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rpn2ez_fast_geo.f.html |
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Source file: rpn2ez_fast_geo.f
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Directory: /home/rjl/git/rjleveque/clawpack-4.x/geoclaw/2d/lib
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Converted: Sun May 15 2011 at 19:15:41
using clawcode2html
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This documentation file will
not reflect any later changes in the source file.
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c======================================================================
subroutine rpn2(ixy,maxm,meqn,mwaves,mbc,mx,ql,qr,auxl,auxr,
& fwave,s,amdq,apdq)
c======================================================================
c
c Solves normal Riemann problems for the 2D SHALLOW WATER equations
c with topography:
c # h_t + (hu)_x + (hv)_y = 0 #
c # (hu)_t + (hu^2 + 0.5gh^2)_x + (huv)_y = -ghb_x #
c # (hv)_t + (huv)_x + (hv^2 + 0.5gh^2)_y = -ghb_y #
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 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
c ql = qr
c
c
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! # This Riemann solver is for the shallow water equations. !
! !
! It allows the user to easily select a Riemann solver in !
! riemannsolvers_geo.f. this routine initializes all the variables !
! for the shallow water equations, accounting for wet dry boundary !
! dry cells, wave speeds etc. !
! !
! David George, Vancouver WA, Feb. 2009 !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
* ! this version rpn2_ez_fast.f is faster by using a simpler fwave
* solver in the deep ocean.
use geoclaw_module
implicit none
!input
integer maxm,meqn,mwaves,mbc,mx,ixy
double precision fwave(1-mbc:maxm+mbc, meqn, mwaves)
double precision s(1-mbc:maxm+mbc, mwaves)
double precision ql(1-mbc:maxm+mbc, meqn)
double precision qr(1-mbc:maxm+mbc, meqn)
double precision apdq(1-mbc:maxm+mbc, meqn)
double precision amdq(1-mbc:maxm+mbc, meqn)
double precision auxl(1-mbc:maxm+mbc, *)
double precision auxr(1-mbc:maxm+mbc, *)
double precision drytol,g
!local only
integer m,i,mw,maxiter,mu,nv
double precision wall(3)
double precision fw(3,3)
double precision sw(3)
double precision hR,hL,huR,huL,uR,uL,hvR,hvL,vR,vL,phiR,phiL
double precision bR,bL,sL,sR,sRoe1,sRoe2,sE1,sE2,uhat,chat
double precision s1m,s2m,s1,s2
double precision hstar,hstartest,hstarHLL,sLtest,sRtest
double precision tw,dxdc
logical rare1,rare2
integer mcapa
common /cmcapa/ mcapa
g=grav
drytol=drytolerance
!loop through Riemann problems at each grid cell
do i=2-mbc,mx+mbc
!-----------------------Initializing-----------------------------------
!inform of a bad riemann problem from the start
if((qr(i-1,1).lt.0.d0).or.(ql(i,1) .lt. 0.d0)) then
write(*,*) 'Negative input: hl,hr,i=',qr(i-1,1),ql(i,1),i
endif
!Initialize Riemann problem for grid interface
do mw=1,mwaves
s(i,mw)=0.d0
do m=1,meqn
fwave(i,m,mw)=0.d0
enddo
enddo
c !set normal direction
if (ixy.eq.1) then
mu=2
nv=3
else
mu=3
nv=2
endif
!zero (small) negative values if they exist
if (qr(i-1,1).lt.0.d0) then
do m=1,meqn
qr(i-1,m)=0.d0
enddo
endif
if (ql(i,1).lt.0.d0) then
do m=1,meqn
ql(i,1)=0.d0
enddo
endif
!skip problem if in a completely dry area
if (qr(i-1,1).le.drytol.and.ql(i,1).le.drytol) then
go to 30
endif
!Riemann problem variables
hL = qr(i-1,1)
hR = ql(i,1)
huL = qr(i-1,mu)
huR = ql(i,mu)
bL = auxr(i-1,1)
bR = auxl(i,1)
hvL=qr(i-1,nv)
hvR=ql(i,nv)
!check for wet/dry boundary
if (hR.gt.drytol) then
uR=huR/hR
vR=hvR/hR
phiR = 0.5d0*g*hR**2 + huR**2/hR
else
hR = 0.d0
huR = 0.d0
hvR = 0.d0
uR = 0.d0
vR = 0.d0
phiR = 0.d0
endif
if (hL.gt.drytol) then
uL=huL/hL
vL=hvL/hL
phiL = 0.5d0*g*hL**2 + huL**2/hL
else
hL=0.d0
huL=0.d0
hvL=0.d0
uL=0.d0
vL=0.d0
phiL = 0.d0
endif
! check if a simple solver will do the trick
if ((abs(hL-hR).lt.0.001d0*min(hL,hR)).and.
& (max(uL**2,uR**2)/max(g*hL,g*hR).lt.0.01d0)) then
s1 = 0.5d0*(uR+uL) - sqrt(g*0.5d0*(hL+hR))
s2 = 0.5d0*(uR+uL) + sqrt(g*0.5d0*(hL+hR))
call riemann_fwave(meqn,mwaves,hL,hR,huL,huR,hvL,hvR,
& bL,bR,uL,uR,vL,vR,phiL,phiR,s1,s2,drytol,g,sw,fw)
go to 25
endif
wall(1) = 1.d0
wall(2) = 1.d0
wall(3) = 1.d0
if (hR.le.drytol) then
call riemanntype(hL,hL,uL,-uL,hstar,s1m,s2m,
& rare1,rare2,1,drytol,g)
hstartest=max(hL,hstar)
if (hstartest+bL.lt.bR) then !right state should become ghost values that mirror left for wall problem
c bR=hstartest+bL
wall(2)=0.d0
wall(3)=0.d0
hR=hL
huR=-huL
bR=bL
phiR=phiL
uR=-uL
vR=vL
elseif (hL+bL.lt.bR) then
bR=hL+bL
endif
elseif (hL.le.drytol) then ! right surface is lower than left topo
call riemanntype(hR,hR,-uR,uR,hstar,s1m,s2m,
& rare1,rare2,1,drytol,g)
hstartest=max(hR,hstar)
if (hstartest+bR.lt.bL) then !left state should become ghost values that mirror right
c bL=hstartest+bR
wall(1)=0.d0
wall(2)=0.d0
hL=hR
huL=-huR
bL=bR
phiL=phiR
uL=-uR
vL=vR
elseif (hR+bR.lt.bL) then
bL=hR+bR
endif
endif
!determine wave speeds
sL=uL-sqrt(g*hL) ! 1 wave speed of left state
sR=uR+sqrt(g*hR) ! 2 wave speed of right state
uhat=(sqrt(g*hL)*uL + sqrt(g*hR)*uR)/(sqrt(g*hR)+sqrt(g*hL)) ! Roe average
chat=sqrt(g*0.5d0*(hR+hL)) ! Roe average
sRoe1=uhat-chat ! Roe wave speed 1 wave
sRoe2=uhat+chat ! Roe wave speed 2 wave
sE1 = min(sL,sRoe1) ! Eindfeldt speed 1 wave
sE2 = max(sR,sRoe2) ! Eindfeldt speed 2 wave
!--------------------end initializing...finally----------
!solve Riemann problem.
maxiter = 1
call riemann_aug_JCP(maxiter,3,3,hL,hR,huL,
& huR,hvL,hvR,bL,bR,uL,uR,vL,vR,phiL,phiR,sE1,sE2,
& drytol,g,sw,fw)
c call riemann_ssqfwave(maxiter,meqn,mwaves,hL,hR,huL,huR,
c & hvL,hvR,bL,bR,uL,uR,vL,vR,phiL,phiR,sE1,sE2,drytol,g,sw,fw)
c call riemann_fwave(meqn,mwaves,hL,hR,huL,huR,hvL,hvR,
c & bL,bR,uL,uR,vL,vR,phiL,phiR,sE1,sE2,drytol,g,sw,fw)
c !eliminate ghost fluxes for wall
do mw=1,3
sw(mw)=sw(mw)*wall(mw)
do m=1,meqn
fw(m,mw)=fw(m,mw)*wall(mw)
enddo
enddo
25 continue
do mw=1,mwaves
s(i,mw)=sw(mw)
fwave(i,1,mw)=fw(1,mw)
fwave(i,mu,mw)=fw(2,mw)
fwave(i,nv,mw)=fw(3,mw)
enddo
30 continue
enddo
c==========Capacity for mapping from latitude longitude to physical space====
if (mcapa.gt.0) then
do i=2-mbc,mx+mbc
if (ixy.eq.1) then
dxdc=(Rearth*pi/180.d0)
else
dxdc=auxl(i,3)
endif
do mw=1,mwaves
c if (s(i,mw) .gt. 316.d0) then
c # shouldn't happen unless h > 10 km!
c write(6,*) 'speed > 316: i,mw,s(i,mw): ',i,mw,s(i,mw)
c endif
s(i,mw)=dxdc*s(i,mw)
do m=1,meqn
fwave(i,m,mw)=dxdc*fwave(i,m,mw)
enddo
enddo
enddo
endif
c===============================================================================
c============= compute fluctuations=============================================
do i=1-mbc,mx+mbc
do m=1,meqn
amdq(i,m)=0.0d0
apdq(i,m)=0.0d0
do mw=1,mwaves
if (s(i,mw).lt.0.d0) then
amdq(i,m)=amdq(i,m) + fwave(i,m,mw)
elseif (s(i,mw).gt.0.d0) then
apdq(i,m)=apdq(i,m) + fwave(i,m,mw)
else
amdq(i,m) = amdq(i,m) + .5d0*fwave(i,m,mw)
apdq(i,m) = apdq(i,m) + .5d0*fwave(i,m,mw)
endif
enddo
enddo
enddo
return
end subroutine