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2d/equations/euler/rp/rpn2euvlg.f

c
c
c     =====================================================
      subroutine rpn2eu(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr,maux,
     &     auxl,auxr,wave,s,fl,fr)
c     =====================================================
c
c     # solve Riemann problems for the 2D Euler equations using 
c     # van Leer's Flux Vector Splitting 
c
c     # On input, ql contains the state vector at the left edge of each cell
c     #           qr contains the state vector at the right edge of each cell
c
c     # This data is along a slice in the x-direction if ixy=1 
c     #                            or the y-direction if ixy=2.
c     # On output, wave contains the waves, s the speeds, 
c     # fl and fr the positive and negative flux.
c
c     # Note that the i'th Riemann problem has left state qr(i-1,:)
c     #                                    and right state ql(i,:)
c     # From the basic routine step1, this routine is called with ql = qr
c
c     Author: Ralf Deiterding
c
      implicit double precision (a-h,o-z)
      dimension wave(1-mbc:maxm+mbc, meqn, mwaves)
      dimension    s(1-mbc:maxm+mbc, mwaves)
      dimension   ql(1-mbc:maxm+mbc, meqn)
      dimension   qr(1-mbc:maxm+mbc, meqn)
      dimension   fl(1-mbc:maxm+mbc, meqn)
      dimension   fr(1-mbc:maxm+mbc, meqn)
      double precision Ml, Mr, sl(3), sr(3), fvl(4), fvr(4)
      common /param/  gamma,gamma1
c
c     # Method returns fluxes
c     ------------
      common /rpnflx/ mrpnflx
      mrpnflx = 1
c
c     # set mu to point to  the component of the system that corresponds
c     # to momentum in the direction of this slice, mv to the orthogonal
c     # momentum:
c
      if (ixy.eq.1) then
         mu = 2
         mv = 3
      else
         mu = 3
         mv = 2
      endif
c
c     # Van Leer's Flux Vector Splitting
c
      gamma2 = gamma**2-1
      do 10 i=2-mbc,mx+mbc
         rhol = qr(i-1,1)
         rhor = ql(i  ,1)
         ul = qr(i-1,mu)/rhol
         ur = ql(i  ,mu)/rhor
         vl = qr(i-1,mv)/rhol
         vr = ql(i  ,mv)/rhor
         El = qr(i-1,4)/rhol
         Er = ql(i  ,4)/rhor
	 pl = gamma1*(qr(i-1,4) - 0.5d0*(qr(i-1,mu)**2+
     &        qr(i-1,mv)**2)/rhol)
	 pr = gamma1*(ql(i  ,4) - 0.5d0*(ql(i  ,mu)**2+
     &        ql(i  ,mv)**2)/rhor)
         al = dsqrt(gamma*pl/rhol)
         ar = dsqrt(gamma*pr/rhor)
c
         Ml = ul/al
         Mr = ur/ar
c
         sl(1) = ul-al
         sl(2) = ul
         sl(3) = ul+al
         sr(1) = ur-ar
         sr(2) = ur
         sr(3) = ur+ar
c
         if (Ml.gt.1d0) then
            fvl(1)  = rhol*ul
            fvl(mu) = fvl(1)*ul+pl
            fvl(mv) = fvl(1)*vl
            fvl(4)  = ul*(rhol*El+pl)
         else if (Ml.lt.-1.d0) then
            do m = 1,meqn
               fvl(m) = 0.d0
            enddo
         else
            fvl(1)  = 0.25d0*rhol*al*(Ml+1.d0)**2
            fvl(mu) = fvl(1)*2.d0*al/gamma*(0.5d0*gamma1*Ml+1.d0)
            fvl(mv) = fvl(1)*vl
            fvl(4)  = fvl(1)*(0.5d0*vl**2 + 2.d0*al**2/gamma2*
     &                        (0.5d0*gamma1*Ml+1.d0)**2)
         endif
c
         if (Mr.lt.-1.d0) then
            fvr(1)  = rhor*ur
            fvr(mu) = fvr(1)*ur+pr
            fvr(mv) = fvr(1)*vr
            fvr(4)  = ur*(rhor*Er+pr)
         else if (Mr.gt.1.d0) then
            do m = 1,meqn
               fvr(m) = 0.d0
            enddo
         else
            fvr(1)  = -0.25d0*rhor*ar*(Mr-1.d0)**2
            fvr(mu) = fvr(1)*2.d0*ar/gamma*(0.5d0*gamma1*Mr-1.d0)
            fvr(mv) = fvr(1)*vr
            fvr(4)  = fvr(1)*(0.5d0*vr**2 + 2.d0*ar**2/gamma2* 
     &                        (0.5d0*gamma1*Mr-1.d0)**2)
         endif
c
         do 20 m = 1,meqn
            fl(i,m) = fvl(m) + fvr(m)
            fr(i,m) = -fl(i,m)
 20      continue
c
         if (dabs(Ml).lt.1.d0) then
            facl = (gamma+3.d0)/(2.d0*gamma+dabs(Ml)*(3.d0-gamma))
         else
            facl = 1.d0
         endif
         if (dabs(Mr).lt.1.d0) then
            facr = (gamma+3.d0)/(2.d0*gamma+dabs(Mr)*(3.d0-gamma))
         else
            facr = 1.d0
         endif
c
         do 10 mw=1,mwaves
            s(i,mw) = dmax1(dabs(facl*sl(mw)),dabs(facr*sr(mw)))
            do 10 m=1,meqn
               wave(i,m,mw) = 0.d0
 10   continue
c
      return
      end
c


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last update: 06/01/04