C CONJP7 SOURCE CHAT 05/01/12 22:17:57 5004 SUBROUTINE CONJP7(JL,WVEC_L,WVEC_R,NVECT,TVECT, & ga,v_inf) C************************************************************************ C C PROJET : CASTEM 2000 C C NOM : CONJP7 C C DESCRIPTION : Voir KONJA5 C C LANGAGE : FORTRAN 77 + ESOPE 2000 (avec estensions CISI) C C AUTEUR : S. KUDRIAKOV, DM2S/SFME/LTMF C C************************************************************************ C c---------------------------------------------------------------------- c GENERAL DESCRIPTION: c This subroutine provides the jacobian which is the derivatives c of the numerical flux function defined at the wall c with respect to the PRIMITIVE variables of the left c cell (relative to the wall). c The low-mach number corrections are made for the flux functions c c EQUATIONS: 2D 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 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 -- 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 v_inf -- parameter for reference velocity, see Ref. 2). c---------------------------------------------------------------------- c c OUTPUT: c c jl -- jakobian matrix 4 by 4 - derivatives of the numerical c flux function with respect to the PRIMITIVE variables c from the left cell; c 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 alpha,beta real*8 ga,gm1,temph real*8 n_x,n_y,t_x,t_y real*8 un_l, un_r, ut_l, ut_r real*8 ml,mr,Mplus,Mmin,mmid real*8 mpl_m, mmin_m,am 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 top,bot,bots real*8 br3,br4,temp_l,temp_r,brac_l,brac_r real*8 aleft, arigh,tcoef,bcoef 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 dMpr_l,dMpr_r,dMpu_l,dMpu_r real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r real*8 dmir_l,dmir_r,dmiu_l,dmiu_r real*8 dmiv_l,dmiv_r,dmip_l,dmip_r real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_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 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 dmhr_l,dmhr_r,dmhu_l,dmhu_r real*8 dmhv_l,dmhv_r,dmhp_l,dmhp_r real*8 dmfr_l,dmfr_r,dmfu_l,dmfu_r real*8 dmfv_l,dmfv_r,dmfp_l,dmfp_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 m1mr_l,m1mr_r,m1mu_l,m1mu_r real*8 m1mv_l,m1mv_r,m1mp_l,m1mp_r real*8 m1pr_l,m1pr_r,m1pu_l,m1pu_r real*8 m1pv_l,m1pv_r,m1pp_l,m1pp_r real*8 tmpr_l,tmpr_r,tmpu_l,tmpu_r real*8 tmpv_l,tmpv_r,tmpp_l,tmpp_r real*8 coef,canc,v_inf real*8 sr_l,sr_r,su_l,su_r,sv_l,sv_r,sp_l,sp_r real*8 rum,rumr_l,rumu_l,rumv_l,rump_l real*8 rumr_r,rumu_r,rumv_r,rump_r integer i parameter(alpha = 0.1875D0, beta = 0.125D0) parameter(epsil = 1.0d0) canc=1.0d0 c------------------------------------------------------------- n_x=nvect(1) n_y=nvect(2) t_x=tvect(1) t_y=tvect(2) c---------------------------- gm1=ga-1.0d0 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------------------------------------------------------------------ c Computation of the specific total energy on the left and right. 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 Computing reference velocity and its derivatives 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) if(qq .lt. (epsil*v_inf)) then ur_l = epsil*v_inf durr_l=0.0d0 duru_l=0.0d0 durv_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 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 durp_l=ga/(2.0d0*aleft*rold_l) endif c------------------------------------------------------------------ c------------------------------------------------------------------- qq=sqrt(uold_r*uold_r+vold_r*vold_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 durp_r=0.0d0 else ur_r=qq durr_r=0.0d0 duru_r=uold_r/qq durv_r=vold_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 durp_r=ga/(2.0d0*arigh*rold_r) 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 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 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------------------------------------------------------------------- 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 see p.370, under (A1). c------------------------------------------------------------------- un_l=uold_l*n_x+vold_l*n_y un_r=uold_r*n_x+vold_r*n_y ut_l=uold_l*t_x+vold_l*t_y ut_r=uold_r*t_x+vold_r*t_y 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 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 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 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 dmfp_r=durp_r/am-top*damp_r c------------------------------------------------------------------- c Scaling function for the speed of sound and its derivatives 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 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 dfmp_r=dfm_mf*dmfp_r+dfm_mh*dmhp_r 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 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 damp_r=canc*coef*dfmp_r*am+fmid*damp_r c-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/ am=amw c------------------------------------------------------------------- c Redefinition of the numerical mach numbers 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. 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 Derivatives of ml and mr with respect to both sets of primitive c variables: 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----------------------------- sr_l=dmlr_l sr_r=dmlr_r su_l=dmlu_l su_r=dmlu_r sv_l=dmlv_l sv_r=dmlv_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 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 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 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 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, see (13),p.366) 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 dMpp_l=dmlp_l c-------------------- dMpr_r=dmlr_r dMpu_r=dmlu_r dMpv_r=dmlv_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 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 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 dMpp_l=0.0d0 c--------------------- dMpr_r=0.0d0 dMpu_r=0.0d0 dMpv_r=0.0d0 dMpp_r=0.0d0 endif endif c----------------------------------------------------------- c addition of low Mach number c----------------------------------------------------------- if(ml .ge. 0.0d0) then m1pr_l=dmlr_l m1pu_l=dmlu_l m1pv_l=dmlv_l m1pp_l=dmlp_l c--------------------- m1pr_r=dmlr_r m1pu_r=dmlu_r m1pv_r=dmlv_r m1pp_r=dmlp_r else m1pr_l=0.0d0 m1pu_l=0.0d0 m1pv_l=0.0d0 m1pp_l=0.0d0 c-------------------- m1pr_r=0.0d0 m1pu_r=0.0d0 m1pv_r=0.0d0 m1pp_r=0.0d0 endif c----------------------------------------------------------- if(mr .ge. 1.0d0) then dMmr_l=0.0d0 dMmu_l=0.0d0 dMmv_l=0.0d0 dMmp_l=0.0d0 c--------------------- dMmr_r=0.0d0 dMmu_r=0.0d0 dMmv_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 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 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 dMmp_l=dmrp_l c-------------------- dMmr_r=dmrr_r dMmu_r=dmru_r dMmv_r=dmrv_r dMmp_r=dmrp_r endif endif c----------------------------------------------------------- c addition of low Mach number c----------------------------------------------------------- if(mr .le. 0.0d0) then m1mr_l=dmrr_l m1mu_l=dmru_l m1mv_l=dmrv_l m1mp_l=dmrp_l c--------------------- m1mr_r=dmrr_r m1mu_r=dmru_r m1mv_r=dmrv_r m1mp_r=dmrp_r else m1mr_l=0.0d0 m1mu_l=0.0d0 m1mv_l=0.0d0 m1mp_l=0.0d0 c-------------------- m1mr_r=0.0d0 m1mu_r=0.0d0 m1mv_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------------- 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), see (A2) on p.370. 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--------------------------- 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--------------------------- 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 d2mp_l=dmip_l c------------ d2mr_r=dmir_r d2mu_r=dmiu_r d2mv_r=dmiv_r d2mp_r=dmip_r c------------ else mpl_m = 0.0d0 d2mr_l=0.0d0 d2mu_l=0.0d0 d2mv_l=0.0d0 d2mp_l=0.0d0 c------------ d2mr_r=0.0d0 d2mu_r=0.0d0 d2mv_r=0.0d0 d2mp_r=0.0d0 endif c--------------------------------------------- cc derivatives for the term termm cc------------------------------------------------------------------ if(mmid .le. 0.0d0) then mmin_m = mmid d3mr_l=dmir_l d3mu_l=dmiu_l d3mv_l=dmiv_l d3mp_l=dmip_l c------------ d3mr_r=dmir_r d3mu_r=dmiu_r d3mv_r=dmiv_r d3mp_r=dmip_r c------------ else mmin_m = 0.0d0 d3mr_l=0.0d0 d3mu_l=0.0d0 d3mv_l=0.0d0 d3mp_l=0.0d0 c------------ d3mr_r=0.0d0 d3mu_r=0.0d0 d3mv_r=0.0d0 d3mp_r=0.0d0 endif c--------------------------------------------------------------- c Computing the calligraphic P+ and P- with their derivatives, c see (21a) & (21b) on p.368. 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, see (20b), p.367. 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 Computation of the mass flux (rho * u)_1/2 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) 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) 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 computing JACOBIAN as a derivative of the numerical flux function c with respect to the primitive variables. c Notation: jl(i,j) --- is the derivative of the i-component of the c flux function with respect to the j-component of the c vector of primitive variables of the left state. c jr(i,j) --- is the derivative of the i-component of the c flux function with respect to the j-component of the c vector of primitive variables of the right state. 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------------------------------------ c--------------------------------------------------------- if(rum .ge. 0.0d0) then br3=rumr_l*un_l br4=rumr_l*ut_l else br3=rumr_l*un_r br4=rumr_l*ut_r endif jl(2,1)=n_x*(br3+dpir_l)+br4*t_x jl(3,1)=n_y*(br3+dpir_l)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rumu_l*un_l+rum*n_x br4=rumu_l*ut_l+rum*t_x else br3=rumu_l*un_r br4=rumu_l*ut_r endif jl(2,2)=n_x*(br3+dpiu_l)+br4*t_x jl(3,2)=n_y*(br3+dpiu_l)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rumv_l*un_l+rum*n_y br4=rumv_l*ut_l+rum*t_y else br3=rumv_l*un_r br4=rumv_l*ut_r endif jl(2,3)=n_x*(br3+dpiv_l)+br4*t_x jl(3,3)=n_y*(br3+dpiv_l)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rump_l*un_l br4=rump_l*ut_l else br3=rump_l*un_r br4=rump_l*ut_r endif jl(2,4)=n_x*(br3+dpip_l)+br4*t_x jl(3,4)=n_y*(br3+dpip_l)+br4*t_y c------------------------------------------------------------- c------------------------------------------------------------- if(rum .ge. 0.0d0) then br3=rumr_r*un_l br4=rumr_r*ut_l else br3=rumr_r*un_r br4=rumr_r*ut_r endif jr(2,1)=n_x*(br3+dpir_r)+br4*t_x jr(3,1)=n_y*(br3+dpir_r)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rumu_r*un_l br4=rumu_r*ut_l else br3=rumu_r*un_r+rum*n_x br4=rumu_r*ut_r+rum*t_x endif jr(2,2)=n_x*(br3+dpiu_r)+br4*t_x jr(3,2)=n_y*(br3+dpiu_r)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rumv_r*un_l br4=rumv_r*ut_l else br3=rumv_r*un_r+rum*n_y br4=rumv_r*ut_r+rum*t_y endif jr(2,3)=n_x*(br3+dpiv_r)+br4*t_x jr(3,3)=n_y*(br3+dpiv_r)+br4*t_y c------------------- if(rum .ge. 0.0d0) then br3=rump_r*un_l br4=rump_r*ut_l else br3=rump_r*un_r br4=rump_r*ut_r endif jr(2,4)=n_x*(br3+dpip_r)+br4*t_x jr(3,4)=n_y*(br3+dpip_r)+br4*t_y c------------------------------------------------------------- c ------ f44444444444444444444444444444 --------- c------------------------------------------------------------- jl(4,1)=0.0d0 jl(4,2)=0.0d0 jl(4,3)=0.0d0 jl(4,4)=0.0d0 c---------------------------------------------------------- jr(4,1)=0.0d0 jr(4,2)=0.0d0 jr(4,3)=0.0d0 jr(4,4)=0.0d0 c------------------------------------------------------------- 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 jl(i,1)=jl(i,1)+jr(i,1) jl(i,2)=jl(i,2)+jr(i,2)*(-tcoef/bcoef)+ & jr(i,3)*2.0d0*nvect(1)*tvect(1)/bcoef jl(i,3)=jl(i,3)+jr(i,2)*(-2.0d0*nvect(2)*tvect(2)/bcoef)+ & jr(i,3)*tcoef/bcoef jl(i,4)=jl(i,4)+jr(i,4) 11 continue c---------------------------------------------------------------------- return end