c
c
c =====================================================
subroutine rpn2ad1(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr,maux,
& auxl,auxr,wave,s,amdq,apdq)
c =====================================================
c
c # Riemann-solver for the advection equation
c # q_t + u*q_x + v*q_y = 0
c # where u and v are a given velocity field.
c
c -----------------------------------------------------------
c # In advective form, with interface velocities specified in
c # the auxiliary variable
c # aux(i,j,1) = u-velocity at left edge of cell (i,j)
c # aux(i,j,2) = v-velocity at bottom edge of cell (i,j)
c -----------------------------------------------------------
c
c # solve Riemann problems along one slice of data.
c # This data is along a slice in the x-direction if ixy=1
c # or the y-direction if ixy=2.
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, s the speeds,
c # and amdq, apdq the left-going and right-going flux differences,
c # respectively. Note that in this advective form, the sum of
c # amdq and apdq is not equal to a difference of fluxes except in the
c # case of constant velocities.
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 # Riemann solver returns flux differences
c ------------
common /rpnflx/ mrpnflx
mrpnflx = 0
c
c # Set wave, speed, and flux differences:
c ------------------------------------------
c
do 30 i = 2-mbc, mx+mbc
wave(i,1,1) = ql(i,1) - qr(i-1,1)
s(i,1) = auxl(i,ixy)
c # The flux difference df = s*wave all goes in the downwind direction:
amdq(i,1) = dmin1(auxl(i,ixy), 0.d0) * wave(i,1,1)
apdq(i,1) = dmax1(auxl(i,ixy), 0.d0) * wave(i,1,1)
30 continue
c
return
end