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src/1d/equations/euler/rpm/rp1eum.f

c
c
c     =========================================================
      subroutine rp1eum(maxmx,meqn,mwaves,mbc,mx,ql,qr,maux,
     &                  auxl,auxr,wave,s,amdq,apdq)
c     =========================================================
c
c     # solve Riemann problems for the 1D two-component 
c     # Euler equations using Roe's approximate Riemann solver.  
c     
c     # Keh-Ming Shyue "An efficient shock-capturing algorithm for
c     # compressible multicomponent problems", J. Comput. Phys., Vol. 142, 
c     # pp 208-242, 1998
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     # On output, wave contains the waves, 
c     #            s the speeds, 
c     #            amdq the  left-going flux difference  A^- \Delta q
c     #            apdq the right-going flux difference  A^+ \Delta q
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, rp is called with ql = qr = q.
c     
c     # Copyright (C) 2002 Ralf Deiterding
c     # Brandenburgische Universitaet Cottbus
c
c     # Copyright (C) 2003-2007 California Institute of Technology
c     # Ralf Deiterding, ralf@amroc.net
c
      implicit double precision (a-h,o-z)
      dimension   ql(1-mbc:maxmx+mbc, meqn)
      dimension   qr(1-mbc:maxmx+mbc, meqn)
      dimension    s(1-mbc:maxmx+mbc, mwaves)
      dimension wave(1-mbc:maxmx+mbc, meqn, mwaves)
      dimension amdq(1-mbc:maxmx+mbc, meqn)
      dimension apdq(1-mbc:maxmx+mbc, meqn)
c
c     # local storage
c     ---------------
      parameter (max2 = 100002)  !# assumes at most 100000 grid points with mbc=2
      dimension delta(5)
      dimension u(-1:max2),enth(-1:max2),a(-1:max2),
     &     g1a2(-1:max2),euv(-1:max2),p(-1:max2) 
      logical efix
c
      data efix /.true./    !# use entropy fix for transonic rarefactions
c
c     # Riemann solver returns flux differences
c     ------------
      common /rpnflx/ mrpnflx
      mrpnflx = 0
c
c     # Compute Roe-averaged quantities:
c
      do 10 i = 2-mbc, mx+mbc
         rhsqrtl = dsqrt(qr(i-1,1))
         rhsqrtr = dsqrt(ql(i,1))
         pl = (qr(i-1,3) - 0.5d0*(qr(i-1,2)**2)/qr(i-1,1) 
     &        - qr(i-1,5) ) / qr(i-1,4)
         pr = (ql(i,3) - 0.5d0*(ql(i,2)**2)/ql(i,1) 
     &        - ql(i,5) ) / ql(i,4)
         rhsq2 = rhsqrtl + rhsqrtr
         gamma1 = rhsq2 / ( qr(i-1,4)*rhsqrtl + ql(i,4)*rhsqrtr ) 
         xjota = ( pl*qr(i-1,4)*rhsqrtl + pr*ql(i,4)*rhsqrtr ) / rhsq2
         p(i) = xjota*gamma1                      
         u(i) = (qr(i-1,2)/rhsqrtl + ql(i,2)/rhsqrtr) / rhsq2
         enth(i) = (((qr(i-1,3)+pl)/rhsqrtl
     &             + (ql(i,3)+pr)/rhsqrtr)) / rhsq2                      
         a2 = gamma1*(enth(i) - .5d0*u(i)**2)
         a(i) = dsqrt(a2)
         g1a2(i) = gamma1 / a2
         euv(i) = enth(i) - u(i)**2
 10   continue
c
c
c     # now split the jump in q at each interface into waves
c
c     # find a1 thru a5, the coefficients of the 5 eigenvectors:
      do 20 i = 2-mbc, mx+mbc
         do n = 1, 5
            delta(n) = ql(i,n) - qr(i-1,n)
         enddo
         a2 = g1a2(i) * (euv(i)*delta(1) + u(i)*delta(2) - delta(3)
     &      + p(i)*delta(4) + delta(5))
         a3 = (delta(2) + (a(i)-u(i))*delta(1) - a(i)*a2) / (2.d0*a(i))
         a1 = delta(1) - a2 - a3
         a4 = delta(4)
         a5 = delta(5)
c
c        # Compute the waves.
c        # Note that the 2-wave as well as the 4-wave and 5-wave
c        # travel at the same speed and are lumped together in wave(.,.,2).
c        # The 3-wave is then stored in wave(.,.,3).
c
         wave(i,1,1) = a1
         wave(i,2,1) = a1*(u(i)-a(i))
         wave(i,3,1) = a1*(enth(i) - u(i)*a(i))
         wave(i,4,1) = 0.d0
         wave(i,5,1) = 0.d0 
         s(i,1) = u(i)-a(i)
c
         wave(i,1,2) = a2
         wave(i,2,2) = a2*u(i)
         wave(i,3,2) = a2*0.5d0*u(i)**2 + a4*p(i) + a5
         wave(i,4,2) =                    a4
         wave(i,5,2) =                              a5
         s(i,2) = u(i)
c
         wave(i,1,3) = a3
         wave(i,2,3) = a3*(u(i)+a(i))
         wave(i,3,3) = a3*(enth(i)+u(i)*a(i))
         wave(i,4,3) = 0.d0
         wave(i,5,3) = 0.d0 
         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=1,5
         do 100 i=2-mbc, mx+mbc
            amdq(i,m) = 0.d0
            apdq(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)
               else
                  apdq(i,m) = apdq(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 = (qr(i-1,3) - 0.5d0*(qr(i-1,2)**2)/qr(i-1,1) 
     &        - qr(i-1,5) ) / qr(i-1,4)
         gamma1 = 1.d0/qr(i-1,4)
         gamma = gamma1 + 1.d0
         pinf = qr(i-1,5)*gamma1/gamma
         cim1 = dsqrt(gamma*(pim1+pinf)/rhoim1)
         s0 = qr(i-1,2)/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=1,5
               amdq(i,m) = 0.d0
 60         continue
            go to 200 
         endif
c
         rho1 = qr(i-1,1) + wave(i,1,1)
         rhou1 = qr(i-1,2) + wave(i,2,1)
         en1 = qr(i-1,3) + wave(i,3,1)
         p1 = (en1-0.5d0*(rhou1**2)/rho1-qr(i-1,5))/qr(i-1,4)
         c1 = dsqrt(gamma*(p1+pinf)/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=1,5
            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=1,5
            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 = (ql(i,3) - 0.5d0*(ql(i,2)**2)/ql(i,1) 
     &        - ql(i,5) ) / ql(i,4)
         gamma1 = 1.d0/ql(i,4)
         gamma = gamma1 + 1.d0
         pinf = ql(i,5)*gamma1/gamma
         ci = dsqrt(gamma*(pi+pinf)/rhoi)
         s3 = ql(i,2)/rhoi + ci     !# u+c in right state  (cell i)
c
         rho2 = ql(i,1) - wave(i,1,3)
         rhou2 = ql(i,2) - wave(i,2,3)
         en2 = ql(i,3) - wave(i,3,3)
         p2 = (en2-0.5d0*(rhou2**2)/rho2-ql(i,5))/ql(i,4)
         c2 = dsqrt(gamma*(p2+pinf)/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=1,5
            amdq(i,m) = amdq(i,m) + sfract*wave(i,m,3)
 160     continue
 200  continue
c
c     # compute the rightgoing flux differences:
c     # df = SUM s*wave   is the total flux difference and apdq = df - amdq
c
      do 220 m=1,5
         do 220 i = 2-mbc, mx+mbc
            df = 0.d0
            do 210 mw=1,mwaves
               df = df + s(i,mw)*wave(i,m,mw)
 210        continue
            apdq(i,m) = df - amdq(i,m)
 220  continue
c
 900  continue
      return
      end

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