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Module_Thermal_GFD_GRAVI_Bercovici.f90
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MODULE MODULE_THERMAL_GFD_GRAVI_BERCOVICI
CONTAINS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!! Subroutine pour résoudre eqaution de la chaleur à l'aide d'une
!!!!!!! schema difference fini
SUBROUTINE THERMAL_GFD_SOLVER_BERCOVICI(Xi,H,P,T,Ts,BL,Dt,Dr,theta,dist,ray,M,sigma,nu,Pe,psi,delta0,el,grav,N1,F_err,z,tmps)
!*****************************************************************
! Solve for the parameter Xi, and split in Temperature and thermal layer
! from the evolution euqation using a center difference in space and a general
! theta scheme is timre
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION, DIMENSION(:,:), INTENT(IN) :: H,P
DOUBLE PRECISION , DIMENSION(:,:), INTENT(INOUT) :: Xi,T,BL,Ts
DOUBLE PRECISION , DIMENSION(:), INTENT(IN) :: dist,ray
!Parametre du model
DOUBLE PRECISION , INTENT(IN) :: Dt,Dr,theta,tmps
!Nombre sans dimensions
DOUBLE PRECISION , INTENT(IN) :: sigma,nu,Pe,psi,delta0,el,grav,N1
INTEGER, INTENT(IN) :: M, z
DOUBLE PRECISION , INTENT(INOUT) :: F_err
!Variable du sous programmes
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: Xi_tmps
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: a,b,c,d,e,f,g,k,l,S
DOUBLE PRECISION ,DIMENSION(:), ALLOCATABLE :: Xi_m
DOUBLE PRECISION :: U
INTEGER :: i,ndyke,N,Size
INTEGER :: err1,col
LOGICAL :: CHO
! Taille de la grille
N = COUNT(H(:,3)>0.D0)
!Systeme a inverser
ALLOCATE(a(1:N),b(1:N),c(1:N),S(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur allocation dans coeff Temperature'; STOP
END IF
CALL FILLING_MATRIX(a,b,c,S,N,H,BL,T,Ts,Xi,P,Dr,dist,ray,nu,&
&N1,Pe,delta0,el,grav,tmps,Dt,theta,psi)
a(1)=0
c(N)=0
!Inversion de la matrice
ALLOCATE(Xi_m(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur d''allocation dans vecteur Hm'; STOP
END IF
CALL TRIDIAG(a,b,c,s,N,Xi_m)
DO i=1,N,1
Xi(i,3)=Xi_m(i)
IF (Xi(i,3) >H(i,3)/2D0) THEN
Xi(i:,3) = H(i:,3)/2D0
EXIT
ELSEIF (XI(i,3)<0.D0) THEN
Xi(i,3) =0.D0
ENDIF
END DO
! Separation variables
CALL XI_SPLIT(Xi,T,BL,Ts,H,N,delta0,Dt,tmps,N1,Pe,el)
! Calcule de l'erreur
IF (DOT_PRODUCT(Xi(:,3),Xi(:,3))==DOT_PRODUCT(H(:,3)/2D0,H(:,3)/2D0)) THEN
F_err = 0D0 ! Cas ou le refroidissemnt est trop important et tout devient nulle
ELSEIF (DOT_PRODUCT(Xi(:,2),Xi(:,2)) == 0D0) THEN
F_err = ABS(MAXVAL(Xi_m(:)))
ELSE
Size = COUNT(Xi(:,2)>1D-10)
F_err = ABS(MAXVAL(((Xi(:Size,3)-Xi(:Size,2))/Xi(:Size,2))))
ENDIF
DEALLOCATE(Xi_m,a,b,c,S)
END SUBROUTINE THERMAL_GFD_SOLVER_BERCOVICI
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!! Routine pour separer les variables
!!!!!!!
SUBROUTINE XI_SPLIT(Xi,T,BL,Ts,H,N,delta0,Dt,tmps,N1,Pe,el)
!*****************************************************************
! Solve for T and BL from Xi deriving Ts directly here
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(INOUT) :: BL,T,Xi,Ts
!Dimensionless parameter
DOUBLE PRECISION, INTENT(IN) :: delta0,N1,Pe,el
!Parametre du model
DOUBLE PRECISION :: Dt,tmps
INTEGER, INTENT(IN) :: N
! Parametre pour le sous programme
INTEGER :: i
DOUBLE PRECISION, PARAMETER :: pi=3.14159265
DOUBLE PRECISION :: Xit,Tss,beta
! Separation des variables
DO i=1,N
beta = N1*Pe**(-0.5d0)/(sqrt(pi*(tmps+Dt)))
Xit = beta*H(i,3)**2/(6.d0*beta*H(i,3)+24.d0)
IF (Xi(i,3) <= Xit) THEN
Ts(i,3) = 3.d0*beta/4.d0*Xi(i,3)&
&-sqrt(3.d0)/4.d0*sqrt(beta*Xi(i,3)*(3.d0*Xi(i,3)*beta+8.d0))+1.d0
T(i,3) = 1.d0
BL(i,3) = 1/(Ts(i,3)*beta)*(2.d0-2.d0*Ts(i,3))
ELSEIF (Xi(i,3)> Xit) THEN
Ts(i,3) =(-12.d0*Xi(i,3)+6.d0*H(i,3))/((beta*H(i,3)+6.d0)*H(i,3))
BL(i,3) = H(i,3)/2.d0
T(i,3) = Ts(i,3)/4.d0*(beta*H(i,3)+4.d0)
ENDIF
END DO
END SUBROUTINE XI_SPLIT
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE TRIDIAG
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE TRIDIAG(A,B,C,S,N,U)
!*****************************************************************
! Solves for a vector U of length N the tridiagonal linear set
! M U = R, where A, B and C are the three main diagonals of matrix
! M(N,N), the other terms are 0. R is the right side vector.
!*****************************************************************
IMPLICIT NONE
DOUBLE PRECISION, DIMENSION(N), INTENT(IN) :: A,B,C,S
DOUBLE PRECISION, DIMENSION(N), INTENT(INOUT) :: U
INTEGER, INTENT(IN) :: N
INTEGER :: CODE
DOUBLE PRECISION, DIMENSION(N) :: GAM
DOUBLE PRECISION :: BET
INTEGER :: j
BET = B(1)
IF (BET == 0.D0) THEN
PRINT*,'ERROR TRIDIAG'
STOP
ENDIF
U(1) = S(1)/BET
DO J=2,N !Decomposition and forward substitution
GAM(j)=C(j-1)/BET
BET=B(j)-A(j)*GAM(j)
IF(BET.EQ.0.D0) THEN !Algorithm fails
PRINT*,'ERRORTRIDIAG2',j,N
STOP
END IF
U(j)=(S(j)-A(j)*U(j-1))/BET
END DO
DO j=N-1,1,-1 !Back substitution
U(j)=U(j)-GAM(j+1)*U(j+1)
END DO
CODE=0
RETURN
END SUBROUTINE TRIDIAG
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE FILLING MATRIX
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE FILLING_MATRIX(a,b,c,S,N,H,BL,T,Ts,Xi,P,Dr,dist,ray,nu,N1,Pe,delta0,el,grav,tmps,Dt,theta,psi)
!*****************************************************************
! Give the jacobian coeficient a1,b1,c1
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:) , INTENT(INOUT) :: a,b,c,S
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H,Xi,T,Ts,P,BL
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: dist,ray
! Prametre du model
DOUBLE PRECISION ,INTENT(IN) :: Dr
INTEGER ,INTENT(IN) :: N
! Nombre sans dimension
DOUBLE PRECISION ,INTENT(IN) :: nu,Pe,delta0,el,grav,N1,tmps,Dt,theta,psi
! Parametre pour le sous programme
DOUBLE PRECISION, PARAMETER :: pi=3.14159265
DOUBLE PRECISION :: h_a,delta_a,delta_a2,eta_a,Ai,T_a
DOUBLE PRECISIOn :: omega_a,sigma_a
DOUBLE PRECISION :: h_b,delta_b,delta_b2,eta_b,Bi,T_b
DOUBLE PRECISIOn :: omega_b,sigma_b,Ts_a,Ts_b,Ds_b,Ds_a
DOUBLE PRECISION :: loss,beta,Crys
INTEGER :: i,col
! Remplissage de f
col = 2
DO i=1,N,1
IF1:IF (i .NE. 1) THEN
Bi=(ray(i-1)/(dist(i)*Dr))*Dt
h_b=0.5d0*(H(i,3)+H(i-1,3))
delta_b=0.5d0*(BL(i,col)+BL(i-1,col))
delta_b2=0.5d0*(BL(i,col)**2+BL(i-1,col)**2)
T_b = 0.5d0*(T(i,col)+T(i-1,col))
Ts_b = 0.5d0*(Ts(i,col)+Ts(i-1,col))
eta_b = (H(i,3)-H(i-1,3))/Dr
Ds_b = T_b-Ts_b
omega_b = (eta_b*delta_b)/10.d0*(nu*(-20.d0*delta_b+30.d0*h_b)+&
&(1.d0-nu)*(6.d0*Ds_b*delta_b-15.d0*Ds_b*h_b-20.d0*T_b*delta_b+30.d0*T_b*h_b))
sigma_b = (-1.d0/210.d0)*Ds_b*delta_b2*eta_b*(nu*(-98.d0*delta_b+105.d0*h_b)+&
&(1-nu)*(22.d0*Ds_b*delta_b-35.d0*Ds_b*h_b-98.d0*T_b*delta_b+105.d0*T_b*h_b))
ENDIF IF1
IF2: IF (i .NE. N) THEN
Ai=(ray(i)/(dist(i)*Dr))*Dt
h_a=0.5d0*(H(i+1,3)+H(i,3))
delta_a=0.5d0*(BL(i+1,col)+BL(i,col))
delta_a2=0.5d0*(BL(i+1,col)**2+BL(i,col)**2)
T_a = 0.5d0*(T(i,col)+T(i+1,col))
Ts_a = 0.5d0*(Ts(i,col)+Ts(i+1,col))
eta_a = (H(i+1,3)-H(i,3))/Dr
Ds_a = T_a-Ts_a
omega_a = (eta_a*delta_a)/10.d0*(nu*(-20.d0*delta_a+30.d0*h_a)+&
&(1.d0-nu)*(6.d0*Ds_a*delta_a-15.d0*Ds_a*h_a-20.d0*T_a*delta_a+30.d0*T_a*h_a))
sigma_a = (-1.d0/210.d0)*Ds_a*delta_a2*eta_a*(nu*(-98.d0*delta_a+105.d0*h_a)+&
&(1-nu)*(22.d0*Ds_a*delta_a-35.d0*Ds_a*h_a-98.d0*T_a*delta_a+105.d0*T_a*h_a))
END IF IF2
beta = N1*Pe**(-0.5d0)/(sqrt(pi*(tmps+Dt)))
loss = Pe*beta*Ts(i,col)*Dt*psi
IF (ABS(N-i)<2) THEN
loss = loss/2.0
ENDIF
IF3:IF (i==1) THEN
a(i) = 0.d0
b(i) = 1D0-Ai*Omega_a
c(i) = 0.d0
S(i) = Xi(i,1)+Ai*Sigma_a+loss
ELSEIF (i == N) THEN
a(i) = Bi*Omega_b
b(i) = 1D0
c(i) = 0.d0
S(i) = Xi(i,1)-Bi*Sigma_b+loss
ELSE
a(i) = Bi*Omega_b
b(i) = 1D0-Ai*Omega_a
c(i) = 0.d0
S(i) = Xi(i,1)+Ai*Sigma_a-Bi*Sigma_b+loss
END IF IF3
ENDDO
END SUBROUTINE FILLING_MATRIX
END MODULE MODULE_THERMAL_GFD_GRAVI_BERCOVICI