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Source file: rpn2acv.f | |
Directory: /Users/rjl/git/rjleveque/clawpack-4.6.3/book/chap21/corner | |
Converted: Mon Jan 21 2013 at 20:15:38 using clawcode2html | |
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c c c ===================================================== subroutine rpn2(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr, & auxl,auxr,wave,s,amdq,apdq) c ===================================================== c c # Riemann solver for the acoustics equations in 2d, with varying c # material properties rho and kappa c c # Note that although there are 3 eigenvectors, the second eigenvalue c # is always zero and so we only need to compute 2 waves. c # 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 # auxl(i,1) holds impedance Z, c # auxl(i,2) holds sound speed c, c # Here it is assumed that auxl=auxr gives the cell values. c c 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 c # This data is along a slice in the x-direction if ixy=1 c # or the y-direction if ixy=2. 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 clawpack routines, this routine is called with ql = qr c c implicit double precision (a-h,o-z) c 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 apdq(1-mbc:maxm+mbc, meqn) dimension amdq(1-mbc:maxm+mbc, meqn) dimension auxl(1-mbc:maxm+mbc, 2) dimension auxr(1-mbc:maxm+mbc, 2) c c local arrays c ------------ dimension delta(3) c common /comxyt/ dtcom,dxcom,dycom,tcom,icom,jcom c c # set mu to point to the component of the system that corresponds c # to velocity in the direction of this slice, mv to the orthogonal c # velocity. c 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 c c # split the jump in q at each interface into waves c # The jump is split into a leftgoing wave traveling at speed -c c # relative to the material properties to the left of the interface, c # and a rightgoing wave traveling at speed +c c # relative to the material properties to the right of the interface, c c # find a1 and a2, the coefficients of the 2 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) c # impedances: zi = auxl(i,1) zim = auxl(i-1,1) a1 = (-delta(1) + zi*delta(2)) / (zim + zi) a2 = (delta(1) + zim*delta(2)) / (zim + zi) c c # Compute the waves. c wave(i,1,1) = -a1*zim wave(i,mu,1) = a1 wave(i,mv,1) = 0.d0 s(i,1) = -auxl(i-1,2) c wave(i,1,2) = a2*zi wave(i,mu,2) = a2 wave(i,mv,2) = 0.d0 s(i,2) = auxl(i,2) c 20 continue c c c c # compute the leftgoing and rightgoing flux differences: c # Note s(i,1) < 0 and s(i,2) > 0. c do 220 m=1,meqn do 220 i = 2-mbc, mx+mbc amdq(i,m) = s(i,1)*wave(i,m,1) apdq(i,m) = s(i,2)*wave(i,m,2) 220 continue c return end