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rp1.f.html |
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Source file: rp1.f
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Directory: /Users/rjl/git/rjleveque/clawpack-4.6.3/book/chap9/acoustics/interface
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Converted: Mon Jan 21 2013 at 20:15:47
using clawcode2html
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This documentation file will
not reflect any later changes in the source file.
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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,
c # variable coefficients
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)*auxl(i,2)
zim = auxl(i-1,1)*auxl(i-1,2)
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
if (mylim .gt. 0) then
c
c # apply limiter here rather than using default in limiter.f
c
do 40 i=1,mx
c # limit 1-wave by looking at wave to right:
a1i = wave(i,2,1)
if (a1i .eq. 0.d0) go to 30
if (mylim .eq. 1) then
c # Lax-Liu limiter:
delta(1) = ql(i+1,1) - qr(i,1)
delta(2) = ql(i+1,2) - qr(i,2)
else if (mylim .eq. 2) then
c # Transmission-based limiter for acoutics:
delta(1) = wave(i+1,1,1)
delta(2) = wave(i+1,2,1)
endif
c # impedances:
zi = auxl(i,1)*auxl(i,2)
zim = auxl(i-1,1)*auxl(i-1,2)
a1ip1 = (-delta(1) + zi*delta(2)) / (zim + zi)
wlimitr = philim(a1i, a1ip1, mrplim(1))
wave(i,1,1) = wlimitr * wave(i,1,1)
wave(i,2,1) = wlimitr * wave(i,2,1)
30 continue
c
c # limit 2-wave by looking at wave to left:
a2i = wave(i,2,2)
if (a2i .eq. 0.d0) go to 40
if (mylim .eq. 1) then
c # Lax-Liu limiter:
delta(1) = ql(i-1,1) - qr(i-2,1)
delta(2) = ql(i-1,2) - qr(i-2,2)
else if (mylim .eq. 2) then
c # Transmission-based limiter for acoutics:
delta(1) = wave(i-1,1,2)
delta(2) = wave(i-1,2,2)
endif
c # impedances:
zi = auxl(i,1)*auxl(i,2)
zim = auxl(i-1,1)*auxl(i-1,2)
a2im1 = (delta(1) + zim*delta(2)) / (zim + zi)
wlimitr = philim(a2i, a2im1, mrplim(2))
wave(i,1,2) = wlimitr * wave(i,1,2)
wave(i,2,2) = wlimitr * wave(i,2,2)
40 continue
endif
return
end