c c c ===================================================== subroutine rp1(maxm,meqn,mwaves,mbc,mx,ql,qr,auxl,auxr, & wave,s,amdq,apdq) c ===================================================== c c # Riemann solver for the acoustics equations in 1d, with c # variable coefficients (heterogeneous media) c c # auxl(i,1) should contain the impedance Z in cell i c # auxl(i,2) should contain the sound speed c in cell i 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 # On output, wave contains the waves, c # s the speeds, c # c # amdq = A^- Delta q, c # apdq = A^+ Delta q, c # the decomposition of the flux difference c # f(qr(i-1)) - f(ql(i)) c # into leftgoing and rightgoing parts respectively. c # 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 auxl(1-mbc:maxm+mbc, 2) dimension auxr(1-mbc:maxm+mbc, 2) 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) common /comlim/ mylim,mrplim(2) c c local arrays c ------------ dimension delta(2) c c c # split the jump in q at each interface into waves 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,2) - qr(i-1,2) 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,2,1) = a1 s(i,1) = -auxl(i-1,2) c wave(i,1,2) = a2*zi wave(i,2,2) = a2 s(i,2) = auxl(i,2) c 20 continue c c c # compute the leftgoing and rightgoing fluctuations: 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