Sources Esope | Cast3M

conjwl
C CONJWL    SOURCE    CB215821  16/04/21    21:16:00     8920
       SUBROUTINE CONJWL(JTL,JTR,WVEC_L,WVEC_R,NVECT,TVECT,
     &                   ga)
C************************************************************************
C
C PROJET            :  CASTEM 2000
C
C NOM               :  CONJWL
C
C DESCRIPTION       :  Voir KONJA2
C
C LANGAGE           :  FORTRAN 77 + ESOPE 2000 (avec estensions CISI)
C
C AUTEUR            :  S. KUDRIAKOV, DM2S/SFME/LTMF
C
C************************************************************************
c----------------------------------------------------------------------
c GENERAL DESCRIPTION:
c             This subroutine provides jacobian jtl at the interfface
c             next to wall.
c For full descriptions please see file 'conjak.eso'.
c----------------------------------------------------------------------
c INPUT:
c
c      alpha   -- parameter of the AUSM+ scheme in the Pressure function;
c                 ( -3/4 &lt;= alpha &lt;= 3/16 )
c
c      beta    -- parameter of the AUSM+ scheme in the Mach function;
c                 ( -1/16 &lt;= beta &lt;= 1/2 )
c
c      wvec_l  -- vector of the primitive variables (rho,ux,uy,p) at the
c                 left cell;
c
c      wvec_r  -- vector of the primitive variables (rho,ux,uy,p) at the
c                 right cell;
c
c      nvect   -- normal vector to the interface (2 components in 2D);
c
c      tvect   -- tangential vector to the interface;
c
c      ga      -- ratio of the specific heats (assumed constant)
c----------------------------------------------------------------------
c
c OUTPUT:
c
c      jtl     -- jakobian matrix 4 by 4 - derivatives of the numerical
c                 flux function with respect to the conservative variables
c                 from the left cell;
c
c      jtr     -- jakobian matrix 4 by 4 - derivatives of the numerical
c                 flux function with respect to the conservative variables
c                 from the right cell.
c----------------------------------------------------------------------
      IMPLICIT INTEGER(I-N)
       real*8 wvec_l(4),wvec_r(4)
       real*8 nvect(2),tvect(2)
       real*8 jl(4,4),jr(4,4)
       real*8 wl(4,4),wr(4,4)
       real*8 jtl(4,4),jtr(4,4)
       real*8 alpha,beta
       real*8 ga, gm1
       real*8 n_x,n_y
       real*8 un_l, un_r
       real*8 ml,mr,Mplus,Mmin
       real*8 rold_l,uold_l,vold_l,pold_l,eold_l
       real*8 rold_r,uold_r,vold_r,pold_r,eold_r
       real*8 Pplus,Pmin
       real*8 temp_l,temp_r,brac_l,brac_r
       real*8 aleft, arigh, am
       real*8 damr_l,damr_r,damu_l,damu_r
       real*8 damv_l,damv_r,damp_l,damp_r
       real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
       real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
       real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
       real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
       real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
       real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
       real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
       real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
       real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
       real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
       real*8 tcoef,bcoef
       integer i,j,k
       parameter(alpha = 0.1875D0, beta = 0.125D0)
c-----------------------
       gm1=ga-1.0d0
c-----------------------
       n_x=nvect(1)
       n_y=nvect(2)
c----------------------------
c-----------------------
       rold_l=wvec_l(1)
       uold_l=wvec_l(2)
       vold_l=wvec_l(3)
       pold_l=wvec_l(4)
c-----------------------
       rold_r=wvec_r(1)
       uold_r=wvec_r(2)
       vold_r=wvec_r(3)
       pold_r=wvec_r(4)
c-----------------------
       eold_l=(uold_l*uold_l+vold_l*vold_l)/2.0d0
       eold_l=eold_l+pold_l/(gm1*rold_l)
       eold_r=(uold_r*uold_r+vold_r*vold_r)/2.0d0
       eold_r=eold_r+pold_r/(gm1*rold_r)
c-------------------------------------------------------------------
c Computation of the speed of sound and its derivatives
c---------------------------------------------------------------------
       aleft=SQRT(ga*pold_l/rold_l)
       arigh=SQRT(ga*pold_r/rold_r)
       am=0.5d0*(aleft+arigh)
c--------------------------------------------------------------------
         damr_r=-arigh/(4.0d0*rold_r)
         damu_r=0.0d0
         damv_r=0.0d0
         damp_r=ga/(4.0d0*arigh*rold_r)
c-----------------------
         damr_l=-aleft/(4.0d0*rold_l)
         damu_l=0.0d0
         damv_l=0.0d0
         damp_l=ga/(4.0d0*aleft*rold_l)
c----------------------------------------------------------------------
c  computing numerical Mach number and its derivatives
c----------------------------------------------------------------------
       un_l=uold_l*n_x+vold_l*n_y
       un_r=uold_r*n_x+vold_r*n_y
c----------------------------------------
       ml=un_l/am
       mr=un_r/am
c       print*,'ml,mr',ml,mr
c-------------------------------------
c  Mplus and Mmin are calligraphic
c  lettes M+ and M- from the paper
c-------------------------------------
       if(ABS(ml) .ge. 1.0d0) then
         Mplus=(ml+ABS(ml))/2.0d0
       else
         Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
         Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
       endif
c-----------------
       if(ABS(mr) .ge. 1.0d0) then
         Mmin=(mr-ABS(mr))/2.0d0
       else
         Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
         Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
       endif
c---------------------------------------
c Derivatives of ml and mr with respect
c to both sets of primitive variables:
c left  and right
c--------------------------------------
       temp_l=-un_l/(am*am)
       temp_r=-un_r/(am*am)
c--------
       dmlr_l=temp_l*damr_l
       dmlr_r=temp_l*damr_r
       dmrr_l=temp_r*damr_l
       dmrr_r=temp_r*damr_r
c--------
       dmlu_l=n_x/am+temp_l*damu_l
       dmlu_r=temp_l*damu_r
       dmru_l=temp_r*damu_l
       dmru_r=n_x/am+temp_r*damu_r
c--------
       dmlv_l=n_y/am+temp_l*damv_l
       dmlv_r=temp_l*damv_r
       dmrv_l=temp_r*damv_l
       dmrv_r=n_y/am+temp_r*damv_r
c--------
       dmlp_l=temp_l*damp_l
       dmlp_r=temp_l*damp_r
       dmrp_l=temp_r*damp_l
       dmrp_r=temp_r*damp_r
c---------------------------------------------------------------
c Computing the calligraphic P+ and P- with their derivatives
c---------------------------------------------------------------
       if(ml .ge. 1.0d0) then
         Pplus = 1.0d0
       else
         if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
           Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
           Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
         else
           Pplus = 0.0d0
         endif
       endif
c---------------------------------------------------------------
       if(mr .ge. 1.0d0) then
         Pmin = 0.0d0
       else
         if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
           Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
           Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
         else
           Pmin = 1.0d0
         endif
       endif
c---------------------------------------------------------------
       brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
       brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
       brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
c--------------
       brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
       brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
       brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
c---------------------------------------------------------------
       if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
         dPpr_l=brac_l*dmlr_l
         dPpr_r=brac_l*dmlr_r
c------------
         dPpu_l=brac_l*dmlu_l
         dPpu_r=brac_l*dmlu_r
c------------
         dPpv_l=brac_l*dmlv_l
         dPpv_r=brac_l*dmlv_r
c------------
         dPpp_l=brac_l*dmlp_l
         dPpp_r=brac_l*dmlp_r
c------------
       else
         dPpr_l=0.0d0
         dPpr_r=0.0d0
c-----------
         dPpu_l=0.0d0
         dPpu_r=0.0d0
c-----------
         dPpv_l=0.0d0
         dPpv_r=0.0d0
c-----------
         dPpp_l=0.0d0
         dPpp_r=0.0d0
c-----------
       endif
c---------------------------------------------------------------
       if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
         dPmr_l=brac_r*dmrr_l
         dPmr_r=brac_r*dmrr_r
c------------
         dPmu_l=brac_r*dmru_l
         dPmu_r=brac_r*dmru_r
c------------
         dPmv_l=brac_r*dmrv_l
         dPmv_r=brac_r*dmrv_r
c------------
         dPmp_l=brac_r*dmrp_l
         dPmp_r=brac_r*dmrp_r
c------------
       else
         dPmr_l=0.0d0
         dPmr_r=0.0d0
c-----------
         dPmu_l=0.0d0
         dPmu_r=0.0d0
c-----------
         dPmv_l=0.0d0
         dPmv_r=0.0d0
c-----------
         dPmp_l=0.0d0
         dPmp_r=0.0d0
c-----------
       endif
c---------------------------------------------------------------------
c computing pmid -- p_{1/2} and its derivatives
c---------------------------------------------------------------------
       dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
       dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
       dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
       dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
c----------------------------
       dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
       dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
       dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
       dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
c---------------------------------------------------------------------
c  !!!!!!!!!!!!!!!!!!  JACOBIAN  !!!!!!!!!!!!!!!!!!!!!!!!!!!!
c---------------------------------------------------------------------
       jl(1,1)=0.0D0
       jl(1,2)=0.0D0
       jl(1,3)=0.0D0
       jl(1,4)=0.0D0
c------------------------------------
       jr(1,1)=0.0D0
       jr(1,2)=0.0D0
       jr(1,3)=0.0D0
       jr(1,4)=0.0D0
c------------------------------------
ccccc    f222222222222  -------------
c------------------------------------
c---------------------------------------------------------
       jl(2,1)=n_x*dpir_l
c-------------------
       jl(2,2)=n_x*dpiu_l
c-------------------
       jl(2,3)=n_x*dpiv_l
c-------------------
       jl(2,4)=n_x*dpip_l
c-------------------------------------------------------------
       jr(2,1)=n_x*dpir_r
c-------------------
       jr(2,2)=n_x*dpiu_r
c-------------------
       jr(2,3)=n_x*dpiv_r
c-------------------
       jr(2,4)=n_x*dpip_r
c-------------------------------------------------------------
c------------    f33333333333333333333   ---------------------
c-------------------------------------------------------------
       jl(3,1)=n_y*dpir_l
c-------------------
       jl(3,2)=n_y*dpiu_l
c-------------------
       jl(3,3)=n_y*dpiv_l
c-------------------
       jl(3,4)=n_y*dpip_l
c-------------------------------------------------------------
       jr(3,1)=n_y*dpir_r
c-------------------
       jr(3,2)=n_y*dpiu_r
c-------------------
       jr(3,3)=n_y*dpiv_r
c-------------------
       jr(3,4)=n_y*dpip_r
c-------------------------------------------------------------
c  ------  f44444444444444444444444444444 ---------
c-------------------------------------------------------------
       jl(4,1)=0.0D0
c---------------------
       jl(4,2)=0.0D0
c---------------------
       jl(4,3)=0.0D0
c---------------------
       jl(4,4)=0.0D0
c----------------------------------------------------------
c----------------------------------------------------------
       jr(4,1)=0.0D0
c---------------------
       jr(4,2)=0.0D0
c---------------------
       jr(4,3)=0.0D0
c---------------------
       jr(4,4)=0.0D0
c----------------------------------------------------------
c  matrixes wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
c----------------------------------------------------------
       wl(1,1)=1.0d0
       wl(1,2)=0.0d0
       wl(1,3)=0.0d0
       wl(1,4)=0.0d0
c------------------------------
       wl(2,1)=-uold_l/rold_l
       wl(2,2)=1.0d0/rold_l
       wl(2,3)=0.0d0
       wl(2,4)=0.0d0
c------------------------------
       wl(3,1)=-vold_l/rold_l
       wl(3,2)=0.0d0
       wl(3,3)=1.0d0/rold_l
       wl(3,4)=0.0d0
c------------------------------
       wl(4,1)=gm1*(uold_l*uold_l+vold_l*vold_l)/2.0d0
       wl(4,2)=-uold_l*gm1
       wl(4,3)=-vold_l*gm1
       wl(4,4)=gm1
c------------------------------
c------------------------------
       wr(1,1)=1.0d0
       wr(1,2)=0.0d0
       wr(1,3)=0.0d0
       wr(1,4)=0.0d0
c------------------------------
       wr(2,1)=-uold_r/rold_r
       wr(2,2)=1.0d0/rold_r
       wr(2,3)=0.0d0
       wr(2,4)=0.0d0
c------------------------------
       wr(3,1)=-vold_r/rold_r
       wr(3,2)=0.0d0
       wr(3,3)=1.0d0/rold_r
       wr(3,4)=0.0d0
c------------------------------
       wr(4,1)=gm1*(uold_r*uold_r+vold_r*vold_r)/2.0d0
       wr(4,2)=-uold_r*gm1
       wr(4,3)=-vold_r*gm1
       wr(4,4)=gm1
c----------------------------------------------
c----------------------------------------------
       do 1 i=1,4
        do 2 j=1,4
         jtl(i,j)=0.0d0
         jtr(i,j)=0.0d0
         do 3 k=1,4
          jtl(i,j)=jtl(i,j)+jl(i,k)*wl(k,j)
          jtr(i,j)=jtr(i,j)+jr(i,k)*wr(k,j)
 3       continue
 2      continue
 1     continue
c-----------------------------
       tcoef=nvect(1)*tvect(2)+tvect(1)*nvect(2)
       bcoef=nvect(1)*tvect(2)-tvect(1)*nvect(2)
c-----------------------------
       do 11 i=1,4
         jtl(i,1)=jtl(i,1)+jtr(i,1)
         jtl(i,2)=jtl(i,2)+jtr(i,2)*(-tcoef/bcoef)+
     &            jtr(i,3)*2.0d0*nvect(1)*tvect(1)/bcoef
         jtl(i,3)=jtl(i,3)+jtr(i,2)*(-2.0d0*nvect(2)*tvect(2)/bcoef)+
     &            jtr(i,3)*tcoef/bcoef
         jtl(i,4)=jtl(i,4)+jtr(i,4)
 11    continue
c----------------------------------------------------------------------
       return
       end