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2d/equations/euler/rp/rpn2eug.f

c
c
c     =====================================================
      subroutine rpn2eu(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr,maux,
     &     auxl,auxr,wave,s,amdq,apdq)
c     =====================================================
c
c     # Roe-solver for the Euler equations
c     # solve Riemann problems along one slice of data.
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     # amdq and apdq 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 routines, this routine is called with ql = qr
c
c     Author:  Randall J. LeVeque
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 auxl(1-mbc:maxm+mbc, maux)
      dimension auxr(1-mbc:maxm+mbc, maux)
      dimension apdq(1-mbc:maxm+mbc, meqn)
      dimension amdq(1-mbc:maxm+mbc, meqn)
c
c     local arrays -- common block comroe is passed to rpt2eu
c     ------------
      parameter (maxm2 = 10002)  !# assumes at most 10000x10000 grid with mbc=2
      dimension delta(4)
      logical efix
      common /param/  gamma,gamma1
      common /comroe/ u2v2(-1:maxm2),
     &       u(-1:maxm2),v(-1:maxm2),enth(-1:maxm2),a(-1:maxm2),
     &       g1a2(-1:maxm2),euv(-1:maxm2) 
c
      data efix /.false./    !# use entropy fix for transonic rarefactions
c
c     # Riemann solver returns fluxes
c     ------------
      common /rpnflx/ mrpnflx
      mrpnflx = 1
c
      if (-1.gt.1-mbc .or. maxm2 .lt. maxm+mbc) then
	 write(6,*) 'need to increase maxm2 in rpA'
	 stop
	 endif
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     # note that notation for u and v reflects assumption that the 
c     # Riemann problems are in the x-direction with u in the normal
c     # direciton and v in the orthogonal direcion, but with the above
c     # definitions of mu and mv the routine also works with ixy=2
c     # and returns, for example, f0 as the Godunov flux g0 for the
c     # Riemann problems u_t + g(u)_y = 0 in the y-direction.
c
c
c     # compute the Roe-averaged variables needed in the Roe solver.
c     # These are stored in the common block comroe since they are
c     # later used in routine rpt2eu to do the transverse wave splitting.
c
      do 10 i = 2-mbc, mx+mbc
         rhsqrtl = dsqrt(qr(i-1,1))
         rhsqrtr = dsqrt(ql(i,1))
         pl = gamma1*(qr(i-1,4) - 0.5d0*(qr(i-1,2)**2 +
     &        qr(i-1,3)**2)/qr(i-1,1))
         pr = gamma1*(ql(i,4) - 0.5d0*(ql(i,2)**2 +
     &        ql(i,3)**2)/ql(i,1))
         rhsq2 = rhsqrtl + rhsqrtr
         u(i) = (qr(i-1,mu)/rhsqrtl + ql(i,mu)/rhsqrtr) / rhsq2
         v(i) = (qr(i-1,mv)/rhsqrtl + ql(i,mv)/rhsqrtr) / rhsq2
         enth(i) = (((qr(i-1,4)+pl)/rhsqrtl
     &             + (ql(i,4)+pr)/rhsqrtr)) / rhsq2
	 u2v2(i) = u(i)**2 + v(i)**2
         a2 = gamma1*(enth(i) - .5d0*u2v2(i))
         a(i) = dsqrt(a2)
	 g1a2(i) = gamma1 / a2
	 euv(i) = enth(i) - u2v2(i) 
   10    continue
c
c
c     # now split the jump in q at each interface into waves
c
c     # find a1 thru a4, the coefficients of the 4 eigenvectors:
      do 20 i = 2-mbc, mx+mbc
         delta(1) = ql(i,1) - qr(i-1,1)
         delta(2) = ql(i,mu) - qr(i-1,mu)
         delta(3) = ql(i,mv) - qr(i-1,mv)
         delta(4) = ql(i,4) - qr(i-1,4)
         a3 = g1a2(i) * (euv(i)*delta(1) 
     &      + u(i)*delta(2) + v(i)*delta(3) - delta(4))
         a2 = delta(3) - v(i)*delta(1)
         a4 = (delta(2) + (a(i)-u(i))*delta(1) - a(i)*a3) / (2.d0*a(i))
         a1 = delta(1) - a3 - a4
c
c        # Compute the waves.
c        # Note that the 2-wave and 3-wave travel at the same speed and 
c        # are lumped together in wave(.,.,2).  The 4-wave is then stored in
c        # wave(.,.,3).
c
         wave(i,1,1) = a1
         wave(i,mu,1) = a1*(u(i)-a(i))
         wave(i,mv,1) = a1*v(i)
         wave(i,4,1) = a1*(enth(i) - u(i)*a(i))
         s(i,1) = u(i)-a(i)
c
         wave(i,1,2) = a3
         wave(i,mu,2) = a3*u(i)
         wave(i,mv,2) = a3*v(i)	 	 + a2
         wave(i,4,2) = a3*0.5d0*u2v2(i)  + a2*v(i)
         s(i,2) = u(i)
c
         wave(i,1,3) = a4
         wave(i,mu,3) = a4*(u(i)+a(i))
         wave(i,mv,3) = a4*v(i)
         wave(i,4,3) = a4*(enth(i)+u(i)*a(i))
         s(i,3) = u(i)+a(i)
   20    continue
c
c
c    # compute flux differences amdq and apdq.
c    ---------------------------------------
c
      if (efix) go to 110
c
c     # no entropy fix
c     ----------------
c
c     # amdq = SUM s*wave   over left-going waves
c     # apdq = SUM s*wave   over right-going waves
c
      do 100 m=1,4
         do 100 i=2-mbc, mx+mbc
	    amdq(i,m) = 0.d0
	    do 90 mw=1,mwaves
	       if (s(i,mw) .lt. 0.d0) then
                  amdq(i,m) = amdq(i,m) + s(i,mw)*wave(i,m,mw)
               endif
 90         continue
 100  continue
      go to 900	    
c
c-----------------------------------------------------
c
  110 continue
c
c     # With entropy fix
c     ------------------
c
c    # compute flux differences amdq and apdq.
c    # First compute amdq as sum of s*wave for left going waves.
c    # Incorporate entropy fix by adding a modified fraction of wave
c    # if s should change sign.
c
      do 200 i = 2-mbc, mx+mbc
c
c        # check 1-wave:
c        ---------------
c
	 rhoim1 = qr(i-1,1)
	 pim1 = gamma1*(qr(i-1,4) - 0.5d0*(qr(i-1,mu)**2 
     &           + qr(i-1,mv)**2) / rhoim1)
	 cim1 = dsqrt(gamma*pim1/rhoim1)
	 s0 = qr(i-1,mu)/rhoim1 - cim1     !# u-c in left state (cell i-1)

c        # check for fully supersonic case:
	 if (s0.ge.0.d0 .and. s(i,1).gt.0.d0)  then
c            # everything is right-going
	     do 60 m=1,4
		amdq(i,m) = 0.d0
   60           continue
	     go to 200 
	     endif
c
         rho1 = qr(i-1,1) + wave(i,1,1)
         rhou1 = qr(i-1,mu) + wave(i,mu,1)
         rhov1 = qr(i-1,mv) + wave(i,mv,1)
         en1 = qr(i-1,4) + wave(i,4,1)
         p1 = gamma1*(en1 - 0.5d0*(rhou1**2 + rhov1**2)/rho1)
         c1 = dsqrt(gamma*p1/rho1)
         s1 = rhou1/rho1 - c1  !# u-c to right of 1-wave
         if (s0.lt.0.d0 .and. s1.gt.0.d0) then
c            # transonic rarefaction in the 1-wave
	     sfract = s0 * (s1-s(i,1)) / (s1-s0)
	   else if (s(i,1) .lt. 0.d0) then
c	     # 1-wave is leftgoing
	     sfract = s(i,1)
	   else
c	     # 1-wave is rightgoing
             sfract = 0.d0   !# this shouldn't happen since s0 < 0
	   endif
	 do 120 m=1,4
	    amdq(i,m) = sfract*wave(i,m,1)
  120       continue
c
c        # check 2-wave:
c        ---------------
c
         if (s(i,2) .ge. 0.d0) go to 200  !# 2- and 3- waves are rightgoing
	 do 140 m=1,4
	    amdq(i,m) = amdq(i,m) + s(i,2)*wave(i,m,2)
  140       continue
c
c        # check 3-wave:
c        ---------------
c
	 rhoi = ql(i,1)
	 pi = gamma1*(ql(i,4) - 0.5d0*(ql(i,mu)**2 
     &           + ql(i,mv)**2) / rhoi)
	 ci = dsqrt(gamma*pi/rhoi)
	 s3 = ql(i,mu)/rhoi + ci     !# u+c in right state  (cell i)
c
         rho2 = ql(i,1) - wave(i,1,3)
         rhou2 = ql(i,mu) - wave(i,mu,3)
         rhov2 = ql(i,mv) - wave(i,mv,3)
         en2 = ql(i,4) - wave(i,4,3)
         p2 = gamma1*(en2 - 0.5d0*(rhou2**2 + rhov2**2)/rho2)
         c2 = dsqrt(gamma*p2/rho2)
         s2 = rhou2/rho2 + c2   !# u+c to left of 3-wave
         if (s2 .lt. 0.d0 .and. s3.gt.0.d0) then
c            # transonic rarefaction in the 3-wave
	     sfract = s2 * (s3-s(i,3)) / (s3-s2)
	   else if (s(i,3) .lt. 0.d0) then
c            # 3-wave is leftgoing
	     sfract = s(i,3)
	   else 
c            # 3-wave is rightgoing
	     go to 200
	   endif
c
	 do 160 m=1,4
	    amdq(i,m) = amdq(i,m) + sfract*wave(i,m,3)
  160       continue
  200    continue
c
  900 continue
      call flx2(ixy,maxm,meqn,mbc,mx,qr,maux,auxr,apdq)
c
      do 300 i = 2-mbc, mx+mbc
         do 300 m=1,meqn
            amdq(i,m) = apdq(i-1,m) + amdq(i,m) 
 300  continue
c
      do 310 i = 2-mbc, mx+mbc
         do 310 m=1,meqn
            apdq(i,m) = -amdq(i,m) 
 310  continue
c
      return
      end
c


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last update: 06/01/04