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<h1>[www.clawpack.org Clawpack] Fortran file rp1.f</h1>

The file can have a different name, but should contain a subroutine called
rp1. 

For additional documentation on Riemann solvers, see the CLAWPACK
documentation at [www.clawpack.org/doc.html], or the book
[www.clawpack.org/book.html FVMHP].

The rp1 subroutine should have the following form:

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c
c
c     =====================================================
      subroutine rp1(maxm,meqn,mwaves,mbc,mx,ql,qr,auxl,auxr,
     &                  wave,s,amdq,apdq)
c     =====================================================
c
      implicit double precision (a-h,o-z)
      dimension   ql(1-mbc:maxmx+mbc, meqn)
      dimension   qr(1-mbc:maxmx+mbc, meqn)
      dimension auxl(1-mbc:maxmx+mbc, *)
      dimension auxr(1-mbc:maxmx+mbc, *)
      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     Compute wave, s, amdq, apdq...
c
      return
      end

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       <dl><dt><b>On input:</b></dt>
         <dd> maxm = leading dimension of the q and aux arrays.</dd>
         <dd> meqn = number of equations in the system (second dimension of q).</dd>
         <dd> mwaves = number of waves returned from the Riemann solver,</dd>
         <dd> mbc = number of ghost cells on left and on right.</dd>
         <dd> mx = number of interior grid cells.</dd>
         <dd> ql contains the state vector at the left edge of each cell,</dd>
         <dd> qr contains the state vector at the right edge of each cell,</dd>
         <dd> auxl contains the auxiliary array at the left edge,</dd>
         <dd> auxr contains the auxiliary array at the right edge,</dd>
<p>
       </dl>
<p>
       The i'th Riemann problem has left state qr(i-1,:) and right state ql(i,:).
<p>
       The Riemann solver may use data in the aux array, in which case the
       values auxr(i-1,:) and auxl(i,:) should generally be used.
<p>
       From the basic clawpack routine step1, rp1 is called with ql = qr = q
            and auxl = auxr = aux.
<p>
<p>
       <dl><dt><b>On output:</b></dt>
         <dd> wave contains the waves, </dd>
         <dd> s the speeds, </dd>
         <dd> amdq the  left-going flux difference  $\A^-\Delta Q$, </dd>
         <dd> apdq the right-going flux difference  $\A^+\Delta Q$ </dd>
       </dl>
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