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TEMPER.FOR
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* Source file TEMPER.FOR |||||||||||||||||||||||||||||||||||||||||||||||
* Calculation of heat transport
subroutine Temper(N,NMat,x,dt,t,MatNum,TempO,TempN,TPar,Ampl,B,D,
! E,F,vOld,vNew,ThOld,ThNew,Cap,Cond,Sink,tPeriod,
! kTopT,tTop,kBotT,tBot,lVapor,ThVOld,ThVNew,
! vVOld,vVNew,g0,lEnBal,HeatFl,xConv,tConv,dtMaxT,
! iCampbell,iTemp)
logical lVapor,lEnBal
double precision B,D,E,F,t
dimension x(N),MatNum(N),TempO(N),TempN(N),TPar(10,NMat),B(N),
! D(N),E(N),F(N),vOld(N),vNew(N),ThOld(N),ThNew(N),Cap(N),
! Cond(N),Sink(N),ThVOld(N),ThVNew(N),vVOld(N),vVNew(N),
! g0(N)
Cw=TPar(9,1)
PI=3.141592654
tTopA=tTop
if(tPeriod.gt.0.) tTopA=tTop+Ampl*sin(2.*PI*sngl(t)/tPeriod-7.*PI/
! 12.)
* Upper Flux BC
if(kTopT.lt.0.and..not.lEnBal) then
HeatFl=Cw*tTopA*(vNew(N)+vOld(N))/2.
if(lVapor) then
Cv=1.8e+6/xConv/tConv/tConv
xLat=xLatent(TempN(N))/xConv/tConv/tConv
HeatFl=HeatFl+Cv*tTopA*(vVNew(N)+vVOld(N))/2.+
! xLat*(vVNew(N)+vVOld(N))/2.
end if
end if
do 11 Level=1,2
if(Level.eq.1) then
call TempCap(N,NMat,MatNum,ThOld,vOld,Cap,Cond,TPar,iCampbell,
! xConv,tConv)
else
call TempCap(N,NMat,MatNum,ThNew,vNew,Cap,Cond,TPar,iCampbell,
! xConv,tConv)
end if
call SetUpHeat(N,Level,lEnBal,kBotT,kTopT,tBot,tTopA,HeatFl,dt,
! x,Cw,B,D,E,F,TempO,Cap,Cond,vNew,vOld,Sink)
11 continue
* Adjust matrix for vapor flow effects
if(lVapor) call TempAdj(N,x,dt,TempN,TempO,B,D,E,F,vVOld,vVNew,g0,
! kTopT,kBotT,tTopA,tBot,ThVNew,ThVOld,
! xConv,tConv)
* Solve matrix equation
call BanSol(N,B,D,E,F)
do 12 i=1,N
TempN(i)=sngl(F(i))
12 continue
* Max time step
dtMaxT=1.e+30
Cv=1.8e+6/xConv/tConv/tConv
if(lEnBal) then
if(iTemp.eq.0) then
dtMaxT=0.
dtMaxT=abs(Cap(N)*(x(N)-x(N-1))/
! (max(0.1,TempN(N))*(Cw*vNew(N)+Cv*vVNew(N))))
end if
dTempMax=2.
dTemp=abs(TempN(N)-TempO(N))
dtMaxT=min(dtMaxT,dTempMax/max(0.1,dTemp)*dt)
end if
return
end
************************************************************************
subroutine SetUpHeat(N,Level,lEnBal,kBotT,kTopT,tBot,tTopA,HeatFl,
! dt,x,Cw,B,D,E,F,TempO,Cap,Cond,vNew,vOld,
! Sink)
logical lEnBal
double precision B,D,E,F
dimension x(N),TempO(N),B(N),D(N),E(N),F(N),vOld(N),vNew(N),
! Cap(N),Cond(N),Sink(N)
dx=x(2)-x(1)
if(kBotT.gt.0) then
D(1)=1.
E(1)=0.
F(1)=tBot
else if(kBotT.lt.0) then
if(Level.eq.2) then
D(1)=dx/2./dt*Cap(1)+(Cond(1)+Cond(2))/dx/4.+
! Cw*(2.*vNew(1)+vNew(2))/12.+
! dx/24.*Cw*(3.*Sink(1)+Sink(2))
E(1)=-(Cond(1)+Cond(2))/4./dx+
! Cw*(2.*vNew(2)+vNew(1))/12.+dx/24.*Cw*(Sink(1)+Sink(2))
else
F(1)=TempO(1)*(dx/2./dt*Cap(1)-
! (Cond(1)+Cond(2))/dx/4.-
! Cw*(2.*vOld(1)+vOld(2))/12.-
! dx/24.*Cw*(3.*Sink(1)+Sink(2)))+
! TempO(2)*((Cond(1)+Cond(2))/4./dx-
! Cw*(2.*vOld(2)+vOld(1))/12.-
! dx/24.*Cw*(Sink(1)+Sink(2)))+
! tBot*Cw*(vNew(1)+vOld(1))/2.
end if
else
D(1)=-1.
E(1)=1.
F(1)=0.
end if
do 12 i=2,N-1
dxA=x(i)-x(i-1)
dxB=x(i+1)-x(i)
dx=(x(i+1)-x(i-1))/2.
if(Level.eq.2) then
B(i)=-(Cond(i)+Cond(i-1))/4./dxA-Cw*(vNew(i)+
! 2.*vNew(i-1))/12.+
! dxA/24.*Cw*(Sink(i-1)+Sink(i))
D(i)=(Cond(i-1)+Cond(i))/4./dxA+(Cond(i)+Cond(i+1))/4./dxB+
! dx/dt*Cap(i)+
! Cw*(vNew(i+1)-vNew(i-1))/12.+
! dxA/24.*Cw*(Sink(i-1)+3.*Sink(i))+
! dxB/24.*Cw*(3.*Sink(i)+Sink(i+1))
E(i)=-(Cond(i)+Cond(i+1))/4./dxB+
! Cw*(2.*vNew(i+1)+vNew(i))/12.+
! dxB/24*Cw*(Sink(i+1)+Sink(i))
else
F(i)=TempO(i-1)*((Cond(i)+Cond(i-1))/4./dxA+
! Cw*(vOld(i)+2.*vOld(i-1))/12.-
! dxA/24.*Cw*(Sink(i-1)+Sink(i)))+
! TempO(i)*(-Cw*(vOld(i+1)-vOld(i-1))/12.+
! dx/dt*Cap(i)-
! (Cond(i+1)+Cond(i))/4./dxB-
! (Cond(i)+Cond(i-1))/4./dxA-
! dxA/24.*Cw*(Sink(i-1)+3.*Sink(i))-
! dxB/24.*Cw*(3.*Sink(i)+Sink(i+1)))+
! TempO(i+1)*((Cond(i+1)+Cond(i))/4./dxB-
! Cw*(2.*vOld(i+1)+vOld(i))/12.-
! dxB/24.*Cw*(Sink(i+1)+Sink(i)))
end if
12 continue
if(kTopT.gt.0) then
B(N)=0.
D(N)=1.
F(N)=tTopA
else if(kTopT.lt.0) then
dx=x(N)-x(N-1)
if(Level.eq.2) then
B(N)=-(Cond(N)+Cond(N-1))/4./dx-
! Cw*(vNew(N)+2.*vNew(N-1))/12.+
! dx/24.*Cw*(Sink(N-1)+Sink(N))
D(N)=dx/2./dt*Cap(N)+
! (Cond(N-1)+Cond(N))/4./dx-
! Cw*(2.*vNew(N)+vNew(N-1))/12.+
! dx/24.*Cw*(Sink(N-1)+3.*Sink(N))
else
F(N)=TempO(N-1)*((Cond(N)+Cond(N-1))/4./dx+
! Cw*(vOld(N)+2.*vOld(N-1))/12.-
! dx/24.*Cw*(Sink(N-1)+Sink(N)))+
! TempO(N)*(dx/2./dt*Cap(N)-
! (Cond(N-1)+Cond(N))/4./dx+
! Cw*(2.*vOld(N)+vOld(N-1))/12.-
! dx/24.*Cw*(Sink(N-1)+3.*Sink(N)))
if(.not.lEnBal) then
F(N)=F(N)-HeatFl
F(N)=F(N)-min(0.,HeatFl)
else
F(N)=F(N)-HeatFl
end if
end if
end if
return
end
************************************************************************
subroutine TempAdj(N,x,dt,TempN,TempO,B,D,E,F,vVOld,vVNew,g0,
! kTopT,kBotT,tTopA,tBot,ThVNew,ThVOld,xConv,
! tConv)
double precision B,D,E,F
real Lat
dimension x(N),TempN(N),TempO(N),B(N),D(N),E(N),F(N),vVOld(N),
! vVNew(N),ThVNew(N),ThVOld(N),g0(N)
* Cv - volumetric specific heat of vapor [J/m3/K,kg/m/s2/K]
* Lat - volumetric latent heat of vaporization of water [J/m3,kg/m/s2]
Cv=1.8e+6/xConv/tConv/tConv
do 13 iLevel=1,2
do 11 i=1,N
if(iLevel.eq.1) then
if(i.eq.1) then
vVGrad=(vVOld(i+1)-vVOld(i))/(x(i+1)-x(i))
else if(i.eq.N) then
vVGrad=(vVOld(i)-vVOld(i-1))/(x(i)-x(i-1))
else
vVGrad=(vVOld(i+1)-vVOld(i-1))/(x(i+1)-x(i-1))*2.
end if
Lat=xLatent(TempO(i))/xConv/tConv/tConv
else
if(i.eq.1) then
vVGrad=(vVNew(i+1)-vVNew(i))/(x(i+1)-x(i))
else if(i.eq.N) then
vVGrad=(vVNew(i)-vVNew(i-1))/(x(i)-x(i-1))
else
vVGrad=(vVNew(i+1)-vVNew(i-1))/(x(i+1)-x(i-1))*2.
end if
Lat=xLatent(TempN(i))/xConv/tConv/tConv
end if
ThVGrad=(ThVNew(i)-ThVOld(i))/dt
g0(i)=-Lat*(vVGrad+ThVGrad)
11 continue
dx=x(2)-x(1)
if(kBotT.lt.0) then
if(iLevel.eq.1) then
F(1)=F(1)+TempO(1)*(-Cv*(2.*vVOld(1)+vVOld(2))/12.)+
! TempO(2)*(-Cv*(2.*vVOld(2)+vVOld(1))/12.)+
! dx/12.*(2.*g0(1)+g0(2))+
! tBot*Cv*(vVNew(1)+vVOld(1))/2.
else
D(1)=D(1)+Cv*(2.*vVNew(1)+vVNew(2))/12.
E(1)=E(1)+Cv*(2.*vVNew(2)+vVNew(1))/12.
F(1)=F(1)+dx/12.*(2.*g0(1)+g0(2))
end if
end if
do 12 i=2,N-1
dxA=x(i)-x(i-1)
dxB=x(i+1)-x(i)
dx=(x(i+1)-x(i-1))/2.
if(iLevel.eq.1) then
F(i)=F(i)+TempO(i-1)*( Cv*(vVOld(i) +2.*vVOld(i-1))/12.)+
! TempO(i) *(-Cv*(vVOld(i+1) -vVOld(i-1))/12.)+
! TempO(i+1)*(-Cv*(2.*vVOld(i+1) +vVOld(i))/12.)+
! dxA*(g0(i-1)+2.*g0(i))/12.+dxB*(2.*g0(i)+g0(i+1))/12.
else
B(i)=B(i)-Cv*(vVNew(i)+2.*vVNew(i-1))/12.
D(i)=D(i)+Cv*(vVNew(i+1)-vVNew(i-1))/12.
E(i)=E(i)+Cv*(2.*vVNew(i+1)+vVNew(i))/12.
F(i)=F(i)+dxA*(g0(i-1)+2.*g0(i))/12.+
! dxB*(2.*g0(i)+g0(i+1))/12.
end if
12 continue
if(kTopT.lt.0) then
dx=x(N)-x(N-1)
if(iLevel.eq.1) then
F(N)=F(N)+TempO(N-1)*(Cv*(vVOld(N)+2.*vVOld(N-1))/12.)+
! TempO(N) *(Cv*(2.*vVOld(N)+vVOld(N-1))/12.)+
! dx/12.*(g0(N-1)+2.*g0(N))
if(kTopT.eq.-1) F(N)=F(N)-tTopA*Cv*(vVNew(N)+vVOld(N))/2.
else
B(N)=B(N)-Cv*(vVNew(N)+2.*vVNew(N-1))/12.
D(N)=D(N)-Cv*(2.*vVNew(N)+vVNew(N-1))/12.
F(N)=F(N)+dx/12.*(g0(N-1)+2.*g0(N))
end if
end if
13 continue
return
end
************************************************************************
subroutine TempCap(N,NMat,MatNum,Theta,Veloc,Cap,Cond,TPar,
! iCampbell,xConv,tConv)
dimension MatNum(N),Theta(N),Veloc(N),Cap(N),Cond(N),
! TPar(10,NMat)
do 11 i=1,N
M=MatNum(i)
th=Theta(i)
v=Veloc(i)
Cap(i)=TPar(7,M)*TPar(1,M)+TPar(8,M)*TPar(2,M)+TPar(9,M)*th
if(Cap(i).eq.0.) then
write(*,*) 'Heat capacity is equal to zero'
read(*,*)
stop
end if
Cond(i)=amax1(0.,TPar(4,M)+TPar(5,M)*th+TPar(6,M)*sqrt(th))
if(iCampbell.eq.1) then
* TPar(1,M) - the volume fraction of solids
* TPar(4,M) - the volume fraction of quartz
* TPar(5,M) - the volume fraction of other minerals
* TPar(6,M) - the volume fraction of clay
AA=(0.57+1.73*TPar(4,M)+0.93*TPar(5,M))/(1.-0.74*TPar(4,M)-
! 0.49*TPar(5,M))-2.8*TPar(1,M)*(1.-TPar(1,M))
BB=2.8*TPar(1,M)
xc=amax1(0.005,TPar(6,M))
CC=1.+2.6/sqrt(xc)
DD=0.03+0.7*TPar(1,M)**2
EE=4.
XLamb=AA+BB*th-(AA-DD)*exp(-(CC*th)**EE)
Cond(i)=amax1(0.,XLamb*xConv/tConv/tConv/tConv)
end if
Cond(i)=Cond(i)+TPar(9,M)*TPar(3,M)*abs(v)
11 continue
return
end
************************************************************************
real function xLatent(Temp)
* Function calculating the volumetric latent heat of vaporization of
* water [J/m3,kg/m/s2]
* row - density of soil water [kg/m3]
* xLw - latent heat of vaporization of water [J/kg,ML2/T2]
row=(1.-7.37e-6*(Temp-4.)**2+3.79e-8*(Temp-4.)**3)*1000.
xLw=2.501e+06-2369.2*Temp
xLatent=row*xLw
return
end
* ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||