bw.f

四十三种差分格式源代码,这只是计算用的

       program beamwarm
c...Solves the Riemann problem for the Euler equations using
c...the Beam-Warming second-order upwind method based on any
c...of three possible flux vector splittings.

c...METHOD = 1     Steger-Warming
c...METHOD = 2     van Leer
c...METHOD = 3     Zha-Bilgen

c...TSTEP = 1      Fixed time step 
c...TSTEP = 2      Fixed CFL number

c...SMOOTH = .false.     Do not smooth initial conditions
c...SMOOTH = .true       Smooth initial conditions

c...ARTVIS = .false.     Do not use artificial viscosity
c...ARTVIS = .true.      Use artificial viscosity

c...Number of grid points.
      parameter(N = 50)

      integer method, tstep
	logical smooth, artvis
      real*8 gamma, pl, pr, ul, ur, p, a, u, rul, rur, delta_t, delta_x
      real*8 aa, bb, t, rhol, rhor, R, cu, cp, lambda, rhomax, x, al, ar
      real*8 u1(-2:N+4), u2(-2:N+4), u3(-2:N+4), retl, retr, rho(1:N+1)
      real*8 ub1(-2:N+4), ub2(-2:N+4), ub3(-2:N+4), tt
      real*8 fp1(-2:N+3), fp2(-2:N+3), fp3(-2:N+3)
      real*8 fm1(-2:N+3), fm2(-2:N+3), fm3(-2:N+3)
      real*8 fbp1(-1:N+2), fbp2(-1:N+2), fbp3(-1:N+2)
      real*8 fbm1(-1:N+2), fbm2(-1:N+2), fbm3(-1:N+2)
      real*8 av1(-2:N+4), av2(-2:N+4), av3(-2:N+4)

      parameter (gamma=1.4,R=287.0,cfl=0.4)
	parameter (method=3,tstep=1,smooth=.false.,artvis=.false.)
      parameter (cu = R/(gamma-1), cp = gamma*R/(gamma-1.))

      open (unit=11,file='input.dat')
      read(11,*) aa, bb, t
      read(11,*) pl, rhol, ul
      read(11,*) pr, rhor, ur
      close(unit=11)

      al = sqrt(gamma*pl/rhol)
      ar = sqrt(gamma*pr/rhor)
      rhomax = max(abs(ul+al),abs(ur+ar),abs(ul-al),abs(ur-ar))
      delta_x = (bb-aa)/real(N)
      delta_t = cfl*delta_x/rhomax
      if(tstep.eq.1) then
        itert = nint(t/delta_t)
      elseif(tstep.eq.2) then
        itert = 10000
      endif
      lambda = delta_t/delta_x
      write(*,*) 'Final time requested =  ', t
      write(*,*) 'Delta_t =  ', delta_t
      write(*,*) 'Delta_x =  ', delta_x
      write(*,*) 'Lambda =  ', lambda
      write(*,*) 'Initial CFL number =  ', lambda*rhomax
      if(tstep.eq.1) write(*,*) '# iterations =  ', itert

c...Convert primitive variables to conservative variables.
      rul = rhol*ul
      rur = rhor*ur
      retl = .5*rul*ul + pl/(gamma-1.)
      retr = .5*rur*ur + pr/(gamma-1.)

c...Construct the initial conditions for the Riemann problem.
      do 30, i=-2,N+4
        x = aa + (bb-aa)*real(i-1)/real(N)
        if(.NOT.smooth) then
          if(x.lt.0.) then
            u1(i) = rhol
            u2(i) = rul
            u3(i) = retl
            ub1(i) = rhol
            ub2(i) = rul
            ub3(i) = retl
          elseif(x.ge.0.) then
            u1(i) = rhor
            u2(i) = rur
            u3(i) = retr
            ub1(i) = rhor
            ub2(i) = rur
            ub3(i) = retr
          endif
        elseif(smooth) then
c...Slightly smoothed initial data
          if(x.lt.-0.5001) then
            u1(i) = rhol
            u2(i) = rul
            u3(i) = retl
            ub1(i) = rhol
            ub2(i) = rul
            ub3(i) = retl
          elseif(x.le.-0.001) then
            u1(i) = .75*rhol+.25*rhor
            u2(i) = .75*rul+.25*rur
            u3(i) = .75*retl+.25*retr
            ub1(i) = .75*rhol+.25*rhor
            ub2(i) = .75*rul+.25*rur
            ub3(i) = .75*retl+.25*retr
          elseif(x.le.0.001) then
            u1(i) = .5*rhol+.5*rhor
            u2(i) = .5*rul+.5*rur
            u3(i) = .5*retl+.5*retr
            ub1(i) = .5*rhol+.5*rhor
            ub2(i) = .5*rul+.5*rur
            ub3(i) = .5*retl+.5*retr
          elseif(x.le.0.5001) then
            u1(i) = .25*rhol+.75*rhor
            u2(i) = .25*rul+.75*rur
            u3(i) = .25*retl+.75*retr
            ub1(i) = .25*rhol+.75*rhor
            ub2(i) = .25*rul+.75*rur
            ub3(i) = .25*retl+.75*retr
          else
            u1(i) = rhor
            u2(i) = rur
            u3(i) = retr
            ub1(i) = rhor
            ub2(i) = rur
            ub3(i) = retr
           endif
         endif
 30   continue

      tt = 0.
C...Main loop.
      do 100, j=1,itert

         rhomax = 0.
C...Find split PREDICTOR fluxes.
         if(method.eq.1) then
           do 40, i=-2,N+3
             call sw(u1(i),u2(i),u3(i),u1(i+1),u2(i+1),
     *       u3(i+1),fp1(i),fp2(i),fp3(i),fm1(i),fm2(i),fm3(i))
 40        continue
         elseif(method.eq.2) then
           do 41, i=-2,N+3
             call vl(u1(i),u2(i),u3(i),u1(i+1),u2(i+1),
     *       u3(i+1),fp1(i),fp2(i),fp3(i),fm1(i),fm2(i),fm3(i))
 41        continue
         elseif(method.eq.3) then
           do 42, i=-2,N+3
             call zb(u1(i),u2(i),u3(i),u1(i+1),u2(i+1),
     *       u3(i+1),fp1(i),fp2(i),fp3(i),fm1(i),fm2(i),fm3(i))
 42        continue
         endif

C...Find PREDICTED solution.
         do 50, i=-1,N+3
           ub1(i) = u1(i) - lambda*(fp1(i)+fm1(i)-fp1(i-1)-fm1(i-1))
           ub2(i) = u2(i) - lambda*(fp2(i)+fm2(i)-fp2(i-1)-fm2(i-1))
           ub3(i) = u3(i) - lambda*(fp3(i)+fm3(i)-fp3(i-1)-fm3(i-1))
           if(u1(i).lt.0..or.u3(i).lt.0.) then
             write(*,*) 'WARNING: Negative density/energy in predictor'
             write(*,*) '# time steps = ', j
             write(*,*) 'Grid point = ', i
             write(*,*) 'x = ', aa + (bb-aa)*real(i-1)/real(N)
             write(*,*) 'Density = ', u1(i)
             write(*,*) 'Total energy per unit volume = ', u3(i)
             stop
           endif
           u = u2(i)/u1(i)
           p = (gamma-1.)*(u3(i) - .5*u2(i)*u2(i)/u1(i))
           if(p.lt.0.) then
             write(*,*) 'WARNING: Negative pressure in predictor'
             write(*,*) '# time steps = ', j
             write(*,*) 'Grid point = ', i
             write(*,*) 'x = ', aa + (bb-aa)*real(i-1)/real(N)
             write(*,*) 'Pressure = ', p
             stop
           endif
 50      continue

C...Find split CORRECTOR fluxes.
         if(method.eq.1) then
           do 60, i=-1,N+2
             call sw(ub1(i),ub2(i),ub3(i),ub1(i+1),ub2(i+1),ub3(i+1),
     *       fbp1(i),fbp2(i),fbp3(i),fbm1(i),fbm2(i),fbm3(i))
 60        continue
         elseif(method.eq.2) then
           do 61, i=-1,N+2
             call vl(ub1(i),ub2(i),ub3(i),ub1(i+1),ub2(i+1),ub3(i+1),
     *       fbp1(i),fbp2(i),fbp3(i),fbm1(i),fbm2(i),fbm3(i))
 61        continue
         elseif(method.eq.3) then
           do 62, i=-1,N+2
             call zb(ub1(i),ub2(i),ub3(i),ub1(i+1),ub2(i+1),ub3(i+1),
     *       fbp1(i),fbp2(i),fbp3(i),fbm1(i),fbm2(i),fbm3(i))
 62        continue
         endif

C...Find CORRECTED solution.
         do 70, i=1,N+1
           if(artvis) then
             av1(i) = .05*(u1(i+1)-2.*u1(i)+u1(i-1))
             av2(i) = .05*(u2(i+1)-2.*u2(i)+u2(i-1))
             av3(i) = .05*(u3(i+1)-2.*u3(i)+u3(i-1))
           else
             av1(i) = 0.
             av2(i) = 0.
             av3(i) = 0.
           endif
           u1(i) = .5*(u1(i)+ub1(i))
     *             -.5*lambda*(fbp1(i)+fbm1(i)-fbp1(i-1)-fbm1(i-1))
     *             -.5*lambda*(fp1(i)-2.*fp1(i-1)+fp1(i-2))
     *             +.5*lambda*(fm1(i+1)-2.*fm1(i)+fm1(i-1))
     *             +av1(i)
           u2(i) = .5*(u2(i)+ub2(i))
     *             -.5*lambda*(fbp2(i)+fbm2(i)-fbp2(i-1)-fbm2(i-1))
     *             -.5*lambda*(fp2(i)-2.*fp2(i-1)+fp2(i-2))
     *             +.5*lambda*(fm2(i+1)-2.*fm2(i)+fm2(i-1))
     *             +av2(i)
           u3(i) = .5*(u3(i)+ub3(i))
     *             -.5*lambda*(fbp3(i)+fbm3(i)-fbp3(i-1)-fbm3(i-1))
     *             -.5*lambda*(fp3(i)-2.*fp3(i-1)+fp3(i-2))
     *             +.5*lambda*(fm3(i+1)-2.*fm3(i)+fm3(i-1))
     *             +av3(i)
           if(u1(i).lt.0..or.u3(i).lt.0.) then
             write(*,*) 'WARNING: Negative density/energy in corrector'
             write(*,*) '# time steps = ', j
             write(*,*) 'Grid point = ', i
             write(*,*) 'x = ', aa + (bb-aa)*real(i-1)/real(N)
             write(*,*) 'Density = ', u1(i)
             write(*,*) 'Total energy per unit volume = ', u3(i)
             stop
           endif
           u = u2(i)/u1(i)
           p = (gamma-1.)*(u3(i) - .5*u2(i)*u2(i)/u1(i))
           if(p.lt.0.) then
             write(*,*) 'WARNING: Negative pressure in corrector'
             write(*,*) '# time steps = ', j
             write(*,*) 'Grid point = ', i
             write(*,*) 'x = ', aa + (bb-aa)*real(i-1)/real(N)
             write(*,*) 'Pressure = ', p
             stop