C JA3DBM SOURCE CHAT 05/01/13 00:47:49 5004 SUBROUTINE JA3DBM(JTL,JTR,WVEC_L,WVEC_R,NVECT,TVEC1,TVEC2, & ga,v_inf) C************************************************************************ C C PROJET : CASTEM 2000 C C NOM : JA3DBM (Bas-Mach jacobian for 3D) C C DESCRIPTION : Voir KONJA2 C C LANGAGE : FORTRAN 77 + ESOPE 2000 (avec estensions CISI) C C AUTEUR : S. KUDRIAKOV, A. BECCANTINI DM2S/SFME/LTMF C C************************************************************************ C c---------------------------------------------------------------------- c GENERAL DESCRIPTION: c This subroutine provides the jacobians, which are c the derivatives of the numerical flux function, c with respect to the right and left conservative variables c The low-mach number corrections are made. c c EQUATIONS: 3D Euler equations of gas dynamics c c c REFERENCE: 1) JCP, 129, 364-382 (1996) c " A Sequel to AUSM: AUSM+ "; c M.S.Liou c 2) AIAA Journal, Sept. 1998 c "Low-Diffusion Flux-Splitting Methods for Flows at All Speeds" c J.R.Edwards and M.S.Liou c---------------------------------------------------------------------- c---------------------------------------------------------------------- c INPUT: c c alpha -- parameter of the AUSM+ scheme in the Pressure function; c ( -3/4 <= alpha <= 3/16 ) (imposed as a parameter) c c beta -- parameter of the AUSM+ scheme in the Mach function; c ( -1/16 <= beta <= 1/2 ) (imposed as a parameter) c c wvec_l == (gamg,rhog,pg,ung,utg,uvg) -- c vector of the primitive variables c at the left cell; c c wvec_r == (gamd,rhod,pd,und,utd,uvd) -- c vector of the primitive variables c at the right cell; c c nvect, tvec1, tvec2 --- normal and tangent vectors c to the cell interface c c ga ---- ratio of the specific heats of the gas c c v_inf -- parameter for choosing the reference velocity c when the magnitude of the physical velocity c is close to zero c---------------------------------------------------------------------- c c OUTPUT: c c jtl -- jakobian matrix 5 by 5 - derivatives of the numerical c flux function with respect to the conservative variables c from the left cell; c c jtr -- jakobian matrix 5 by 5 - 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(5),wvec_r(5) real*8 nvect(3),tvec1(3),tvec2(3) real*8 jl(5,5),jr(5,5) real*8 wl(5,5),wr(5,5) real*8 jtl(5,5),jtr(5,5) real*8 alpha,beta,upr_l,upr_r,v_inf real*8 ga, gm1,temph real*8 n_x,n_y,n_z,t1_x,t1_y,t1_z,t2_x,t2_y,t2_z real*8 un_l,un_r,ut1_l,ut1_r,ut2_l,ut2_r real*8 ml,mr,Mplus,Mmin,mmid real*8 mpl_m, mmin_m,am real*8 rold_l,uold_l,vold_l,wold_l,pold_l,eold_l real*8 rold_r,uold_r,vold_r,wold_r,pold_r,eold_r real*8 Pplus,Pmin real*8 hr_l,hr_r real*8 br1,br2,br3,temp_l,temp_r,brac_l,brac_r real*8 aleft, arigh real*8 damr_l,damr_r,damu_l,damu_r real*8 damv_l,damv_r,damp_l,damp_r real*8 damw_l,damw_r real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r real*8 dmlw_l,dmlw_r real*8 dmrr_l,dmrr_r,dmru_l,dmru_r real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r real*8 dmrw_l,dmrw_r real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r real*8 dMpw_l,dMpw_r real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r real*8 dMmw_l,dMmw_r real*8 dmir_l,dmir_r,dmiu_l,dmiu_r real*8 dmiv_l,dmiv_r,dmip_l,dmip_r real*8 dmiw_l,dmiw_r real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r real*8 d3mw_l,d3mw_r real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r real*8 d2mw_l,d2mw_r real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r real*8 dPpw_l,dPpw_r real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r real*8 dPmw_l,dPmw_r real*8 dpir_l,dpir_r,dpiu_l,dpiu_r real*8 dpiv_l,dpiv_r,dpip_l,dpip_r real*8 dpiw_l,dpiw_r real*8 epsil,qq,amw,Mmin1,Mplus1 real*8 fmid,mlw,mrw,termp real*8 ur_r,ur_l,urm,mhalf,mhalfr real*8 durr_l,durr_r,duru_l,duru_r real*8 durv_l,durv_r,durp_l,durp_r real*8 durw_l,durw_r real*8 dmhr_l,dmhr_r,dmhu_l,dmhu_r real*8 dmhv_l,dmhv_r,dmhp_l,dmhp_r real*8 dmhw_l,dmhw_r real*8 dmfr_l,dmfr_r,dmfu_l,dmfu_r real*8 dmfv_l,dmfv_r,dmfp_l,dmfp_r real*8 dmfw_l,dmfw_r real*8 dfm_mf,dfm_mh real*8 dfmr_l,dfmr_r,dfmu_l,dfmu_r real*8 dfmv_l,dfmv_r,dfmp_l,dfmp_r real*8 dfmw_l,dfmw_r real*8 m1mr_l,m1mr_r,m1mu_l,m1mu_r real*8 m1mv_l,m1mv_r,m1mp_l,m1mp_r real*8 m1mw_l,m1mw_r real*8 m1pr_l,m1pr_r,m1pu_l,m1pu_r real*8 m1pv_l,m1pv_r,m1pp_l,m1pp_r real*8 m1pw_l,m1pw_r real*8 tmpr_l,tmpr_r,tmpu_l,tmpu_r real*8 tmpv_l,tmpv_r,tmpp_l,tmpp_r real*8 tmpw_l,tmpw_r,rum real*8 rumr_l,rumu_l,rumv_l,rumw_l,rump_l real*8 rumr_r,rumu_r,rumv_r,rumw_r,rump_r real*8 sw_l,sw_r,top,bot,bots,coef,canc real*8 sr_l,sr_r,su_l,su_r,sv_l,sv_r,sp_l,sp_r integer i,j,k parameter(alpha = 0.1875D0, beta = 0.125D0) parameter(epsil = 1.0d0) canc=1.0d0 upr_l=0.0d0 upr_r=0.0d0 c----------------------- gm1=ga-1.0d0 c----------------------- n_x=nvect(1) n_y=nvect(2) n_z=nvect(3) c------------------- t1_x=tvec1(1) t1_y=tvec1(2) t1_z=tvec1(3) c------------------- t2_x=tvec2(1) t2_y=tvec2(2) t2_z=tvec2(3) c------------------------------------- rold_l=wvec_l(1) uold_l=wvec_l(2) vold_l=wvec_l(3) wold_l=wvec_l(4) pold_l=wvec_l(5) c----------------------- rold_r=wvec_r(1) uold_r=wvec_r(2) vold_r=wvec_r(3) wold_r=wvec_r(4) pold_r=wvec_r(5) c----------------------- eold_l=(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0 eold_l=eold_l+pold_l/(gm1*rold_l) eold_r=(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0 eold_r=eold_r+pold_r/(gm1*rold_r) c------------------------------------------------------------------ c Computing reference velocity and its derivatives c see Eq.(2) of the Ref.(2). c------------------------------------------------------------------ aleft=sqrt(ga*pold_l/rold_l) arigh=sqrt(ga*pold_r/rold_r) qq=sqrt(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l) if(qq .lt. (epsil*v_inf)) then ur_l = epsil*v_inf durr_l=0.0d0 duru_l=0.0d0 durv_l=0.0d0 durw_l=0.0d0 durp_l=0.0d0 else ur_l=qq durr_l=0.0d0 duru_l=uold_l/qq durv_l=vold_l/qq durw_l=wold_l/qq durp_l=0.0d0 endif c------------------------------------------------------------------- if(ur_l .ge. aleft) then ur_l=aleft durr_l=-aleft/(2.0d0*rold_l) duru_l=0.0d0 durv_l=0.0d0 durw_l=0.0d0 durp_l=ga/(2.0d0*aleft*rold_l) endif c------------------------------------------------------------------- if(ur_l .lt. upr_l) then ur_l=upr_l durr_l=0.0d0 duru_l=0.0d0 durv_l=0.0d0 durw_l=0.0d0 durp_l=0.0d0 endif c------------------------------------------------------------------- qq=sqrt(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r) if(qq .lt. (epsil*v_inf)) then ur_r = epsil*v_inf durr_r=0.0d0 duru_r=0.0d0 durv_r=0.0d0 durw_r=0.0d0 durp_r=0.0d0 else ur_r=qq durr_r=0.0d0 duru_r=uold_r/qq durv_r=vold_r/qq durw_r=wold_r/qq durp_r=0.0d0 endif c------------------------------------------------------------------ if(ur_r .ge. arigh) then ur_r=arigh durr_r=-arigh/(2.0d0*rold_r) duru_r=0.0d0 durv_r=0.0d0 durw_r=0.0d0 durp_r=ga/(2.0d0*arigh*rold_r) endif c------------------------------------------------------------------ if(ur_r .lt. upr_r) then ur_r=upr_r durr_r=0.0d0 duru_r=0.0d0 durv_r=0.0d0 durw_r=0.0d0 durp_r=0.0d0 endif c------------------------------------------------------------------ c Reference velocity at the interface is taken as an average c of the reference velocities of the neighbouring cells c------------------------------------------------------------------- urm=0.5d0*(ur_l+ur_r) durr_l=0.5d0*durr_l duru_l=0.5d0*duru_l durv_l=0.5d0*durv_l durw_l=0.5d0*durw_l durp_l=0.5d0*durp_l c------------------------- durr_r=0.5d0*durr_r duru_r=0.5d0*duru_r durv_r=0.5d0*durv_r durw_r=0.5d0*durw_r durp_r=0.5d0*durp_r c------------------------------------------------------------------- c Computation of the speed of sound and its derivatives; c numerical speed of sound at the interface is taken as an average c of the speeds of sounds of the neighbouring cells c------------------------------------------------------------------- am=0.5d0*(aleft+arigh) c------------------------------------------------------------------- if(abs(urm/am-1.0d0).le.0.000001d0) then coef=0.0d0 else coef=1.0d0 endif c------------------------------------------------------------------- c Computation of the speed of sound and its derivatives; c numerical speed of sound at the interface is taken as an average c of the speeds of sounds of the neighbouring cells c-------------------------------------------------------------------- damr_r=-arigh/(4.0d0*rold_r) damu_r=0.0d0 damv_r=0.0d0 damw_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 damw_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+wold_l*n_z un_r=uold_r*n_x+vold_r*n_y+wold_r*n_z c---------- ut1_l=uold_l*t1_x+vold_l*t1_y+wold_l*t1_z ut1_r=uold_r*t1_x+vold_r*t1_y+wold_r*t1_z c---------- ut2_l=uold_l*t2_x+vold_l*t2_y+wold_l*t2_z ut2_r=uold_r*t2_x+vold_r*t2_y+wold_r*t2_z c---------------------------------------- ml=un_l/am mr=un_r/am mhalf=0.5d0*(un_l+un_r)/am c--------------------- top=0.5d0*(un_l+un_r)/(am*am) dmhr_l=-top*damr_l dmhu_l=n_x/2.0d0/am-top*damu_l dmhv_l=n_y/2.0d0/am-top*damv_l dmhw_l=n_z/2.0d0/am-top*damw_l dmhp_l=-top*damp_l c--------------------- dmhr_r=-top*damr_r dmhu_r=n_x/2.0d0/am-top*damu_r dmhv_r=n_y/2.0d0/am-top*damv_r dmhw_r=n_z/2.0d0/am-top*damw_r dmhp_r=-top*damp_r c-------------------------------- mhalfr=urm/am c-------------------------------- top=urm/(am*am) dmfr_l=durr_l/am-top*damr_l dmfu_l=duru_l/am-top*damu_l dmfv_l=durv_l/am-top*damv_l dmfw_l=durw_l/am-top*damw_l dmfp_l=durp_l/am-top*damp_l c--------------------- dmfr_r=durr_r/am-top*damr_r dmfu_r=duru_r/am-top*damu_r dmfv_r=durv_r/am-top*damv_r dmfw_r=durw_r/am-top*damw_r dmfp_r=durp_r/am-top*damp_r c------------------------------------------------------------------- c Scaling function for the speed of sound and its derivatives c see Eq.(32) of the Ref.2) c------------------------------------------------------------------- top=(1.0d0-mhalfr*mhalfr)*(1.0d0-mhalfr*mhalfr) top=top*mhalf*mhalf+4.0d0*mhalfr*mhalfr bot=1.0d0+mhalfr*mhalfr if(abs(canc-0.0d0).lt.0.000001d0) then fmid=1.0d0 else fmid=sqrt(top)/bot endif c-------------------------- temph=-4.0d0*(1.0d0-mhalfr*mhalfr)*mhalfr temph=temph*mhalf*mhalf+8.0d0*mhalfr dfm_mf=temph/(sqrt(top)*2.0d0*bot) dfm_mf=dfm_mf-sqrt(top)*2.0d0*mhalfr/(bot*bot) c-------------------------- temph=2.0d0*(1.0d0-mhalfr*mhalfr)*(1.0d0-mhalfr*mhalfr)*mhalf dfm_mh=temph/(2.0d0*bot*sqrt(top)) c-------------------------- dfmr_l=dfm_mf*dmfr_l+dfm_mh*dmhr_l dfmu_l=dfm_mf*dmfu_l+dfm_mh*dmhu_l dfmv_l=dfm_mf*dmfv_l+dfm_mh*dmhv_l dfmw_l=dfm_mf*dmfw_l+dfm_mh*dmhw_l dfmp_l=dfm_mf*dmfp_l+dfm_mh*dmhp_l c-------------------------- dfmr_r=dfm_mf*dmfr_r+dfm_mh*dmhr_r dfmu_r=dfm_mf*dmfu_r+dfm_mh*dmhu_r dfmv_r=dfm_mf*dmfv_r+dfm_mh*dmhv_r dfmw_r=dfm_mf*dmfw_r+dfm_mh*dmhw_r dfmp_r=dfm_mf*dmfp_r+dfm_mh*dmhp_r c------------------------------------------------------------------ c 'New' speed of sound 'amw' defined as a product of the scaling c function 'fmid' and the 'Old' speed of sound 'am'; see (31) of Ref.2) c------------------------------------------------------------------ amw=fmid*am mlw=un_l/amw mrw=un_r/amw c-------------------------- damr_l=canc*coef*dfmr_l*am+fmid*damr_l damu_l=canc*coef*dfmu_l*am+fmid*damu_l damv_l=canc*coef*dfmv_l*am+fmid*damv_l damw_l=canc*coef*dfmw_l*am+fmid*damw_l damp_l=canc*coef*dfmp_l*am+fmid*damp_l c-------------------------- damr_r=canc*coef*dfmr_r*am+fmid*damr_r damu_r=canc*coef*dfmu_r*am+fmid*damu_r damv_r=canc*coef*dfmv_r*am+fmid*damv_r damw_r=canc*coef*dfmw_r*am+fmid*damw_r damp_r=canc*coef*dfmp_r*am+fmid*damp_r c-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/ am=amw c------------------------------------------------------------------- c Redefinition of the numerical mach numbers; c see Eqs. (33) and (34) of the Ref.2) c------------------------------------------------------------------- if(abs(canc-0.0d0).lt.0.000001d0) then top=2.0d0 bot=0.0d0 else top=1.0d0+mhalfr*mhalfr bot=1.0d0-mhalfr*mhalfr endif ml=0.5d0*(top*mlw+bot*mrw) mr=0.5d0*(top*mrw+bot*mlw) c------------------------------------------------------------------- c Mplus and Mmin are calligraphic lettes M+ and M- from the paper, c see (19a) and (19b), p.367. of the Ref.1) 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 Mplus1=(ml+abs(ml))/2.0d0 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 Mmin1=(mr-abs(mr))/2.0d0 c------------------------------------------------------------------- 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-------- dmlw_l=n_z/am+temp_l*damw_l dmlw_r=temp_l*damw_r dmrw_l=temp_r*damw_l dmrw_r=n_z/am+temp_r*damw_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----------------------------- sr_l=dmlr_l sr_r=dmlr_r su_l=dmlu_l su_r=dmlu_r sv_l=dmlv_l sv_r=dmlv_r sw_l=dmlw_l sw_r=dmlw_r sp_l=dmlp_l sp_r=dmlp_r c----------------------------------------------------------------- c Redefinition of the derivatives of the ml & mr c----------------------------------------------------------------- temp_l=(mlw-mrw)*mhalfr temp_r=-temp_l c-------- dmlr_l=0.5d0*(top*dmlr_l+bot*dmrr_l)+canc*coef*temp_l*dmfr_l dmlu_l=0.5d0*(top*dmlu_l+bot*dmru_l)+canc*coef*temp_l*dmfu_l dmlv_l=0.5d0*(top*dmlv_l+bot*dmrv_l)+canc*coef*temp_l*dmfv_l dmlw_l=0.5d0*(top*dmlw_l+bot*dmrw_l)+canc*coef*temp_l*dmfw_l dmlp_l=0.5d0*(top*dmlp_l+bot*dmrp_l)+canc*coef*temp_l*dmfp_l c-------- dmlr_r=0.5d0*(top*dmlr_r+bot*dmrr_r)+canc*coef*temp_l*dmfr_r dmlu_r=0.5d0*(top*dmlu_r+bot*dmru_r)+canc*coef*temp_l*dmfu_r dmlv_r=0.5d0*(top*dmlv_r+bot*dmrv_r)+canc*coef*temp_l*dmfv_r dmlw_r=0.5d0*(top*dmlw_r+bot*dmrw_r)+canc*coef*temp_l*dmfw_r dmlp_r=0.5d0*(top*dmlp_r+bot*dmrp_r)+canc*coef*temp_l*dmfp_r c-------- dmrr_l=0.5d0*(top*dmrr_l+bot*sr_l)+canc*coef*temp_r*dmfr_l dmru_l=0.5d0*(top*dmru_l+bot*su_l)+canc*coef*temp_r*dmfu_l dmrv_l=0.5d0*(top*dmrv_l+bot*sv_l)+canc*coef*temp_r*dmfv_l dmrw_l=0.5d0*(top*dmrw_l+bot*sw_l)+canc*coef*temp_r*dmfw_l dmrp_l=0.5d0*(top*dmrp_l+bot*sp_l)+canc*coef*temp_r*dmfp_l c-------- dmrr_r=0.5d0*(top*dmrr_r+bot*sr_r)+canc*coef*temp_r*dmfr_r dmru_r=0.5d0*(top*dmru_r+bot*su_r)+canc*coef*temp_r*dmfu_r dmrv_r=0.5d0*(top*dmrv_r+bot*sv_r)+canc*coef*temp_r*dmfv_r dmrw_r=0.5d0*(top*dmrw_r+bot*sw_r)+canc*coef*temp_r*dmfw_r dmrp_r=0.5d0*(top*dmrp_r+bot*sp_r)+canc*coef*temp_r*dmfp_r c----------------------------------------------------------- c mmid is m_{1/2} (notation as in the paper) c see Eq.(13),p.366 of the Ref.1) c---------------------------------------------------------- mmid=Mplus+Mmin c----------------------------------------------------------- c Computing the derivatives of M+ and M- c----------------------------------------------------------- if(ml .ge. 1.0d0) then dMpr_l=dmlr_l dMpu_l=dmlu_l dMpv_l=dmlv_l dMpw_l=dmlw_l dMpp_l=dmlp_l c-------------------- dMpr_r=dmlr_r dMpu_r=dmlu_r dMpv_r=dmlv_r dMpw_r=dmlw_r dMpp_r=dmlp_r else if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then temph=(ml+1.0d0)/2.0d0 dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l dMpw_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_l dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l c-------------------- dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r dMpw_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_r dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r else dMpr_l=0.0d0 dMpu_l=0.0d0 dMpv_l=0.0d0 dMpw_l=0.0d0 dMpp_l=0.0d0 c--------------------- dMpr_r=0.0d0 dMpu_r=0.0d0 dMpv_r=0.0d0 dMpw_r=0.0d0 dMpp_r=0.0d0 endif endif c----------------------------------------------------------- c addition of low Mach number terms c----------------------------------------------------------- if(ml .ge. 0.0d0) then m1pr_l=dmlr_l m1pu_l=dmlu_l m1pv_l=dmlv_l m1pw_l=dmlw_l m1pp_l=dmlp_l c--------------------- m1pr_r=dmlr_r m1pu_r=dmlu_r m1pv_r=dmlv_r m1pw_r=dmlw_r m1pp_r=dmlp_r else m1pr_l=0.0d0 m1pu_l=0.0d0 m1pv_l=0.0d0 m1pw_l=0.0d0 m1pp_l=0.0d0 c-------------------- m1pr_r=0.0d0 m1pu_r=0.0d0 m1pv_r=0.0d0 m1pw_r=0.0d0 m1pp_r=0.0d0 endif c----------------------------------------------------------- c----------------------------------------------------------- if(mr .ge. 1.0d0) then dMmr_l=0.0d0 dMmu_l=0.0d0 dMmv_l=0.0d0 dMmw_l=0.0d0 dMmp_l=0.0d0 c--------------------- dMmr_r=0.0d0 dMmu_r=0.0d0 dMmv_r=0.0d0 dMmw_r=0.0d0 dMmp_r=0.0d0 else if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then temph=(-mr+1.0d0)/2.0d0 dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l dMmw_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_l dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l c-------------------- dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r dMmw_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_r dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r else dMmr_l=dmrr_l dMmu_l=dmru_l dMmv_l=dmrv_l dMmw_l=dmrw_l dMmp_l=dmrp_l c-------------------- dMmr_r=dmrr_r dMmu_r=dmru_r dMmv_r=dmrv_r dMmw_r=dmrw_r dMmp_r=dmrp_r endif endif c----------------------------------------------------------- c addition of low Mach number terms c----------------------------------------------------------- if(mr .le. 0.0d0) then m1mr_l=dmrr_l m1mu_l=dmru_l m1mv_l=dmrv_l m1mw_l=dmrw_l m1mp_l=dmrp_l c--------------------- m1mr_r=dmrr_r m1mu_r=dmru_r m1mv_r=dmrv_r m1mw_r=dmrw_r m1mp_r=dmrp_r else m1mr_l=0.0d0 m1mu_l=0.0d0 m1mv_l=0.0d0 m1mw_l=0.0d0 m1mp_l=0.0d0 c-------------------- m1mr_r=0.0d0 m1mu_r=0.0d0 m1mv_r=0.0d0 m1mw_r=0.0d0 m1mp_r=0.0d0 endif c----------------------------------------------------------------- c computing the derivatives of m_{1/2} (notation as in the paper) c----------------------------------------------------------------- dmir_l=dMpr_l+dMmr_l dmir_r=dMpr_r+dMmr_r c------------- dmiu_l=dMpu_l+dMmu_l dmiu_r=dMpu_r+dMmu_r c------------- dmiv_l=dMpv_l+dMmv_l dmiv_r=dMpv_r+dMmv_r c------------- dmiw_l=dMpw_l+dMmw_l dmiw_r=dMpw_r+dMmw_r c------------- dmip_l=dMpp_l+dMmp_l dmip_r=dMpp_r+dMmp_r c------------------------------------------------------------- c computing the main convective variables and their derivatives c mpl_m is m^{+}_{1/2} (paper's notation) and c mmin_m is m^{-}_{1/2} (paper's notation), c see Eq.(A2) on p.370 of the Ref.1) c---------------------------------------------------------------- termp=(Mmin1-Mmin+Mplus-Mplus1)*(1.0d0/(mhalfr*mhalfr)-1.0d0) termp=termp*(pold_l-pold_r)/(pold_l/rold_l+pold_r/rold_r) c------------------------------------------------------------- c derivatives of the termp c------------------------------------------------------------- top=(Mmin1-Mmin+Mplus-Mplus1) bots=1.0d0/(pold_l/rold_l+pold_r/rold_r) bot=(pold_l-pold_r)*bots temph=1.0d0/(mhalfr*mhalfr)-1.0d0 c--------------------------- tmpr_l=(m1mr_l-dMmr_l+dMpr_l-m1pr_l)*bot*temph tmpr_l=tmpr_l-2.0d0*bot*top*dmfr_l/(mhalfr*mhalfr*mhalfr) tmpr_l=tmpr_l+temph*top*bot*bots*(pold_l/rold_l/rold_l) c--------------------------- tmpu_l=(m1mu_l-dMmu_l+dMpu_l-m1pu_l)*bot*temph tmpu_l=tmpu_l-2.0d0*bot*top*dmfu_l/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpv_l=(m1mv_l-dMmv_l+dMpv_l-m1pv_l)*bot*temph tmpv_l=tmpv_l-2.0d0*bot*top*dmfv_l/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpw_l=(m1mw_l-dMmw_l+dMpw_l-m1pw_l)*bot*temph tmpw_l=tmpw_l-2.0d0*bot*top*dmfw_l/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpp_l=(m1mp_l-dMmp_l+dMpp_l-m1pp_l)*bot*temph tmpp_l=tmpp_l-2.0d0*bot*top*dmfp_l/(mhalfr*mhalfr*mhalfr) tmpp_l=tmpp_l+temph*top*bots*(1.0d0-bot/rold_l) c------------rrrrrrrr------- c------------rrrrrrrr------- tmpr_r=(m1mr_r-dMmr_r+dMpr_r-m1pr_r)*bot*temph tmpr_r=tmpr_r-2.0d0*bot*top*dmfr_r/(mhalfr*mhalfr*mhalfr) tmpr_r=tmpr_r+temph*top*bot*bots*(pold_r/rold_r/rold_r) c--------------------------- tmpu_r=(m1mu_r-dMmu_r+dMpu_r-m1pu_r)*bot*temph tmpu_r=tmpu_r-2.0d0*bot*top*dmfu_r/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpv_r=(m1mv_r-dMmv_r+dMpv_r-m1pv_r)*bot*temph tmpv_r=tmpv_r-2.0d0*bot*top*dmfv_r/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpw_r=(m1mw_r-dMmw_r+dMpw_r-m1pw_r)*bot*temph tmpw_r=tmpw_r-2.0d0*bot*top*dmfw_r/(mhalfr*mhalfr*mhalfr) c--------------------------- tmpp_r=(m1mp_r-dMmp_r+dMpp_r-m1pp_r)*bot*temph tmpp_r=tmpp_r-2.0d0*bot*top*dmfp_r/(mhalfr*mhalfr*mhalfr) tmpp_r=tmpp_r-temph*top*bots*(1.0d0+bot/rold_r) c------------------------------------------------------------- if(mmid .ge. 0.0d0) then mpl_m = mmid d2mr_l=dmir_l d2mu_l=dmiu_l d2mv_l=dmiv_l d2mw_l=dmiw_l d2mp_l=dmip_l c------------ d2mr_r=dmir_r d2mu_r=dmiu_r d2mv_r=dmiv_r d2mw_r=dmiw_r d2mp_r=dmip_r c------------ else mpl_m = 0.0d0 d2mr_l=0.0d0 d2mu_l=0.0d0 d2mv_l=0.0d0 d2mw_l=0.0d0 d2mp_l=0.0d0 c------------ d2mr_r=0.0d0 d2mu_r=0.0d0 d2mv_r=0.0d0 d2mw_r=0.0d0 d2mp_r=0.0d0 endif c------------------------------------------------------------------ if(mmid .le. 0.0d0) then mmin_m = mmid d3mr_l=dmir_l d3mu_l=dmiu_l d3mv_l=dmiv_l d3mw_l=dmiw_l d3mp_l=dmip_l c------------ d3mr_r=dmir_r d3mu_r=dmiu_r d3mv_r=dmiv_r d3mw_r=dmiw_r d3mp_r=dmip_r c------------ else mmin_m = 0.0d0 d3mr_l=0.0d0 d3mu_l=0.0d0 d3mv_l=0.0d0 d3mw_l=0.0d0 d3mp_l=0.0d0 c------------ d3mr_r=0.0d0 d3mu_r=0.0d0 d3mv_r=0.0d0 d3mw_r=0.0d0 d3mp_r=0.0d0 endif 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------------ dPpw_l=brac_l*dmlw_l dPpw_r=brac_l*dmlw_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----------- dPpw_l=0.0d0 dPpw_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------------ dPmw_l=brac_r*dmrw_l dPmw_r=brac_r*dmrw_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----------- dPmw_l=0.0d0 dPmw_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 dpiw_l=dPpw_l*pold_l+dPmw_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 dpiw_r=dPpw_r*pold_l+dPmw_r*pold_r dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r c--------------------------------------------------------------------- c !!!!!!!!!!!!!!!!!! JACOBIAN !!!!!!!!!!!!!!!!!!!!!!!!!!!! c--------------------------------------------------------------------- rum=am*(mpl_m*rold_l+mmin_m*rold_r)+canc*am*termp c--------------------------------------------------------------------- rumr_l=damr_l*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mr_l*rold_l+mpl_m+d3mr_l*rold_r) rumr_l=rumr_l+canc*coef*(damr_l*termp+am*tmpr_l) rumu_l=damu_l*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mu_l*rold_l+d3mu_l*rold_r) rumu_l=rumu_l+canc*coef*(damu_l*termp+am*tmpu_l) rumv_l=damv_l*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mv_l*rold_l+d3mv_l*rold_r) rumv_l=rumv_l+canc*coef*(damv_l*termp+am*tmpv_l) rumw_l=damw_l*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mw_l*rold_l+d3mw_l*rold_r) rumw_l=rumw_l+canc*coef*(damw_l*termp+am*tmpw_l) rump_l=damp_l*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mp_l*rold_l+d3mp_l*rold_r) rump_l=rump_l+canc*coef*(damp_l*termp+am*tmpp_l) c------------------------------------------------- rumr_r=damr_r*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mr_r*rold_l+mmin_m+d3mr_r*rold_r) rumr_r=rumr_r+canc*coef*(damr_r*termp+am*tmpr_r) rumu_r=damu_r*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mu_r*rold_l+d3mu_r*rold_r) rumu_r=rumu_r+canc*coef*(damu_r*termp+am*tmpu_r) rumv_r=damv_r*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mv_r*rold_l+d3mv_r*rold_r) rumv_r=rumv_r+canc*coef*(damv_r*termp+am*tmpv_r) rumw_r=damw_r*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mw_r*rold_l+d3mw_r*rold_r) rumw_r=rumw_r+canc*coef*(damw_r*termp+am*tmpw_r) rump_r=damp_r*(mpl_m*rold_l+mmin_m*rold_r)+ & am*(d2mp_r*rold_l+d3mp_r*rold_r) rump_r=rump_r+canc*coef*(damp_r*termp+am*tmpp_r) c--------------------------------------------------------------------- c--------------------------------------------------------------------- jl(1,1)=rumr_l jl(1,2)=rumu_l jl(1,3)=rumv_l jl(1,4)=rumw_l jl(1,5)=rump_l c------------------------------------ jr(1,1)=rumr_r jr(1,2)=rumu_r jr(1,3)=rumv_r jr(1,4)=rumw_r jr(1,5)=rump_r c------------------------------------ ccccc f222222222222 ------------- c derivatives with respect to left set of c primitive variables c------------------------------------ if(rum .ge. 0.0d0) then br1=rum*un_l br2=rum*ut1_l br3=rum*ut2_l else br1=rum*un_r br2=rum*ut1_r br3=rum*ut2_r endif c------------------------------------ if(rum .ge. 0.0d0) then br1=rumr_l*un_l br2=rumr_l*ut1_l br3=rumr_l*ut2_l else br1=rumr_l*un_r br2=rumr_l*ut1_r br3=rumr_l*ut2_r endif jl(2,1)=n_x*(br1+dpir_l)+br2*t1_x+br3*t2_x jl(3,1)=n_y*(br1+dpir_l)+br2*t1_y+br3*t2_y jl(4,1)=n_z*(br1+dpir_l)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumu_l*un_l+rum*n_x br2=rumu_l*ut1_l+rum*t1_x br3=rumu_l*ut2_l+rum*t2_x else br1=rumu_l*un_r br2=rumu_l*ut1_r br3=rumu_l*ut2_r endif jl(2,2)=n_x*(br1+dpiu_l)+br2*t1_x+br3*t2_x jl(3,2)=n_y*(br1+dpiu_l)+br2*t1_y+br3*t2_y jl(4,2)=n_z*(br1+dpiu_l)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumv_l*un_l+rum*n_y br2=rumv_l*ut1_l+rum*t1_y br3=rumv_l*ut2_l+rum*t2_y else br1=rumv_l*un_r br2=rumv_l*ut1_r br3=rumv_l*ut2_r endif jl(2,3)=n_x*(br1+dpiv_l)+br2*t1_x+br3*t2_x jl(3,3)=n_y*(br1+dpiv_l)+br2*t1_y+br3*t2_y jl(4,3)=n_z*(br1+dpiv_l)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumw_l*un_l+rum*n_z br2=rumw_l*ut1_l+rum*t1_z br3=rumw_l*ut2_l+rum*t2_z else br1=rumw_l*un_r br2=rumw_l*ut1_r br3=rumw_l*ut2_r endif jl(2,4)=n_x*(br1+dpiw_l)+br2*t1_x+br3*t2_x jl(3,4)=n_y*(br1+dpiw_l)+br2*t1_y+br3*t2_y jl(4,4)=n_z*(br1+dpiw_l)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rump_l*un_l br2=rump_l*ut1_l br3=rump_l*ut2_l else br1=rump_l*un_r br2=rump_l*ut1_r br3=rump_l*ut2_r endif jl(2,5)=n_x*(br1+dpip_l)+br2*t1_x+br3*t2_x jl(3,5)=n_y*(br1+dpip_l)+br2*t1_y+br3*t2_y jl(4,5)=n_z*(br1+dpip_l)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------- c rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr c------------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumr_r*un_l br2=rumr_r*ut1_l br3=rumr_r*ut2_l else br1=rumr_r*un_r br2=rumr_r*ut1_r br3=rumr_r*ut2_r endif jr(2,1)=n_x*(br1+dpir_r)+br2*t1_x+br3*t2_x jr(3,1)=n_y*(br1+dpir_r)+br2*t1_y+br3*t2_y jr(4,1)=n_z*(br1+dpir_r)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------ if(rum .ge. 0.0d0) then br1=rumu_r*un_l br2=rumu_r*ut1_l br3=rumu_r*ut2_l else br1=rumu_r*un_r+rum*n_x br2=rumu_r*ut1_r+rum*t1_x br3=rumu_r*ut2_r+rum*t2_x endif jr(2,2)=n_x*(br1+dpiu_r)+br2*t1_x+br3*t2_x jr(3,2)=n_y*(br1+dpiu_r)+br2*t1_y+br3*t2_y jr(4,2)=n_z*(br1+dpiu_r)+br2*t1_z+br3*t2_z c------------------------------------------------------------------------ if(rum .ge. 0.0d0) then br1=rumv_r*un_l br2=rumv_r*ut1_l br3=rumv_r*ut2_l else br1=rumv_r*un_r+rum*n_y br2=rumv_r*ut1_r+rum*t1_y br3=rumv_r*ut2_r+rum*t2_y endif jr(2,3)=n_x*(br1+dpiv_r)+br2*t1_x+br3*t2_x jr(3,3)=n_y*(br1+dpiv_r)+br2*t1_y+br3*t2_y jr(4,3)=n_z*(br1+dpiv_r)+br2*t1_z+br3*t2_z c----------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumw_r*un_l br2=rumw_r*ut1_l br3=rumw_r*ut2_l else br1=rumw_r*un_r+rum*n_z br2=rumw_r*ut1_r+rum*t1_z br3=rumw_r*ut2_r+rum*t2_z endif jr(2,4)=n_x*(br1+dpiw_r)+br2*t1_x+br3*t2_x jr(3,4)=n_y*(br1+dpiw_r)+br2*t1_y+br3*t2_y jr(4,4)=n_z*(br1+dpiw_r)+br2*t1_z+br3*t2_z c----------------------------------------------------------------------- if(rum .ge. 0.0d0) then br1=rump_r*un_l br2=rump_r*ut1_l br3=rump_r*ut2_l else br1=rump_r*un_r br2=rump_r*ut1_r br3=rump_r*ut2_r endif jr(2,5)=n_x*(br1+dpip_r)+br2*t1_x+br3*t2_x jr(3,5)=n_y*(br1+dpip_r)+br2*t1_y+br3*t2_y jr(4,5)=n_z*(br1+dpip_r)+br2*t1_z+br3*t2_z c------------------------------------------------------- c------------------------------------------------------- hr_l=(eold_l+pold_l/rold_l) hr_r=(eold_r+pold_r/rold_r) c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumr_l*hr_l-rum*ga*pold_l/gm1/rold_l/rold_l else br1=rumr_l*hr_r endif jl(5,1)=br1 c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumu_l*hr_l+rum*uold_l else br1=rumu_l*hr_r endif jl(5,2)=br1 c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumv_l*hr_l+rum*vold_l else br1=rumv_l*hr_r endif jl(5,3)=br1 c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumw_l*hr_l+rum*wold_l else br1=rumw_l*hr_r endif jl(5,4)=br1 c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rump_l*hr_l+rum*ga/gm1/rold_l else br1=rump_l*hr_r endif jl(5,5)=br1 c------------------------------------------------- c------------------------------------------------- if(rum .ge. 0.0d0) then br1=rumr_r*hr_l else br1=rumr_r*hr_r-rum*ga*pold_r/gm1/rold_r/rold_r endif jr(5,1)=br1 c--------------------- if(rum .ge. 0.0d0) then br1=rumu_r*hr_l else br1=rumu_r*hr_r+rum*uold_r endif jr(5,2)=br1 c--------------------- if(rum .ge. 0.0d0) then br1=rumv_r*hr_l else br1=rumv_r*hr_r+rum*vold_r endif jr(5,3)=br1 c--------------------- if(rum .ge. 0.0d0) then br1=rumw_r*hr_l else br1=rumw_r*hr_r+rum*wold_r endif jr(5,4)=br1 c--------------------- if(rum .ge. 0.0d0) then br1=rump_r*hr_l else br1=rump_r*hr_r+rum*ga/gm1/rold_r endif jr(5,5)=br1 c--------------------------------------------------- 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 wl(1,5)=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 wl(2,5)=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 wl(3,5)=0.0d0 c------------------------------ wl(4,1)=-wold_l/rold_l wl(4,2)=0.0d0 wl(4,3)=0.0d0 wl(4,4)=1.0d0/rold_l wl(4,5)=0.0d0 c------------------------------ wl(5,1)=gm1*(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0 wl(5,2)=-uold_l*gm1 wl(5,3)=-vold_l*gm1 wl(5,4)=-wold_l*gm1 wl(5,5)=gm1 c------------------------------ c------------------------------ wr(1,1)=1.0d0 wr(1,2)=0.0d0 wr(1,3)=0.0d0 wr(1,4)=0.0d0 wr(1,5)=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 wr(2,5)=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 wr(3,5)=0.0d0 c------------------------------ wr(4,1)=-wold_r/rold_r wr(4,2)=0.0d0 wr(4,3)=0.0d0 wr(4,4)=1.0d0/rold_r wr(4,5)=0.0d0 c------------------------------ wr(5,1)=gm1*(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0 wr(5,2)=-uold_r*gm1 wr(5,3)=-vold_r*gm1 wr(5,4)=-wold_r*gm1 wr(5,5)=gm1 c---------------------------------------------- c---------------------------------------------- do 1 i=1,5 do 2 j=1,5 jtl(i,j)=0.0d0 jtr(i,j)=0.0d0 do 3 k=1,5 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---------------------------------------------- return end