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flux2fw.f.html |
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Source file: flux2fw.f
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Directory: /Users/rjl/git/rjleveque/clawpack-4.6.3/amrclaw/2d/lib
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Converted: Mon Jan 21 2013 at 20:15:11
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 flux2(ixy,maxm,meqn,maux,mbc,mx,
& q1d,dtdx1d,aux1,aux2,aux3,
& faddm,faddp,gaddm,gaddp,cfl1d,fwave,s,
& amdq,apdq,cqxx,bmasdq,bpasdq,rpn2,rpt2)
c =====================================================
c
c # clawpack routine ... modified for AMRCLAW
c
c--------------------------------------------------------------------
c # flux2fw is a modified version of flux2 to use fwave instead of wave.
c # A modified Riemann solver rp2n must be used in conjunction with this
c # routine, which returns fwave's instead of wave's.
c # See http://amath.washington.edu/~claw/fwave.html
c
c # Limiters are applied to the fwave's, and the only significant
c # modification of this code is in the "do 119" loop, for the
c # second order corrections.
c
c--------------------------------------------------------------------
c
c
c # Compute the modification to fluxes f and g that are generated by
c # all interfaces along a 1D slice of the 2D grid.
c # ixy = 1 if it is a slice in x
c # 2 if it is a slice in y
c # This value is passed into the Riemann solvers. The flux modifications
c # go into the arrays fadd and gadd. The notation is written assuming
c # we are solving along a 1D slice in the x-direction.
c
c # fadd(i,.) modifies F to the left of cell i
c # gadd(i,.,1) modifies G below cell i
c # gadd(i,.,2) modifies G above cell i
c
c # The method used is specified by method(2:3):
c
c method(2) = 1 if only first order increment waves are to be used.
c = 2 if second order correction terms are to be added, with
c a flux limiter as specified by mthlim.
c
c method(3) = 0 if no transverse propagation is to be applied.
c Increment and perhaps correction waves are propagated
c normal to the interface.
c = 1 if transverse propagation of increment waves
c (but not correction waves, if any) is to be applied.
c = 2 if transverse propagation of correction waves is also
c to be included.
c
c Note that if mcapa>0 then the capa array comes into the second
c order correction terms, and is already included in dtdx1d:
c If ixy = 1 then
c dtdx1d(i) = dt/dx if mcapa= 0
c = dt/(dx*aux(i,jcom,mcapa)) if mcapa = 1
c If ixy = 2 then
c dtdx1d(j) = dt/dy if mcapa = 0
c = dt/(dy*aux(icom,j,mcapa)) if mcapa = 1
c
c Notation:
c The jump in q (q1d(i,:)-q1d(i-1,:)) is split by rpn2 into
c amdq = the left-going flux difference A^- Delta q
c apdq = the right-going flux difference A^+ Delta q
c Each of these is split by rpt2 into
c bmasdq = the down-going transverse flux difference B^- A^* Delta q
c bpasdq = the up-going transverse flux difference B^+ A^* Delta q
c where A^* represents either A^- or A^+.
c
c
implicit double precision (a-h,o-z)
include "call.i"
external rpn2, rpt2
dimension q1d(1-mbc:maxm+mbc, meqn)
dimension amdq(1-mbc:maxm+mbc, meqn)
dimension apdq(1-mbc:maxm+mbc, meqn)
dimension bmasdq(1-mbc:maxm+mbc, meqn)
dimension bpasdq(1-mbc:maxm+mbc, meqn)
dimension cqxx(1-mbc:maxm+mbc, meqn)
dimension faddm(1-mbc:maxm+mbc, meqn)
dimension faddp(1-mbc:maxm+mbc, meqn)
dimension gaddm(1-mbc:maxm+mbc, meqn, 2)
dimension gaddp(1-mbc:maxm+mbc, meqn, 2)
dimension dtdx1d(1-mbc:maxm+mbc)
dimension aux1(1-mbc:maxm+mbc, maux)
dimension aux2(1-mbc:maxm+mbc, maux)
dimension aux3(1-mbc:maxm+mbc, maux)
c
dimension s(1-mbc:maxm+mbc, mwaves)
dimension fwave(1-mbc:maxm+mbc, meqn, mwaves)
c
logical limit
common /comxyt/ dtcom,dxcom,dycom,tcom,icom,jcom
c
limit = .false.
do 5 mw=1,mwaves
if (mthlim(mw) .gt. 0) limit = .true.
5 continue
c
c # initialize flux increments:
c -----------------------------
c
do 30 jside=1,2
do 20 m=1,meqn
do 10 i = 1-mbc, mx+mbc
faddm(i,m) = 0.d0
faddp(i,m) = 0.d0
gaddm(i,m,jside) = 0.d0
gaddp(i,m,jside) = 0.d0
10 continue
20 continue
30 continue
c
c
c # solve Riemann problem at each interface and compute Godunov updates
c ---------------------------------------------------------------------
c
call rpn2(ixy,maxm,meqn,mwaves,mbc,mx,q1d,q1d,
& aux2,aux2,fwave,s,amdq,apdq)
c
c # Set fadd for the donor-cell upwind method (Godunov)
do 40 i=1,mx+1
do 40 m=1,meqn
faddp(i,m) = faddp(i,m) - apdq(i,m)
faddm(i,m) = faddm(i,m) + amdq(i,m)
40 continue
c
c # compute maximum wave speed for checking Courant number:
cfl1d = 0.d0
do 50 mw=1,mwaves
do 50 i=1,mx+1
c # if s>0 use dtdx1d(i) to compute CFL,
c # if s<0 use dtdx1d(i-1) to compute CFL:
cfl1d = dmax1(cfl1d, dtdx1d(i)*s(i,mw),
& -dtdx1d(i-1)*s(i,mw))
50 continue
c
if (method(2).eq.1) go to 130
c
c # modify F fluxes for second order q_{xx} correction terms:
c -----------------------------------------------------------
c
c # apply limiter to fwaves:
if (limit) call limiter(maxm,meqn,mwaves,mbc,mx,fwave,s,mthlim)
c
do 120 i = 1, mx+1
c
c # For correction terms below, need average of dtdx in cell
c # i-1 and i. Compute these and overwrite dtdx1d:
c
c # modified in Version 4.3 to use average only in cqxx, not transverse
dtdxave = 0.5d0 * (dtdx1d(i-1) + dtdx1d(i))
c
do 120 m=1,meqn
cqxx(i,m) = 0.d0
do 119 mw=1,mwaves
c
c # second order corrections:
cqxx(i,m) = cqxx(i,m) + dsign(1.d0,s(i,mw))
& * (1.d0 - dabs(s(i,mw))*dtdxave) * fwave(i,m,mw)
c
119 continue
faddm(i,m) = faddm(i,m) + 0.5d0 * cqxx(i,m)
faddp(i,m) = faddp(i,m) + 0.5d0 * cqxx(i,m)
120 continue
c
c
130 continue
c
if (method(3).eq.0) go to 999 !# no transverse propagation
c
if (method(3).eq.2) then
c # incorporate cqxx into amdq and apdq so that it is split also.
do 150 i = 1, mx+1
do 150 m=1,meqn
amdq(i,m) = amdq(i,m) + cqxx(i,m)
apdq(i,m) = apdq(i,m) - cqxx(i,m)
150 continue
endif
c
c
c # modify G fluxes for transverse propagation
c --------------------------------------------
c
c
c # split the left-going flux difference into down-going and up-going:
call rpt2(ixy,maxm,meqn,mwaves,mbc,mx,
& q1d,q1d,aux1,aux2,aux3,
& 1,amdq,bmasdq,bpasdq)
c
c # modify flux below and above by B^- A^- Delta q and B^+ A^- Delta q:
do 160 m=1,meqn
do 160 i = 1, mx+1
gupdate = 0.5d0*dtdx1d(i-1) * bmasdq(i,m)
gaddm(i-1,m,1) = gaddm(i-1,m,1) - gupdate
gaddp(i-1,m,1) = gaddp(i-1,m,1) - gupdate
c
gupdate = 0.5d0*dtdx1d(i-1) * bpasdq(i,m)
gaddm(i-1,m,2) = gaddm(i-1,m,2) - gupdate
gaddp(i-1,m,2) = gaddp(i-1,m,2) - gupdate
160 continue
c
c # split the right-going flux difference into down-going and up-going:
call rpt2(ixy,maxm,meqn,mwaves,mbc,mx,
& q1d,q1d,aux1,aux2,aux3,
& 2,apdq,bmasdq,bpasdq)
c
c # modify flux below and above by B^- A^+ Delta q and B^+ A^+ Delta q:
do 180 m=1,meqn
do 180 i = 1, mx+1
gupdate = 0.5d0*dtdx1d(i) * bmasdq(i,m)
gaddm(i,m,1) = gaddm(i,m,1) - gupdate
gaddp(i,m,1) = gaddp(i,m,1) - gupdate
c
gupdate = 0.5d0*dtdx1d(i) * bpasdq(i,m)
gaddm(i,m,2) = gaddm(i,m,2) - gupdate
gaddp(i,m,2) = gaddp(i,m,2) - gupdate
180 continue
c
999 continue
return
end