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SOLUTE.FOR
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SOLUTE.FOR
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* Source file SOLUTE.FOR |||||||||||||||||||||||||||||||||||||||||||||||
* To assemble and solve the solute transport equation
* Mass-lumping finite elements
subroutine Solute(N,NMat,NS,NSD,x,dt,t,tPulse,ChPar,MatNum,thO,
! thN,vO,vN,Disp,epsi,kTopCh,cTop,kBotCh,cBot,
! Conc,B,D,E,F,g0,g1,Retard,cvTop,cvBot,cvCh0,
! cvCh1,lUpW,wc,Peclet,Courant,dtMaxC,TempO,TempN,
! cNew,cPrevO,cTemp,TDep,thSat,cTolA,cTolR,IterC,
! MaxItC,vCorr,Sorb,SorbN,lLinear,lEquil,lArtD,
! PeCr,q0,q1,dSurf,cAtm,lTort,Sink,cRootMax,sSink,
! cvChR,lMobIm,cvChIm,TLevel,lBact,Sorb2,SorbN2,
! dtMin,dtOpt,lWat,lFiltr,iDualPor,ThOIm,ThNIm,
! SinkIm,STrans,iTort,xConv,tConv,lVapor,rBot,
! ierr,iMoistDep,NMatD,DMoist,WDep,iConcType,Beta,
! lDualNEq,AtmBC,SinkF,lActRSU,OmegaS,OmegaW,SPot,
! rKM,cMin,lDensity)
logical lUpW,lConv,lLinear(NSD),lEquil,lArtD,lTort,lMobIm(NMat),
! lBact,lWat,lFiltr,lVapor,SinkF,lNEquil,lDualNEq,AtmBC,
! lActRSU,lDensity
double precision B,D,E,F,t
integer TLevel
dimension x(N),ChPar(NSD*16+4,NMat),MatNum(N),thO(N),thN(N),vO(N),
! vN(N),Disp(N),cTop(NS),cBot(NS),Conc(NSD,N),B(N),D(N),
! E(N),F(N),g0(N),g1(N),Retard(N),cvTop(NS),cvBot(NS),
! cvCh0(NS),cvCh1(NS),wc(N),TempO(N),TempN(N),cNew(N),
! cPrevO(N),cTemp(N),TDep(NSD*16+4),thSat(NMat),sSink(N),
! vCorr(N),Sorb(NSD,N),SorbN(N),q0(N),q1(N),Sink(N),
! cvChR(NS),cRootMax(NS),cvChIm(NS),Sorb2(NSD,N),SorbN2(N)
! ,ThOIm(N),ThNIm(N),SinkIm(N),STrans(N),Beta(N),
! DMoist(NMatD,NSD,13,6),WDep(2+NMatD,NSD*9)
alf=1.-epsi
IterC=1.
NLevel=2
Peclet=0.
Courant=0.
dtMaxC=1.e+30
rMin=1.e-30
Tr=293.15
R=8.314
* Sequential first order decay goes into equilibrium phase (lNEquil=.false.) or nonequilbrium phase (lNEquil=.true.)
lNEquil=.false.
10 continue
* Loop on species in the chain
do 18 jS=1,NS
Iter=0
jjj=(jS-1)*16
cvTop(jS)=0.
cvBot(jS)=0.
cvCh0(jS)=0.
cvCh1(jS)=0.
cvChR(jS)=0.
cvChIm(jS)=0.
if(t-tPulse.gt.dtMin.and..not.AtmBC) then
cTop(jS)=0.
cBot(jS)=0.
end if
if(kBotCh.lt.0) then
if(vO(1).ge.0.) cvBot(jS)=alf*cBot(jS) *vO(1)
if(vO(1).lt.0.) cvBot(jS)=alf*Conc(jS,1)*vO(1)
if(lVapor.and.rBot.eq.0.) cvBot(jS)=0.
else if(kBotCh.eq.0) then
cvBot(jS)=alf*Conc(jS,1)*vO(1)
end if
if(kTopCh.lt.0..and.TLevel.ne.1) then
if(vO(N).lt.0.) cvTop(jS)=alf*cTop(jS)*vO(N)
end if
if(kTopCh.eq.-2) then
M=MatNum(N)
Tr=293.15
R=8.314
TT=(TempO(N)+273.15-Tr)/R/(TempO(N)+273.15)/Tr
Dg =ChPar(jjj+ 6,M)*exp(TDep(jjj+ 6)*TT)
Henry=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TT)
dSurfT=dSurf*exp(TDep(jjj+9)*TT)
cvTop(jS)=cvTop(jS)+alf*Dg/dSurfT*Henry*Conc(jS,N)-
! Dg/dSurfT*cAtm
end if
if(.not.lLinear(jS)) then
do 11 i=1,N
cNew(i)=Conc(jS,i)
if(.not.lEquil) SorbN(i) =Sorb(jS,i)
if(lBact.or.lDualNEq) SorbN2(i)=Sorb2(jS,i)
11 continue
end if
* Root Solute Uptake
if(SinkF)
! call SetSSnk(jS,NS,N,t,x,Beta,Sink,sSink,NSD,Conc,OmegaW,
! cRootMax(jS),lActRSU,OmegaS,SPot,rKM,cMin)
* Iterative loop for a nonlinear adsorption isotherm
12 Iter=Iter+1
if(.not.lLinear(jS)) then
do 13 i=1,N
cTemp(i)=cNew(i)
13 continue
end if
* To construct the matrix equation
do 15 Level=1,NLevel
* Calculate the dispersion coefficients, retardation factors, source/
* decay coefficients, Peclet and Courant numbers, upstream weighting
* factors
call Coeff(jS,Level,NLevel,N,NMat,NSD,x,Disp,vO,vN,thO,thN,
! thSat,ChPar,MatNum,TempN,TempO,TDep,g0,g1,Retard,
! Conc,cNew,cPrevO,dt,Pecl,Cour,dtMxC,lLinear,lEquil,
! lUpW,lArtD,Iter,wc,vCorr,Sorb,SorbN,epsi,PeCr,q0,
! q1,lTort,sSink,lMobIm,lBact,Sorb2,SorbN2,lFiltr,
! iDualPor,ThOIm,ThNIm,SinkIm,iTort,xConv,tConv,
! iMoistDep,NMatD,DMoist,WDep,lNEquil,lDualNEq)
Peclet=amax1(Peclet,Pecl)
Courant=amax1(Courant,Cour)
dtMaxC=amin1(dtMaxC,dtMxC)
* Set up the matrix equation
call MatSet(jS,N,NS,NSD,Level,epsi,alf,dt,kBotCh,kTopCh,cBot,
! cTop,x,thO,thN,vO,vN,Conc,Disp,Retard,wc,g0,g1,B,
! D,E,F,E1,D1,F1,BN,DN,FN,NMat,ChPar,TempO,TempN,
! TDep,dSurfT,cAtm,MatNum,lMobIm,iDualPor,lVapor,
! rBot,lBact)
do 14 i=1,N
if(Level.eq.1) vO(i)=vO(i)+vCorr(i)
if(Level.eq.2) vN(i)=vN(i)+vCorr(i)
14 continue
* Calculate mass-transfer fluxes at the beginning of the time interval
if(Level.eq.1.and.Iter.eq.1)
! call MassTran(jS,NS,NSD,N,MatNum,TempO,lMobIm,lEquil,ChPar,
! TDep,Sorb,Conc,NMat,x,cvCh0,cvCh1,cvChR,
! cvChIm,alf,q0,q1,sSink,lBact,ThO,Sorb2,lFiltr,
! vO,iDualPor,SinkIm,xConv,tConv,lDualNEq,
! STrans,lLinear)
15 continue
* Solve matrix equation
call BanSol(N,B,D,E,F)
* Test for convergence for nonlinear problem
lConv=.true.
do 16 i=1,N
if((NS.gt.1.and.Iter.eq.1).or.lDensity) cPrevO(i)=Conc(jS,i)
if(lLinear(jS)) then
Conc(jS,i)=amax1(sngl(F(i)),0.)
if(Conc(jS,i).lt.1.e-30.and.Conc(jS,i).gt.0.) Conc(jS,i)=0.
else
cNew(i)=sngl(F(i))
if(cNew(i).lt.1.0e-30) cNew(i)=0.
if(abs(cNew(i)-cTemp(i)).gt.cTolA+cTolR*Conc(jS,i))
! lConv=.false.
end if
16 continue
if(.not.lLinear(jS)) then
if(.not.lConv) then
if(iter.lt.MaxItC) then
goto 12
else if(dt.gt.dtMin.and..not.lWat) then
c ierr=1
dtOld=dt
dt=amax1(dt/3.,dtMin)
dtOpt=dt
t=t-dtOld+dt
goto 10
else
ierr=1
end if
end if
do 17 i=1,N
Conc(jS,i)=cNew(i)
if(.not.lEquil) Sorb(jS,i) =SorbN(i)
if(lBact.or.lDualNEq) Sorb2(jS,i)=SorbN2(i)
17 continue
end if
* Calculate sorbed concentration for linear noneq. adsorption or
* concentration in the imobile water.
if(.not.lEquil.and.lLinear(jS))
! call SorbConc(jS,NSD,N,MatNum,TempN,lMobIm,ChPar,TDep,Sorb,
! Conc,dt,NMat,lBact,thN,Sorb2,lFiltr,vN,iDualPor,
! ThNIm,ThOIm,SinkIm,STrans,iMoistDep,NMatD,
! DMoist,WDep,xConv,tConv,lDualNEq)
* Calculate mass-transfer fluxes at the end of the time interval
call MassTran(jS,NS,NSD,N,MatNum,TempN,lMobIm,lEquil,ChPar,TDep,
! Sorb,Conc,NMat,x,cvCh0,cvCh1,cvChR,cvChIm,epsi,
! q0,q1,sSink,lBact,ThN,Sorb2,lFiltr,vN,iDualPor,
! SinkIm,xConv,tConv,lDualNEq,STrans,lLinear)
* Set up mass fluxes
if(kTopCh.lt.0) then
if(TLevel.ne.1) then
if(vN(N).lt.0.) cvTop(jS)=cvTop(jS)+epsi*vN(N)*cTop(jS)
else
if(vN(N).lt.0.) cvTop(jS)=cvTop(jS)+ vN(N)*cTop(jS)
end if
else
cvTop(jS)=FN-BN*Conc(jS,N-1)-DN*Conc(jS,N)
end if
if(kTopCh.eq.-2) then
M=MatNum(N)
TT=(TempN(N)+273.15-Tr)/R/(TempN(N)+273.15)/Tr
Dg =ChPar(jjj+ 6,M)*exp(TDep(jjj+ 6)*TT)
Henry=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TT)
cvTop(jS)=cvTop(jS)+epsi*Dg/dSurfT*Henry*Conc(jS,N)-
! Dg/dSurfT*cAtm
end if
if(kBotCh.lt.0) then
if(vN(1).ge.0.) cvBot(jS)=cvBot(jS)+epsi*cBot(jS) *vN(1)
if(vN(1).lt.0.) cvBot(jS)=cvBot(jS)+epsi*Conc(jS,1)*vN(1)
if(lVapor.and.rBot.eq.0.) cvBot(jS)=0.
else if(kBotCh.eq.0) then
cvBot(jS)=cvBot(jS)+epsi*Conc(jS,1)*vN(1)
else
cvBot(jS)=D1*Conc(jS,1)+E1*Conc(jS,2)-F1
end if
IterC=max0(IterC,Iter)
if(abs(cvTop(jS)).lt.rMin) cvTop(jS)=0.
if(abs(cvBot(jS)).lt.rMin) cvBot(jS)=0.
18 continue
* Calculate flux concentrations
if(iConcType.eq.2)
! call FluxConc(N,NMat,NSD,x,vN,thN,thSat,ChPar,MatNum,TempN,TDep,
! Conc,cNew,lTort,lMobIm,iDualPor,ThNIm,1)
return
end
************************************************************************
* Calculate the dispersion coefficients, retardation factors, source/
* decay coefficients, Peclet and Courant numbers, upstream weighting
* factors
subroutine Coeff(jS,Level,NLevel,NumNP,NMat,NSD,x,Disp,vO,vN,thO,
! thN,thSat,ChPar,MatNum,TempN,TempO,TDep,g0,g1,
! Retard,Conc,cNew,cPrevO,dt,Peclet,Courant,dtMaxC,
! lLinear,lEquil,lUpW,lArtD,Iter,wc,vCorr,Sorb,
! SorbN,epsi,PeCr,q0,q1,lTort,sSink,lMobIm,lBact,
! Sorb2,SorbN2,lFiltr,iDualPor,ThOIm,ThNIm,SinkIm,
! iTort,xConv,tConv,iMoistDep,NMatD,DMoist,WDep,
! lNEquil,lDualNEq)
logical lUpW,lLinear(NSD),lEquil,lArtD,lTort,lMobIm(NMat),lBact,
! lFiltr,lNEquil,
! lDualNEq
dimension x(NumNP),Disp(NumNP),vO(NumNP),vN(NumNP),thO(NumNP),
! thN(NumNP),thSat(NMat),ChPar(NSD*16+4,NMat),g0(NumNP),
! g1(NumNP),MatNum(NumNP),Conc(NSD,NumNP),TempO(NumNP),
! TempN(NumNP),TDep(NSD*16+4),cNew(NumNP),cPrevO(NumNP),
! Retard(NumNP),wc(NumNP),Sorb(NSD,NumNP),SorbN(NumNP),
! vCorr(NumNP),q0(NumNP),q1(NumNP),
! sSink(NumNP),Sorb2(NSD,NumNP),SorbN2(NumNP),
! ThOIm(NumNP),ThNIm(NumNP),SinkIm(NumNP),
! DMoist(NMatD,NSD,13,6),WDep(2+NMatD,NSD*9)
* Inicialization
jjj=(jS-1)*16
if(jS.gt.1) jj1=jjj-16
Peclet=0.
Courant=0.
CourMax=1.
dtMaxC=1.e+30
Tr=293.15
R=8.314
do 11 i=NumNP,1,-1
j=i+1
k=i-1
M=MatNum(i)
if(Level.eq.NLevel) then
ThW=ThN(i)
ThWO=ThO(i)
ThG=amax1(0.,thSat(M)-ThW)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact) then
ThImob=ChPar(4,M)
ThImobO=ThImob
ThW=amax1(ThW-ThImob,0.001)
end if
if(iDualPor.gt.0) then
ThImob=ThNIm(i)
ThImobO=ThOIm(i)
end if
v=vN(i)
if(i.ne.NumNP) then
vj=vN(j)
Thj=ThN(j)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact)
! Thj=amax1(Thj-ThImob,0.001)
end if
TT=(TempN(i)+273.15-Tr)/R/(TempN(i)+273.15)/Tr
if(jS.gt.1) cPrev=Conc(jS-1,i)
else
ThW=ThO(i)
ThG=amax1(0.,thSat(M)-ThW)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact) then
ThImob=ChPar(4,M)
ThW=amax1(ThW-ThImob,0.001)
end if
if(iDualPor.gt.0) then
ThImob=ThOIm(i)
end if
v=vO(i)
if(i.ne.NumNP) then
vj=vO(j)
Thj=ThO(j)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact)
! Thj=amax1(Thj-ThImob,0.001)
end if
TT=(TempO(i)+273.15-Tr)/R/(TempO(i)+273.15)/Tr
if(jS.gt.1) cPrev=cPrevO(i)
end if
* Temperature dependence
f1=1.
ro =ChPar(1, M)*exp(TDep(1) *TT)
Frac =ChPar(3, M)*exp(TDep(3) *TT)
Dw =ChPar(jjj+ 5,M)*exp(TDep(jjj+ 5)*TT)
Dg =ChPar(jjj+ 6,M)*exp(TDep(jjj+ 6)*TT)
xKs =ChPar(jjj+ 7,M)*exp(TDep(jjj+ 7)*TT)
xNu =ChPar(jjj+ 8,M)*exp(TDep(jjj+ 8)*TT)
fExp =ChPar(jjj+ 9,M)
Henry=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TT)
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,1,DMoist,1,WDep,ThW,iMoistDep)
GamL =ChPar(jjj+11,M)*exp(TDep(jjj+11)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,10,DMoist,1,WDep,ThImob,iMoistDep)
GamLi =ChPar(jjj+11,M)*exp(TDep(jjj+11)*TT)*f1 ! reaction in the immobile phase
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,2,DMoist,2,WDep,ThW,iMoistDep)
GamS =ChPar(jjj+12,M)*exp(TDep(jjj+12)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,11,DMoist,2,WDep,ThImob,iMoistDep)
GamSi =ChPar(jjj+12,M)*exp(TDep(jjj+12)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,3,DMoist,3,WDep,ThW,iMoistDep)
GamG =ChPar(jjj+13,M)*exp(TDep(jjj+13)*TT)*f1
GamGi=GamG
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,4,DMoist,4,WDep,ThW,iMoistDep)
GamL1 =ChPar(jjj+14,M)*exp(TDep(jjj+14)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,12,DMoist,4,WDep,ThImob,iMoistDep)
GamL1i=ChPar(jjj+14,M)*exp(TDep(jjj+14)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,5,DMoist,5,WDep,ThW,iMoistDep)
GamS1 =ChPar(jjj+15,M)*exp(TDep(jjj+15)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,13,DMoist,5,WDep,ThImob,iMoistDep)
GamS1i=ChPar(jjj+15,M)*exp(TDep(jjj+15)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,6,DMoist,6,WDep,ThW,iMoistDep)
GamG1 =ChPar(jjj+16,M)*exp(TDep(jjj+16)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,7,DMoist,7,WDep,ThW,iMoistDep)
xMuL =ChPar(jjj+17,M)*exp(TDep(jjj+17)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,8,DMoist,8,WDep,ThW,iMoistDep)
xMuS =ChPar(jjj+18,M)*exp(TDep(jjj+18)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,9,DMoist,9,WDep,ThW,iMoistDep)
xMuG =ChPar(jjj+19,M)*exp(TDep(jjj+19)*TT)*f1
Omega =ChPar(jjj+20,M)*exp(TDep(jjj+20)*TT)
f_em=1.
if(lDualNEq) f_em =ChPar(jjj+13,M)*exp(TDep(jjj+13)*TT)
if(lDualNEq) OmegaS=ChPar(jjj+16,M)*exp(TDep(jjj+16)*TT)
if(lBact) then
Dg=0.
GamG =0.
GamGi=0.
GamL1=0.
GamL1i=0.
GamS1=0.
GamS1i=0.
GamG1=0.
GamG1i=0.
xMuL =0.
xMuS =0.
xMuG =0.
Omega=0.
SMax2 =ChPar(jjj+15,M)*exp(TDep(jjj+15)*TT)
rKa2 =ChPar(jjj+16,M)*exp(TDep(jjj+16)*TT)
rKd2 =ChPar(jjj+17,M)*exp(TDep(jjj+17)*TT)
SMax1 =ChPar(jjj+18,M)*exp(TDep(jjj+18)*TT)
rKa1 =ChPar(jjj+19,M)*exp(TDep(jjj+19)*TT)
rKd1 =ChPar(jjj+20,M)*exp(TDep(jjj+20)*TT)
iPsi1=0
iPsi2=0
if(.not.lFiltr) iPsi2=int(ChPar(jjj+13,M))
if(.not.lFiltr) iPsi1=int(ChPar(jjj+14,M))
if(iPsi1.eq.0.and.SMax1.gt.0.) iPsi1=1
if(iPsi2.eq.0.and.SMax2.gt.0.) iPsi2=1
if(iPsi1.ge.3.or.iPsi2.ge.3)
! Dc=ChPar(jjj+6,M)*exp(TDep(jjj+6)*TT)
if(iPsi1.eq.5.or.iPsi2.eq.5) aa=ChPar(jjj+15,M)
if(Level.eq.NLevel) then
ss1=SorbN(i)
ss2=SorbN2(i)
else
ss1=Sorb(jS,i)
ss2=Sorb2(jS,i)
end if
psi1=1.
psi2=1.
if(iPsi1.gt.0) call Blocking(iPsi1,SMax1,psi1,x(i),ss1,dc,aa)
if(iPsi2.gt.0) call Blocking(iPsi2,SMax2,psi2,x(i),ss2,dc,aa)
* recalculate ka1 and ka2 based on filtration theory
if(lFiltr) then
GamG =0.
GamL1=0.
Dc=ChPar(jjj+13,M)*exp(TDep(jjj+13)*TT)
Dp=ChPar(jjj+14,M)*exp(TDep(jjj+14)*TT)
Alfa1=rKa1
Alfa2=rKa2
call Deposit(rKa1,rKa2,Dc,Dp,Alfa1,Alfa2,ThW,v,TempN(i),
! xConv,tConv)
end if
end if
if(jS.gt.1) then
xKsP =ChPar(jj1+ 7,M)*exp(TDep(jj1+ 7)*TT)
xNuP =ChPar(jj1+ 8,M)*exp(TDep(jj1+ 8)*TT)
fExpP =ChPar(jj1+ 9,M) !*exp(TDep(jj1+ 9)*TT)
HenryP=ChPar(jj1+10,M)*exp(TDep(jj1+10)*TT)
f1=1.
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS-1,4,DMoist,4,WDep,ThW,iMoistDep)
GamL1P =ChPar(jj1+14,M)*exp(TDep(jj1+14)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS-1,12,DMoist,4,WDep,ThImob,iMoistDep)
GamL1Pi=ChPar(jj1+14,M)*exp(TDep(jj1+14)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS-1,5,DMoist,5,WDep,ThW,iMoistDep)
GamS1P =ChPar(jj1+15,M)*exp(TDep(jj1+15)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS-1,13,DMoist,5,WDep,ThImob,iMoistDep)
GamS1Pi=ChPar(jj1+15,M)*exp(TDep(jj1+15)*TT)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS-1,6,DMoist,6,WDep,ThW,iMoistDep)
GamG1P=ChPar(jj1+16,M)*exp(TDep(jj1+16)*TT)*f1
if(lBact) then
GamL1P=0.
GamL1Pi=0.
GamS1P=0.
GamS1Pi=0.
GamG1P=0.
end if
end if
if(Level.eq.NLevel) then
TTO=(TempO(i)+273.15-Tr)/R/(TempO(i)+273.15)/Tr
xKsO =ChPar(jjj+ 7,M)*exp(TDep(jjj+ 7)*TTO)
xNuO =ChPar(jjj+ 8,M)*exp(TDep(jjj+ 8)*TTO)
fExpO =ChPar(jjj+ 9,M)
HenryO=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TTO)
f1=1.
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,1,DMoist,1,WDep,ThO(i),iMoistDep)
GamLO =ChPar(jjj+11,M)*exp(TDep(jjj+11)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,10,DMoist,1,WDep,ThImobO,iMoistDep)
GamLOi=ChPar(jjj+11,M)*exp(TDep(jjj+11)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,2,DMoist,2,WDep,ThO(i),iMoistDep)
GamSO =ChPar(jjj+12,M)*exp(TDep(jjj+12)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,11,DMoist,2,WDep,ThImobO,iMoistDep)
GamSOi=ChPar(jjj+12,M)*exp(TDep(jjj+12)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,4,DMoist,4,WDep,ThO(i),iMoistDep)
GamL1O =ChPar(jjj+14,M)*exp(TDep(jjj+14)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,12,DMoist,4,WDep,ThImobO,iMoistDep)
GamL1Oi=ChPar(jjj+14,M)*exp(TDep(jjj+14)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,5,DMoist,5,WDep,ThO(i),iMoistDep)
GamS1O=ChPar(jjj+15,M)*exp(TDep(jjj+15)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,13,DMoist,5,WDep,ThImobO,iMoistDep)
GamS1Oi=ChPar(jjj+15,M)*exp(TDep(jjj+15)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,7,DMoist,7,WDep,ThO(i),iMoistDep)
xMuLO =ChPar(jjj+17,M)*exp(TDep(jjj+17)*TTO)*f1
if(iMoistDep.gt.0)
! f1=rMD(NMatD,NSD,M,jS,8,DMoist,8,WDep,ThO(i),iMoistDep)
xMuSO =ChPar(jjj+18,M)*exp(TDep(jjj+18)*TTO)*f1
OmegaO=ChPar(jjj+20,M)*exp(TDep(jjj+20)*TTO)
dKs =(xKs - xKsO)/dt
dNu =(xNu - xNuO)/dt
ddExp =(fExp - fExpO)/dt
dHenry=(Henry-HenryO)/dt
if(i.ne.1) TTi=(TempN(k)+273.15-Tr)/R/(TempN(k)+273.15)/Tr
if(i.ne.NumNP) TTj=(TempN(j)+273.15-Tr)/R/(TempN(j)+273.15)/Tr
if(lBact) then
GamS1O=0.
GamS1Oi=0.
xMuLO =0.
xMuSO =0.
xMuGO =0.
OmegaO=0.
SMax2O =ChPar(jjj+15,M)*exp(TDep(jjj+15)*TTO)
rKa2O =ChPar(jjj+16,M)*exp(TDep(jjj+16)*TTO)
rKd2O =ChPar(jjj+17,M)*exp(TDep(jjj+17)*TTO)
SMax1O =ChPar(jjj+18,M)*exp(TDep(jjj+18)*TTO)
rKa1O =ChPar(jjj+19,M)*exp(TDep(jjj+19)*TTO)
rKd1O =ChPar(jjj+20,M)*exp(TDep(jjj+20)*TTO)
iPsi1=0
iPsi2=0
if(.not.lFiltr) iPsi2=int(ChPar(jjj+13,M))
if(.not.lFiltr) iPsi1=int(ChPar(jjj+14,M))
if(iPsi1.eq.0.and.SMax1O.gt.0.) iPsi1=1
if(iPsi2.eq.0.and.SMax2O.gt.0.) iPsi2=1
if(iPsi1.ge.3.or.iPsi2.ge.3)
! Dc=ChPar(jjj+6,M)*exp(TDep(jjj+6)*TT)
if(iPsi1.eq.5.or.iPsi2.eq.5) aa=ChPar(jjj+15,M)
psi1O=1.
psi2O=1.
if(iPsi1.gt.0)
! call Blocking(iPsi1,SMax1O,psi1O,x(i),Sorb(jS,i),dc,aa)
if(iPsi2.gt.0)
! call Blocking(iPsi2,SMax2O,psi2O,x(i),Sorb2(jS,i),dc,aa)
if(lFiltr) then
GamL1O=0.
Dc=ChPar(jjj+13,M)*exp(TDep(jjj+13)*TTO)
Dp=ChPar(jjj+14,M)*exp(TDep(jjj+14)*TTO)
Alfa1=rKa1O
Alfa2=rKa2O
call Deposit(rKa1O,rKa2O,Dc,Dp,Alfa1,Alfa2,ThWO,vO(i),
! TempO(i),xConv,tConv)
end if
end if
else
TTN=(TempN(i)+273.15-Tr)/R/(TempN(i)+273.15)/Tr
xKsN =ChPar(jjj+ 7,M)*exp(TDep(jjj+ 7)*TTN)
xNuN =ChPar(jjj+ 8,M)*exp(TDep(jjj+ 8)*TTN)
fExpN =ChPar(jjj+ 9,M) !*exp(TDep(jjj+ 9)*TTN)
HenryN=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TTN)
dKs =(xKsN - xKs)/dt
dNu =(xNuN - xNu)/dt
ddExp =(fExpN - fExp)/dt
dHenry=(HenryN-Henry)/dt
if(i.ne.1) TTi=(TempO(k)+273.15-Tr)/R/(TempO(k)+273.15)/Tr
if(i.ne.NumNP) TTj=(TempO(j)+273.15-Tr)/R/(TempO(j)+273.15)/Tr
end if
if(i.ne.1) Henryi=ChPar(jjj+10,MatNum(k))*exp(TDep(jjj+10)*TTi)
if(i.ne.NumNP)
! Henryj=ChPar(jjj+10,MatNum(j))*exp(TDep(jjj+10)*TTj)
dSConc=1.
dConc=1.
SConcP=1.
SConc=1.
SConcO=1.
dRetard=0.
SConcS=1.
SConcOS=1.
dSConcS=1.
dConcS=1.
SConcPS=1.
dRetardS=0.
* Effects of nonlinear adsorption
if(.not.lLinear(jS)) then
cc=Conc(jS,i)
cMid=(Conc(jS,i)+cNew(i))/2.
if(Level.eq.NLevel) cc=cNew(i)
if(cc.gt.0.) then
dSConc=fExp*cc**(fExp-1.)/(1.+xNu*cc**fExp)**2
SConc = cc**(fExp-1.)/(1.+xNu*cc**fExp)
end if
if(cMid.gt.0.) then
dConc=fExp*cMid**(fExp-1.)/(1.+xNu*cMid**fExp)**2
dRetard=cMid**fExp/(1.+xNu*cMid**fExp)*dKs-
! xKs*cMid**(2.*fExp)/(1.+xNu*cMid**fExp)**2*dNu+
! xKs*alog(cMid)*cMid**fExp/(1.+xNu*cMid**fExp)**2*ddExp
end if
if(Level.eq.NLevel.and..not.lEquil.and.Conc(jS,i).gt.0.)
! SConcO=Conc(jS,i)**(fExpO-1.)/(1.+xNuO*Conc(jS,i)**fExpO)
if(lMobIm(M).or.iDualPor.gt.0) then ! mobile-immobile model
ss=Sorb(jS,i)
sMid=(Sorb(jS,i)+SorbN(i))/2.
if(Level.eq.NLevel) ss=SorbN(i)
if(ss.gt.0.) then
dSConcS=fExp*ss**(fExp-1.)/(1.+xNu*ss**fExp)**2
SConcS = ss**(fExp-1.)/(1.+xNu*ss**fExp)
end if
if(sMid.gt.0.) then
dConcS=fExp*sMid**(fExp-1.)/(1.+xNu*sMid**fExp)**2
dRetardS=sMid**fExp/(1.+xNu*sMid**fExp)*dKs-
! xKs*sMid**(2.*fExp)/(1.+xNu*sMid**fExp)**2*dNu+
! xKs*alog(sMid)*sMid**fExp/(1.+xNu*sMid**fExp)**2*ddExp
end if
if(Level.eq.NLevel.and..not.lEquil.and.Sorb(jS,i).gt.0.)
! SConcOS=Sorb(jS,i)**(fExpO-1.)/(1.+xNuO*Sorb(jS,i)**fExpO)
end if
else
if(Conc(jS,i).gt.0.) dRetard=Conc(jS,i)*dKs
if(lMobIm(M).or.iDualPor.gt.0) then ! mobile-immobile model
if(Sorb(jS,i).gt.0) dRetardS=Sorb(jS,i)*dKs
end if
end if
if(jS.gt.1) then
if(.not.lLinear(jS-1)) then
if(cPrev.gt.0.)
! SConcP=cPrev**(fExpP-1.)/(1.+xNuP*cPrev**fExpP)
if(Sorb(jS-1,i).gt.0.)
! SConcPS=Sorb(jS-1,i)**(fExpP-1.)/
! (1.+xNuP*Sorb(jS-1,i)**fExpP)
end if
end if
* Calculate the retardation factors
Retard(i)=(ro*Frac*f_em*xKs*dConc+ThG*Henry)/ThW+1.
* Calculate the dispersion coefficients
call Disper(i,M,NMat,NSD,NumNP,dt,lTort,lArtD,lUpW,lMobIm,
! iDualPor,Level,NLevel,ChPar,Retard,Disp,thSat,
! ThImob,ThW,ThG,v,Dw,Dg,Henry,ro,Frac,xKs,fExp,xNu,
! cMid,dSConc,PeCr,TauG,iTort,lBact)
* Calculate the adsorbed concentration on kinetic sites or
* the concentration in an imobile zone, before solving matrix equation
if(.not.lEquil)
! call NEquil(i,jS,NSD,NumNP,NMat,M,Conc,Sorb,Sorb2,cNew,SorbN,
! SorbN2,SSorb,SSorb2,lMobIm,lLinear,lBact,Level,
! NLevel,dt,epsi,ro,xKs,xKsO,cc,SConc,SConcO,SConcS,
! SConcOS,dSConcS,xMuL,xMuLO,xMuS,xMuSO,dRetardS,
! GamLi,GamL1i,GamLOi,GamL1Oi,GamSi,GamS1i,GamSOi,
! GamS1Oi,Omega,OmegaO,rKa1,rKa1O,rKa2,rKa2O,rKd1,
! rKd1O,rKd2,rKd2O,ThW,ThWO,psi1,psi1O,psi2,psi2O,
! DMobI,Frac,ThImob,ThImobO,iDualPor,SinkIm,FlMacro,
! lNEquil,GamL1Pi,GamS1Pi,xKsP,SConcPS,lDualNEq,
! f_em,OmegaS)
* Calculate zero-order coefficient g0
g0(i)=xMuL*ThW+Frac*f_em*ro*xMuS+ThG*xMuG-sSink(i)
q0(i)=xMuL*ThW+ ro*xMuS+ThG*xMuG
if(.not.lEquil) then
if((lMobIm(M).or.iDualPor.gt.0).and..not.lBact) then
g0(i)=g0(i)+Omega*SSorb
if(iDualPor.gt.0.and.SinkIm(i).le.0) g0(i)=g0(i)-FlMacro
if(lDualNEq) g0(i)=g0(i)+OmegaS*ro*SSorb2
else if(.not.lBact) then
g0(i)=g0(i)+Omega*ro*SSorb
else if(lBact) then
g0(i)=g0(i)+rKd1*ro*SSorb+rKd2*ro*SSorb2
end if
end if
if(jS.gt.1) then
cG=cPrev*(GamL1P*ThW+ro*Frac*f_em*xKsP*GamS1P*SConcP+
! ThG*HenryP*GamG1P)
cG1=cG
if(.not.lEquil) then
if((lMobIm(M).or.iDualPor.gt.0).and..not.lBact) then
aa=Sorb(jS-1,i)*(ThImob*GamL1Pi+
! (1.-Frac)*ro*GamS1Pi*xKsP*SConcPS)
if(.not.lNEquil) cG=cG+aa
cG1=cG1+aa
if(lDualNEq) then
aa=GamS1Pi*ro*Sorb2(jS-1,i)
if(.not.lNEquil) cG=cG+aa
cG1=cG1+aa
end if
else if(.not.lBact) then
aa=GamS1Pi*ro*Sorb(jS-1,i)
if(.not.lNEquil) cG=cG+aa
cG1=cG1+aa
else if(lBact) then
write(*,*) 'Attachment/dettachment model is implemented
!only for one solute'
write(*,*)'Press Enter to continue'
read(*,*)
stop
end if
end if
g0(i)=g0(i)+cG
q0(i)=q0(i)+cG1
end if
if(cMid.gt.0.) g0(i)=g0(i)-ro*Frac*f_em*dRetard
* Calculate first-order coefficient g1
g1(i)=-(GamL+GamL1)*ThW-(GamS+GamS1)*ro*Frac*f_em*xKs*SConc-
! (GamG+GamG1)*ThG*Henry
c if(Level.eq.NLevel) g1(i)=g1(i)-ThG*dHenry-Henry*(ThWO-ThW)/dt
if(.not.lEquil) then
if((lMobIm(M).or.iDualPor.gt.0).and..not.lBact) then ! mobile-immobile model
g1(i)=g1(i)-Omega
if(iDualPor.gt.0.and.SinkIm(i).gt.0) g1(i)=g1(i)-SinkIm(i)
if(Level.eq.NLevel.and.lLinear(jS))
! g1(i)=g1(i)+Omega*dt*Omega/DMobI
if(lDualNEq) then
g1(i)=g1(i)-OmegaS*ro*Frac*(1.-f_em)*SConc*xKs
if(Level.eq.NLevel.and.lLinear(jS)) g1(i)=g1(i)+OmegaS*ro*
! (dt*OmegaS*Frac*(1.-f_em)*xKs/
! (2.+dt*(OmegaS+GamSi+GamS1i)))
end if
else if(.not.lBact) then ! two-site sorption model
g1(i)=g1(i)-Omega*ro*(1.-Frac)*SConc*xKs
if(Level.eq.NLevel.and.lLinear(jS)) g1(i)=g1(i)+Omega*ro*
! (dt*Omega*(1.-Frac)*xKs/(2.+dt*(Omega+GamSi+GamS1i)))
else if(lBact) then ! filtration model
g1(i)=g1(i)-ThW*(rKa1*psi1+rKa2*psi2)
if(Level.eq.NLevel.and.lLinear(jS)) g1(i)=g1(i)+dt*ThW*
! (rKd1*rKa1/(2.+dt*(rKd1+GamSi))+
! rKd2*rKa2/(2.+dt*(rKd2+GamSi)))
end if
end if
q1(i)=(-(GamL+GamL1)*ThW-(GamS+GamS1)*ro*Frac*f_em*xKs*SConc-
! (GamG+GamG1)*ThG*Henry)*Conc(jS,i)
if(.not.lEquil) then
if((lMobIm(M).or.iDualPor.gt.0).and..not.lBact) then
q1(i)=q1(i)-Sorb(jS,i)*(ThImob*(GamLi+GamL1i)+
! (1.-Frac)*ro*xKs*SConcS*(GamSi+GamS1i))
if(lDualNEq) q1(i)=q1(i)-(GamSi+GamS1i)*ro*Sorb2(jS,i)
else if(.not.lBact) then
q1(i)=q1(i)-(GamSi+GamS1i)*ro*Sorb(jS,i)
else if(lBact) then
q1(i)=q1(i)-ro*(GamSi+GamS1i)*(Sorb(jS,i)+Sorb2(jS,i))
end if
end if
* Velocity corrections
if(i.eq.1) then
dx=x(2)-x(1)
derK=(Henryj-Henry)/dx
else if(i.eq.NumNP) then
dx=x(NumNP)-x(NumNP-1)
derK=(Henry-Henryi)/dx
else
dx=(x(j)-x(k))/2.
derK=(Henryj-Henryi)/dx
end if
vCorr(i)=ThG*Dg*TauG*derK
if(Level.eq.1) vO(i)=vO(i)-vCorr(i)
if(Level.eq.NLevel) vN(i)=vN(i)-vCorr(i)
* Calculate the maximum local Peclet and Courant numbers
call PeCour(i,j,NumNP,Level,NLevel,lUpW,lArtD,dt,x,v,wc,ThW,vj,
! Thj,Disp,Retard,Peclet,Courant,CourMax,PeCr,dtMaxC,
! Iter,epsi)
11 continue
return
end
************************************************************************
subroutine MatSet(jS,N,NS,NSD,Level,epsi,alf,dt,kBotCh,kTopCh,
! cBot,cTop,x,thO,thN,vO,vN,Conc,Disp,Retard,wc,
! g0,g1,B,D,E,F,E1,D1,F1,BN,DN,FN,NMat,ChPar,
! TempO,TempN,TDep,dSurf,cAtm,MatNum,lMobIm,
! iDualPor,lVapor,rBot,lBact)
logical lMobIm(NMat),lVapor,lBact
double precision B,D,E,F
dimension cBot(NS),cTop(NS),x(N),thO(N),thN(N),vO(N),vN(N),
! Conc(NSD,N),Disp(N),Retard(N),wc(N),g0(N),g1(N),B(N),
! D(N),E(N),F(N),ChPar(NSD*16+4,NMat),TempO(N),TempN(N),
! TDep(NSD*16+4),MatNum(N)
do 10 i=1,N
M=MatNum(i)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact) then
ThImob=ChPar(4,M)
if(ThImob.gt.thO(i)) write(*,*) "Warning !!! ThImob > Theta"
thN(i)=max(thN(i)-ThImob,0.001)
thO(i)=max(thO(i)-ThImob,0.001)
end if
10 continue
* Lower boundary condition
b1=x(2)-x(1)
if(Level.eq.1) then
F1= Conc(jS,1)*
! (b1/2./dt*thO(1)*Retard(1)+
! alf*(-(thO(1)*Disp(1)+thO(2)*Disp(2))/b1/2.-
! ((2.+3.*wc(1))*vO(1)+vO(2))/6.+
! b1/12.*(3.*g1(1)+g1(2))))+
! Conc(jS,2)*
! alf*((thO(1)*Disp(1)+thO(2)*Disp(2))/b1/2.-
! (vO(1)+(2.-3.*wc(1))*vO(2))/6.+b1/12.*(g1(1)+g1(2)))+
! alf*b1/6.*(2.*g0(1)+g0(2))
* 3. type BC
if(kBotCh.eq.-1) F(1)=F1+alf*cBot(jS)*vO(1)
else
E1=epsi*(-(thN(1)*Disp(1)+thN(2)*Disp(2))/b1/2.+
! (vN(1)+(2.-3.*wc(1))*vN(2))/6.-b1/12.*(g1(1)+g1(2)))
D1=b1/2./dt*thN(1)*Retard(1)+
! epsi*((thN(1)*Disp(1)+thN(2)*Disp(2))/b1/2.+
! ((2.+3.*wc(1))*vN(1)+vN(2))/6.-b1/12.*(3.*g1(1)+g1(2)))
F2=epsi*b1/6.*(2.*g0(1)+g0(2))
F1=F1+F2
* 1.type BC
if(kBotCh.eq.1) then
D(1)=1.
E(1)=0.
F(1)=cBot(jS)
end if
* 3. type BC
if(kBotCh.eq.-1) then
if(vN(1).gt.0..or.(lVapor.and.rBot.eq.0.)) then
E(1)=E1
D(1)=D1
F(1)=F(1)+F2+epsi*cBot(jS)*vN(1)
else
D(1)=-1.
E(1)=1.
F(1)=0.
end if
end if
* Free drainage
if(kBotCh.eq.0) then
D(1)=-1.
E(1)=1.
F(1)=0.
end if
end if
do 11 i=2,N-1
a1=b1
b1=x(i+1)-x(i)
dx=(x(i+1)-x(i-1))/2.
if(Level.eq.1) then
F(i)= Conc(jS,i-1)*
! alf*((thO(i-1)*Disp(i-1)+thO(i)*Disp(i))/a1/2.+
! ((2.+3.*wc(i-1))*vO(i-1)+vO(i))/6.+
! a1/12.*(g1(i-1)+g1(i)))+
! Conc(jS,i)*
! (dx/dt*thO(i)*Retard(i)+
! alf*(-(thO(i-1)*Disp(i-1)+thO(i)*Disp(i))/a1/2.-
! (thO(i+1)*Disp(i+1)+thO(i)*Disp(i))/b1/2.-
! (vO(i+1)+3.*(wc(i-1)+wc(i))*vO(i)-vO(i-1))/6.+
! (a1*(g1(i-1)+3.*g1(i))+b1*(3.*g1(i)+g1(i+1)))/12.))+
! Conc(jS,i+1)*
! alf*((thO(i+1)*Disp(i+1)+thO(i)*Disp(i))/b1/2.-
! (vO(i)+(2.-3.*wc(i))*vO(i+1))/6.+
! b1/12.*(g1(i)+g1(i+1)))+
! alf*(a1*(g0(i-1)+2.*g0(i))+b1*(2.*g0(i)+g0(i+1)))/6.
else
B(i)=epsi*(-(thN(i-1)*Disp(i-1)+thN(i)*Disp(i))/a1/2.-
! ((2.+3.*wc(i-1))*vN(i-1)+vN(i))/6.-
! a1/12.*(g1(i-1)+g1(i)))
D(i)=dx/dt*thN(i)*Retard(i)+
! epsi*((thN(i-1)*Disp(i-1)+thN(i)*Disp(i))/a1/2.+
! (thN(i+1)*Disp(i+1)+thN(i)*Disp(i))/b1/2.+
! (vN(i+1)+3.*(wc(i-1)+wc(i))*vN(i)-vN(i-1))/6.-
! (a1*(g1(i-1)+3.*g1(i))+b1*(3.*g1(i)+g1(i+1)))/12.)
E(i)=epsi*(-(thN(i+1)*Disp(i+1)+thN(i)*Disp(i))/b1/2.+
! (vN(i)+(2.-3.*wc(i))*vN(i+1))/6.-
! b1/12.*(g1(i)+g1(i+1)))
F(i)=F(i)+epsi*(a1*(g0(i-1)+2.*g0(i))+
! b1*(2.*g0(i)+g0(i+1)))/6.
end if
11 continue
* Upper boundary condition
if(Level.eq.1) then
FN= Conc(jS,N-1)*
! alf*((thO(N-1)*Disp(N-1)+thO(N)*Disp(N))/b1/2.+
! ((2.+3.*wc(N-1))*vO(N-1)+vO(N))/6.+b1/12.*(g1(N-1)+g1(N)))+
! Conc(jS,N)*
! (b1/2./dt*thO(N)*Retard(N)+
! alf*(-(thO(N-1)*Disp(N-1)+thO(N)*Disp(N))/b1/2.+
! (vO(N-1)+(2.-3.*wc(N-1))*vO(N))/6.+
! b1/12.*(g1(N-1)+3*g1(N))))+
! alf*b1/6.*(g0(N-1)+2.*g0(N))
* 3. type BC
if(kTopCh.le.0) then
F(N)=FN
if(vO(N).lt.0.) F(N)=F(N)-alf*vO(N)*cTop(jS)
if(kTopCh.eq.-2) then
M=MatNum(N)
Tr=293.15
R=8.314
jjj=(jS-1)*16
TT=(TempO(N)+273.15-Tr)/R/(TempO(N)+273.15)/Tr
Dg=ChPar(jjj+6,M)*exp(TDep(jjj+6)*TT)
Henry=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TT)
F(N)=F(N)-alf*Dg/dSurf*Henry*Conc(jS,N)+Dg/dSurf*cAtm
end if
end if
else
BN=epsi*(-(thN(N-1)*Disp(N-1)+thN(N)*Disp(N))/b1/2.-
! ((2.+3.*wc(N-1))*vN(N-1)+vN(N))/6.-b1/12.*(g1(N-1)+g1(N)))
DN=b1/2./dt*thN(N)*Retard(N)+
! epsi*((thN(N-1)*Disp(N-1)+thN(N)*Disp(N))/b1/2.-
! (vN(N-1)+(2.-3.*wc(N-1))*vN(N))/6.-
! b1/12.*(g1(N-1)+3.*g1(N)))
FE=epsi*b1/6.*(g0(N-1)+2.*g0(N))
FN=FN+FE
* 1. type BC
if(kTopCh.gt.0) then
B(N)=0.
D(N)=1.
F(N)=cTop(jS)
* 3. type BC
else
B(N)=BN
D(N)=DN
F(N)=F(N)+FE
if(vN(N).lt.0.) F(N)=F(N)-epsi*vN(N)*cTop(jS)
if(kTopCh.eq.-2) then
M=MatNum(N)
Tr=293.15
R=8.314
jjj=(jS-1)*16
TT=(TempN(N)+273.15-Tr)/R/(TempN(N)+273.15)/Tr
Dg=ChPar(jjj+6,M)*exp(TDep(jjj+6)*TT)
Henry=ChPar(jjj+10,M)*exp(TDep(jjj+10)*TT)
D(N)=D(N)+epsi*Dg/dSurf*Henry
end if
end if
end if
do 12 i=1,N
M=MatNum(i)
if(lMobIm(M).and.iDualPor.eq.0.or.lBact) then
ThImob=ChPar(4,M)
thN(i)=thN(i)+ThImob
thO(i)=thO(i)+ThImob
end if
12 continue
return
end
*************************************************************************
* Solve matrix equation
subroutine BanSol(N,A,B,C,F)
double precision A,B,C,F
dimension A(N),B(N),C(N),F(N)
do 11 i=2,N
B(i)=B(i)-A(i)*C(i-1)/B(i-1)
F(i)=F(i)-A(i)*F(i-1)/B(i-1)
11 continue
F(N)=F(N)/B(N)
do 12 i=2,N
j=N-i+1
F(j)=(F(j)-C(j)*F(j+1))/B(j)
12 continue
return
end
*************************************************************************
* Calculate the maximum local Peclet and Courant numbers
subroutine PeCour(i,j,NumNP,Level,NLevel,lUpW,lArtD,dt,x,v,wc,ThW,
! vj,Thj,Disp,Retard,Peclet,Courant,CourMax,PeCr,
! dtMaxC,Iter,epsi)
logical lUpW,lArtD
dimension x(NumNP),Disp(NumNP),Retard(NumNP),wc(NumNP)
TanH(z)=(exp(z)-exp(-z))/(exp(z)+exp(-z))
if(i.ne.NumNP) then
dx=x(j)-x(i)
vv=0.
if(ThW.gt.1.e-6.and.Thj.gt.1.e-6) vv=(abs(v)/ThW+abs(vj)/Thj)/2.
vv1=0.
if(ThW.gt.1.e-6.and.Thj.gt.1.e-6) vv1=(v/ThW+vj/Thj)/2.
DD=(Disp(i)+Disp(j))/2.
if(Level.eq.NLevel) then
Pec=99999.
dtMax=1.e+30
c vMax=amax1(abs(v)/ThW,abs(vj)/Thj)
vMax=(abs(v)+abs(vj))/(ThW+Thj)
RMin=amin1(Retard(i),Retard(j))
if(DD.gt.0.) Pec=abs(vv)*dx/DD
Cour=vMax*dt/dx/RMin
Peclet=amax1(Peclet,Pec)
Courant=amax1(Courant,Cour)
Cour1=CourMax
if(.not.lUpW.and..not.lArtD) then
if(Pec.ne.99999.) Cour1=amin1(1.,PeCr/amax1(0.5,Pec))
end if
if(epsi.lt.1..and.vMax.gt.1.e-20) dtMax=Cour1*dx*RMin/vMax
* the von Neumann time step limit
c RThE=(ThW+thj)/2.*RMin
c if(abs(DD).gt.1.e-20)dtMax=amin1(dtMax,10.*RThE*dx*dx/2./DD)
dtMaxC=amin1(dtMaxC,dtMax)