c
c =========================================================
subroutine rpn2euznd(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr,maux,
& auxl,auxr,wave,s,amdq,apdq)
c =========================================================
c
c # solve Riemann problems for the 2D ZND-Euler equations using Roe's
c # approximate Riemann solver.
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 # This data is along a slice in the x-direction if ixy=1
c # or the y-direction if ixy=2.
c # On output, wave contains the waves, s the speeds,
c # amdq and apdq the positive and negative flux.
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 routines, this routine is called with ql = qr
c
c # Author: Ralf Deiterding (based on rpn2eu.f)
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 amdq(1-mbc:maxm+mbc, meqn)
dimension apdq(1-mbc:maxm+mbc, meqn)
c
c local arrays -- common block comroe is passed to rpt2eu
c ------------
parameter (maxm2 = 10005) !# assumes at most 10000x10000 grid with mbc=5
parameter (minm2 = -4) !# assumes at most mbc=5
dimension delta(5)
logical efix, pfix
common /param/ gamma,gamma1,q0
common /comroe/ u2v2(minm2:maxm2),u(minm2:maxm2),v(minm2:maxm2),
& enth(minm2:maxm2),a(minm2:maxm2),Y(2,minm2:maxm2)
dimension fr(minm2:maxm2,5), fl(minm2:maxm2,5)
c
data efix /.true./ !# use entropy fix for transonic rarefactions
data pfix /.true./ !# use Larrouturou's positivity fix for species
c
c # Riemann solver returns fluxes
c ------------
common /rpnflx/ mrpnflx
mrpnflx = 1
c
if (minm2.gt.1-mbc .or. maxm2 .lt. maxm+mbc) then
write(6,*) 'need to increase maxm2 in rpA'
stop
endif
c
c # set mu to point to the component of the system that corresponds
c # to momentum in the direction of this slice, mv to the orthogonal
c # momentum:
c
if (ixy.eq.1) then
mu = 3
mv = 4
else
mu = 4
mv = 3
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 # and returns, for example, f0 as the Godunov flux g0 for the
c # Riemann problems u_t + g(u)_y = 0 in the y-direction.
c
c
c # compute the Roe-averaged variables needed in the Roe solver.
c # These are stored in the common block comroe since they are
c # later used in routine rpt2eu to do the transverse wave splitting.
c
do 10 i=2-mbc,mx+mbc
c
pl = gamma1*(qr(i-1,5) - qr(i-1,2)*q0 -
& 0.5d0*(qr(i-1,mu)**2+qr(i-1,mv)**2)/(qr(i-1,1)+qr(i-1,2)))
pr = gamma1*(ql(i, 5) - ql(i, 2)*q0 -
& 0.5d0*(ql(i, mu)**2+ql(i, mv)**2)/(ql(i, 1)+ql(i, 2)))
rhsqrtl = dsqrt(qr(i-1,1) + qr(i-1,2))
rhsqrtr = dsqrt(ql(i, 1) + ql(i, 2))
rhsq2 = rhsqrtl + rhsqrtr
u(i) = (qr(i-1,mu)/rhsqrtl + ql(i,mu)/rhsqrtr) / rhsq2
v(i) = (qr(i-1,mv)/rhsqrtl + ql(i,mv)/rhsqrtr) / rhsq2
u2v2(i) = u(i)**2 + v(i)**2
enth(i) = (((qr(i-1,5)+pl)/rhsqrtl
& + (ql(i ,5)+pr)/rhsqrtr)) / rhsq2
Y(1,i) = (qr(i-1,1)/rhsqrtl + ql(i,1)/rhsqrtr) / rhsq2
Y(2,i) = (qr(i-1,2)/rhsqrtl + ql(i,2)/rhsqrtr) / rhsq2
c # speed of sound
a2 = gamma1*(enth(i) - 0.5d0*u2v2(i) - Y(2,i)*q0)
a(i) = dsqrt(a2)
c
10 continue
c
do 30 i=2-mbc,mx+mbc
c
c # find a1 thru a3, the coefficients of the 4 eigenvectors:
c
do k = 1, 5
delta(k) = ql(i,k) - qr(i-1,k)
enddo
drho = delta(1) + delta(2)
c
a2 = gamma1/a(i)**2 * (drho*0.5d0*u2v2(i) - delta(2)*q0
& - (u(i)*delta(mu)+v(i)*delta(mv)) + delta(5))
a3 = delta(mv) - v(i)*drho
a4 = 0.5d0*( a2 - ( u(i)*drho - delta(mu) )/a(i) )
a1 = a2 - a4
c
c # Compute the waves.
c
c # 1-wave
wave(i,1,1) = a1*Y(1,i)
wave(i,2,1) = a1*Y(2,i)
wave(i,mu,1) = a1*(u(i) - a(i))
wave(i,mv,1) = a1*v(i)
wave(i,5,1) = a1*(enth(i) - u(i)*a(i))
s(i,1) = u(i)-a(i)
c
c # 2-wave
wave(i,1,2) = delta(1) - Y(1,i)*a2
wave(i,2,2) = delta(2) - Y(2,i)*a2
wave(i,mu,2) = (drho - a2)*u(i)
wave(i,mv,2) = (drho - a2)*v(i) + a3
wave(i,5,2) = (drho - a2)*0.5d0*u2v2(i) +
& q0*(delta(2) - Y(2,i)*a2) + a3*v(i)
s(i,2) = u(i)
c
c # 3-wave
wave(i,1,3) = a4*Y(1,i)
wave(i,2,3) = a4*Y(2,i)
wave(i,mu,3) = a4*(u(i) + a(i))
wave(i,mv,3) = a4*v(i)
wave(i,5,3) = a4*(enth(i) + u(i)*a(i))
s(i,3) = u(i)+a(i)
c
30 continue
c
c # compute Godunov flux f0:
c --------------------------
c
if (efix) go to 110
c
c # no entropy fix
c ----------------
c
c # amdq = SUM s*wave over left-going waves
c # apdq = SUM s*wave over right-going waves
c
do 100 m=1,meqn
do 100 i=2-mbc, mx+mbc
amdq(i,m) = 0.d0
apdq(i,m) = 0.d0
do 90 mw=1,mwaves
if (s(i,mw) .lt. 0.d0) then
amdq(i,m) = amdq(i,m) + s(i,mw)*wave(i,m,mw)
else
apdq(i,m) = apdq(i,m) + s(i,mw)*wave(i,m,mw)
endif
90 continue
100 continue
go to 900
110 continue
c
c # With entropy fix
c ------------------
c
c # compute flux differences amdq and apdq.
c # First compute amdq as sum of s*wave for left going waves.
c # Incorporate entropy fix by adding a modified fraction of wave
c # if s should change sign.
c
do 200 i=2-mbc,mx+mbc
c
c # check 1-wave:
c ---------------
c
rk1 = qr(i-1,1)
rk2 = qr(i-1,2)
rhou = qr(i-1,mu)
rhov = qr(i-1,mv)
rhoE = qr(i-1,5)
rho = rk1 + rk2
p = gamma1*(rhoE - rk2*q0 - 0.5d0*(rhou**2+rhov**2)/rho)
if ((rho.le.0.d0.or.p.le.0.d0).and.hll) go to 200
c = dsqrt(gamma*p/rho)
s0 = rhou/rho - c !# u-c in left state (cell i-1)
* write(6,*) 'left state 0', a(i), c, T
c
c # check for fully supersonic case:
if (s0.ge.0.d0 .and. s(i,1).gt.0.d0) then
c # everything is right-going
do 60 m=1,meqn
amdq(i,m) = 0.d0
60 continue
go to 200
endif
c
rk1 = rk1 + wave(i,1,1)
rk2 = rk2 + wave(i,2,1)
rhou = rhou + wave(i,mu,1)
rhov = rhov + wave(i,mv,1)
rhoE = rhoE + wave(i,5,1)
rho = rk1 + rk2
p = gamma1*(rhoE - rk2*q0 - 0.5d0*(rhou**2+rhov**2)/rho)
if ((rho.le.0.d0.or.p.le.0.d0).and.hll) go to 200
c = dsqrt(gamma*p/rho)
s1 = rhou/rho - c !# u-c to right of 1-wave
* write(6,*) 'left state 1', a(i), c, T
c
if (s0.lt.0.d0 .and. s1.gt.0.d0) then
c # transonic rarefaction in the 1-wave
sfract = s0 * (s1-s(i,1)) / (s1-s0)
else if (s(i,1) .lt. 0.d0) then
c # 1-wave is leftgoing
sfract = s(i,1)
else
c # 1-wave is rightgoing
sfract = 0.d0 !# this shouldn't happen since s0 < 0
endif
do 120 m=1,meqn
amdq(i,m) = sfract*wave(i,m,1)
120 continue
c
c # check 2-wave:
c ---------------
c
if (s(i,2) .ge. 0.d0) go to 200 !# 2-wave is rightgoing
do 140 m=1,meqn
amdq(i,m) = amdq(i,m) + s(i,2)*wave(i,m,2)
140 continue
c
c # check 3-wave:
c ---------------
c
rk1 = ql(i,1)
rk2 = ql(i,2)
rhou = ql(i,mu)
rhov = ql(i,mv)
rhoE = ql(i,5)
rho = rk1 + rk2
p = gamma1*(rhoE - rk2*q0 - 0.5d0*(rhou**2+rhov**2)/rho)
if ((rho.le.0.d0.or.p.le.0.d0).and.hll) go to 200
c = dsqrt(gamma*p/rho)
s3 = rhou/rho + c !# u+c in right state (cell i)
* write(6,*) 'right state 1', a(i), c, T
c
rk1 = rk1 - wave(i,1,3)
rk2 = rk2 - wave(i,2,3)
rhou = rhou - wave(i,mu,3)
rhov = rhov - wave(i,mv,3)
rhoE = rhoE - wave(i,5,3)
rho = rk1 + rk2
p = gamma1*(rhoE - rk2*q0 - 0.5d0*(rhou**2+rhov**2)/rho)
if ((rho.le.0.d0.or.p.le.0.d0).and.hll) go to 200
c = dsqrt(gamma*p/rho)
s2 = rhou/rho + c !# u+c to left of 3-wave
* write(6,*) 'right state 0', a(i), c, T
c
if (s2 .lt. 0.d0 .and. s3.gt.0.d0) then
c # transonic rarefaction in the 3-wave
sfract = s2 * (s3-s(i,3)) / (s3-s2)
else if (s(i,3) .lt. 0.d0) then
c # 3-wave is leftgoing
sfract = s(i,3)
else
c # 3-wave is rightgoing
go to 200
endif
c
do 160 m=1,meqn
amdq(i,m) = amdq(i,m) + sfract*wave(i,m,3)
160 continue
200 continue
c
c # compute the rightgoing flux differences:
c # df = SUM s*wave is the total flux difference and apdq = df - amdq
c
do 220 m=1,meqn
do 220 i = 2-mbc, mx+mbc
df = 0.d0
do 210 mw=1,mwaves
df = df + s(i,mw)*wave(i,m,mw)
210 continue
apdq(i,m) = df - amdq(i,m)
220 continue
c
900 continue
c
if (pfix) then
do 300 i=2-mbc,mx+mbc
amdr = amdq(i,1)+amdq(i,2)
apdr = apdq(i,1)+apdq(i,2)
rhol = qr(i-1,1)+qr(i-1,2)
rhor = ql(i ,1)+ql(i ,2)
do 300 m=1,2
if (qr(i-1,mu)+amdr.gt.0.d0) then
Z = qr(i-1,m)/rhol
else
Z = ql(i ,m)/rhor
endif
amdq(i,m) = Z*amdr + (Z-qr(i-1,m)/rhol)*qr(i-1,mu)
apdq(i,m) = Z*apdr - (Z-ql(i ,m)/rhor)*ql(i ,mu)
300 continue
endif
c
call flx2(ixy,maxm,meqn,mbc,mx,qr,maux,auxr,fr)
call flx2(ixy,maxm,meqn,mbc,mx,ql,maux,auxl,fl)
c
do 400 i = 2-mbc, mx+mbc
do 400 m=1,meqn
amdq(i,m) = fr(i-1,m) + amdq(i,m)
apdq(i,m) = -(fl(i ,m) - apdq(i,m))
400 continue
c
return
c
return
end
c