( Q(IXYC) - Q(IXYU) ) / DQNZ
QCN = MIN ( 1.1_rkind, MAX ( -0.1_rkind , QCN ) )
QBN = MAX ( (QB-Q(IXYU))/DQNZ , QCN )
QBN = MIN ( QBN , ONE , QCN/MAX(1.E-10_rkind,ABS(CFL)) )
QBR = Q(IXYU) + QBN*DQ
CFAC = MyREAL ( INT( 2. * ABS(QCN-0.5_rkind) ) )
QB = (1.-CFAC)*QBR + CFAC*Q(IXYC)
FLA(IXY) = CSM * QB
END DO
!
! Fluxes for points with boundary above
!
IXY = 0
IXYC = IXY - 1 * INT( MIN( 0.0_rkind, SIGN(1.1_rkind,CFL) ) )
FLA(0) = CS(0) * Q(0) ! The flux at the uper boundary of the spectrum is given in the calling routine ...
!
! Fluxes for points with boundary below
!
IXY = MX
IXYC = IXY - 1 * INT( MIN( 0.0_rkind, SIGN(1.1_rkind,CFL) ) )
FLA(MX) = CS(MX+1) * Q(MX+1) ! The flux at the uper boundary of the spectrum is given in the calling routine ...
!
! Fluxes for points with boundary above
!
! IXY = 0
! IXYC = IXY - INT( MIN( 0.0_rkind, SIGN(1.1_rkind,CS(IXY)) ) )
! FLA(IXY) = CS(IXY) * Q(IXYC)
!
! Fluxes for points with boundary below
!
! IXY = MX
! IXYC = IXY - INT( MIN( 0.0_rkind, SIGN(1.1_rkind,CS(IXY)) ) )
! FLA(IXY) = CS(IXY) * Q(IXYC)
DO IXY = 1, MX
Q(IXY) = MAX(ZERO, Q(IXY) - (FLA(IXY)-FLA(IXY-1)) * DT/DX1(IXY))
END DO
END SUBROUTINE
!**********************************************************************
!* *
!**********************************************************************