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Module_Thermal_IntE_Newton_Bercovici.f90
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MODULE MODULE_THERMAL_INTE_NEWTON_BERCOVICI
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!! Equation : Heat equation
!!!!!!!! Model : Integration sur l'epaisseur de l'intrusion
!!!!!!!! Schema : Newton_Rhapsod method
!!!!!!!! Model couplage : Bercovici rheology (1995)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CONTAINS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!! SUBROUTINE THICKNESS_NEWTON_SOLVER
SUBROUTINE THERMAL_INTE_NEWTON_BERCOVICI(Xi,H,P,T,Ts,BL,Dt,Dr,theta,dist,ray,M,sigma,nu,Pe,psi,&
&delta0,el,grav,N1,gam,Inter_Q,F_err,z,tmps)
!*****************************************************************
! Solve for the parameter Xi, and split in Temperature and thermal layer
! from evolution equation using the Newton
! method
!*****************************************************************
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,gam,Inter_Q
INTEGER, INTENT(IN) :: M, z
DOUBLE PRECISION , INTENT(INOUT) :: F_err
!Variable du sous programmes
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: Xi_guess,Xi_tmps
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: a,b,c,S
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: a1,b1,c1
DOUBLE PRECISION ,DIMENSION(:), ALLOCATABLE :: Xi_m,qa
DOUBLE PRECISION :: U
INTEGER :: i,ndyke,N,Size
INTEGER :: err1,col
LOGICAL :: CHO
! Taille de la grille
ndyke=sigma/Dr
CHO=COUNT(H(:,1)>delta0)<ndyke
SELECT CASE (CHO)
CASE(.TRUE.)
N = ndyke +10 ! Cas ou on donne pas de profile initiale...
CASE(.FALSE.)
N = COUNT(H(:,1)>delta0) +10
END SELECT
! Caracterisation du flux
ALLOCATE(qa(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur alloc flux';STOP
END IF
InterInjectionRate:IF (mod(tmps,Inter_Q)<Inter_Q/2D0) THEN
DO i = 1,N,1
U = 2.d0/(sigma)**4.
Flux:IF (i<ndyke+1) THEN
qa(i) = U*(1-gam*H(i,2))*(sigma**2.-dist(i)**2.)
ELSE
qa(i) = 0.d0
END IF Flux
END DO
ELSE
qa(:)=0D0
ENDIF InterInjectionRate
! Calcule de f tmps n et n+
ALLOCATE(Xi_tmps(1:N),Xi_guess(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur alloc xi_tmps-xi_guess'; STOP
END IF
col=1
CALL TEMPERATURE(Xi_tmps,col,N,Xi,H,T,Ts,BL,P,dist,ray,Dr,nu,Pe,delta0,el,grav,N1,tmps+Dt,psi,Dt,qa)
col=2
CALL TEMPERATURE(Xi_guess,col,N,Xi,H,T,Ts,BL,P,dist,ray,Dr,nu,Pe,delta0,el,grav,N1,tmps+Dt,psi,Dt,qa)
! Jacobienner
ALLOCATE(a1(1:N),b1(1:N),c1(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur allocation dans coeff Temperature'; STOP
END IF
CALL JACOBI_TEMPERATURE(a1,b1,c1,N,H,BL,T,Ts,Xi,P,Dr,dist,ray,nu,Pe,delta0,el,grav,psi,Dt)
!Systeme a inverser
ALLOCATE(a(1:N),b(1:N),c(1:N),S(1:N),stat= err1)
IF (err1>1) THEN
PRINT*, 'Erreur d''allocation dans coeff du systeme'; STOP
END IF
DO i=1,N,1
a(i)=-theta*Dt*a1(i)
b(i)=(1D0+psi)-theta*Dt*b1(i)
c(i)=-theta*Dt*c1(i)
S(i)=(1D0+psi)*(Xi(i,1)-Xi(i,2))+theta*Dt*Xi_guess(i)+(1D0-theta)*Dt*Xi_tmps(i)
END DO
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)
! CALL NONA_DIAGO(N,Xi_m,a,b,a,b,c,0,g,k,l,S)
! CALL NONA_DIAGO(N,Xi_m,c*0D0,c*0D0,c*0D0,a,b,c,c*0D0,c*0D0,c*0D0,S)
DO i=1,N,1
Xi(i,3)=Xi_m(i)+Xi(i,2)
! IF (Xi(i,3)>(H(i,3))) THEN
! XI(i,3) = (1D0-1D-7)*H(i,3)
! ELSEIF (XI(i,3)<0.D0) THEN
! Xi(i,3) =1D-7
! 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(:,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)
DEALLOCATE(Xi_guess,Xi_tmps,a1,b1,c1)
END SUBROUTINE THERMAL_INTE_NEWTON_BERCOVICI
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!-------------------------------------------------------------------------------------
! SUBROUTINE NONA DIAG
!-------------------------------------------------------------------------------------
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE NONA_DIAGO(N,Hm,a,b,c,d,e,f,g,k,l,S)
!*****************************************************************
! Solves for a vector Hm of length N the nano diagonal linear set
! M Hm = S, where A, B, C, D, E, F, G, K and L are the three main
! diagonals of matrix M(N,N), the other terms are 0.
! S is the right side vector.
!*****************************************************************
IMPLICIT NONE
INTEGER , INTENT(IN) :: N
INTEGER :: i
INTEGER :: err3,err4
DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: a,b,c,d,e,f,g,k,l,S
DOUBLE PRECISION, DIMENSION(:),INTENT(INOUT) :: Hm
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: zeta,alpha,beta,mu,xi,lambda,eta,omega,gamma
AllOCATE(zeta(1:N),alpha(1:N),beta(1:N),mu(1:N),xi(1:N),stat=err3)
ALLOCATE(lambda(1:N),eta(1:N),omega(1:N),gamma(1:N),stat=err4)
IF (err3>1 .OR. err4>1) THEN
PRINT*, 'Erreur d''allocation dans vecteur P,Q'; STOP
END IF
zeta(1)=b(1)
alpha(1)=c(1)
beta(1)=d(1)
mu(1)=e(1)
xi(1)=f(1)/mu(1)
lambda(1)=g(1)/mu(1)
eta(1)=k(1)/mu(1)
omega(1)=l(1)/mu(1)
gamma(1)=S(1)/mu(1)
zeta(2)=b(2)
alpha(2)=c(2)
beta(2)=d(2)
mu(2)=e(2)-xi(1)*beta(2)
xi(2)=(f(2)-lambda(1)*beta(2))/mu(2)
lambda(2)=(g(2)-eta(1)*beta(2))/mu(2)
eta(2)=(k(2)-omega(1)*beta(2))/mu(2)
omega(2)=l(2)/mu(2)
gamma(2)=(S(2)-beta(2)*gamma(1))/mu(2)
zeta(3)=b(3)
alpha(3)=c(3)
beta(3)=d(3)-xi(1)*alpha(3)
mu(3)=e(3)-lambda(1)*alpha(3)-xi(2)*beta(3)
xi(3)=(f(3)-eta(1)*alpha(3)-lambda(2)*beta(3))/mu(3)
lambda(3)=(g(3)-omega(1)*alpha(3)-eta(2)*beta(3))/mu(3)
eta(3)=(k(3)-omega(2)*beta(3))/mu(3)
omega(3)=l(3)/mu(3)
gamma(3)=(S(3)-alpha(3)*gamma(1)-beta(3)*gamma(2))/mu(3)
zeta(4)=b(4)
alpha(4)=c(4)-xi(1)*zeta(4)
beta(4)=d(4)-lambda(1)*zeta(4)-xi(2)*alpha(4)
mu(4)=e(4)-eta(1)*zeta(4)-lambda(2)*alpha(4)-xi(3)*beta(4)
xi(4)=(f(4)-omega(1)*zeta(4)-eta(2)*alpha(4)-lambda(3)*beta(4))/mu(4)
lambda(4)=(g(4)-omega(2)*alpha(4)-eta(3)*beta(4))/mu(4)
eta(4)=(k(4)-omega(3)*beta(4))/mu(4)
omega(4)=l(4)/mu(4)
gamma(4)=(S(4)-zeta(4)*gamma(1)-alpha(4)*gamma(2)-beta(4)*gamma(3))/mu(4)
DO i=5,N
zeta(i)=b(i)-a(i)*xi(i-4)
alpha(i)=c(i)-a(i)*lambda(i-4)-xi(i-3)*zeta(i)
beta(i)=d(i)-a(i)*eta(i-4)-lambda(i-3)*zeta(i)-alpha(i)*xi(i-2)
mu(i)=e(i)-a(i)*omega(i-4)-zeta(i)*eta(i-3)-lambda(i-2)*alpha(i)-beta(i)*xi(i-1)
xi(i)=(f(i)-omega(i-3)*zeta(i)-eta(i-2)*alpha(i)-lambda(i-1)*beta(i))/mu(i)
lambda(i)=(g(i)-alpha(i)*omega(i-2)-eta(i-1)*beta(i))/mu(i)
eta(i)=(k(i)-omega(i-1)*beta(i))/mu(i)
omega(i)=l(i)/mu(i)
gamma(i)=(S(i)-a(i)*gamma(i-4)-zeta(i)*gamma(i-3)-alpha(i)*gamma(i-2)-beta(i)*gamma(i-1))/mu(i)
END DO
Hm(N)=gamma(N)
Hm(N-1)=gamma(N-1)-xi(N-1)*Hm(N)
Hm(N-2)=gamma(N-2)-lambda(N-2)*Hm(N)-xi(N-2)*Hm(N-1)
Hm(N-3)=gamma(N-3)-eta(N-3)*Hm(N)-lambda(N-3)*Hm(N-1)-xi(N-3)*Hm(N-2)
DO i=N-4,1,-1
Hm(i)=gamma(i)-xi(i)*Hm(i+1)-lambda(i)*Hm(i+2)-eta(i)*Hm(i+3)-omega(i)*Hm(i+4)
END DO
DEALLOCATE(zeta,alpha,beta,mu,xi,lambda,eta,omega,gamma)
END SUBROUTINE NONA_DIAGO
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! 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(OUT) :: U
INTEGER, INTENT(IN) :: N
INTEGER :: CODE
DOUBLE PRECISION, DIMENSION(N) :: GAM
DOUBLE PRECISION :: BET
INTEGER :: j
IF(B(1) .EQ. 0.D0) THEN
CODE=1
RETURN
END IF
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*,'ERRORTRIDIAG'
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 XI_SPLIT(Xi,T,BL,Ts,H,N,delta0,Dt,tmps,N1,Pe,el)
!*****************************************************************
! Solve for T and BL from xi for balmofrth with Ts=0
!*****************************************************************
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,d1,d2,Dr
! Separation des variables
DO i=1,N
Xit =2D0*H(i,3)/3.d0
IF (Xi(i,3) <= Xit) THEN
T(i,3) = 3D0*Xi(i,3)/(2D0*H(i,3))
BL(i,3) = H(i,3)/2.d0
ELSEIF (Xi(i,3)> Xit) THEN
T(i,3)= 1D0
BL(i,3)= 3D0*H(i,3)/2D0-3D0*Xi(i,3)/2D0
ENDIF
END DO
END SUBROUTINE XI_SPLIT
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE X_SPLIT_Balmforth
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE XI_SPLIT_BALMFORTH(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
IF (T(i,3)<1D-8) THEN
T(i,3) =0.d0
Ts(i,3) =0.d0
ENDIF
END DO
END SUBROUTINE XI_SPLIT_BALMFORTH
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE TEMPERATURE
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE TEMPERATURE(f,col,N,Xi,H,T,Ts,BL,P,dist,ray,Dr,nu,Pe,delta0,el,grav,N1,tmps,psi,Dt,qa)
!*****************************************************************
! Give the vector f
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:) , INTENT(INOUT) :: f
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H,Xi,T,Ts,BL,P
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: dist,ray,qa
! Prametre du model
DOUBLE PRECISION ,INTENT(IN) :: Dr
INTEGER ,INTENT(IN) :: col,N
! Nombre sans dimension
DOUBLE PRECISION ,INTENT(IN) :: nu,Pe,delta0,el,grav,N1,tmps,psi,Dt
! Parametre pour le sous programme
DOUBLE PRECISION, PARAMETER :: pi=3.14159265
DOUBLE PRECISION :: Ai
DOUBLE PRECISION :: h_a,h_a2,delta_a,delta_a2,delta_a3,eta_a
DOUBLE PRECISION :: T_a,T_a2,omega_a,sigma_a,delta_a4
DOUBLE PRECISION :: Bi
DOUBLE PRECISION :: h_b,h_b2,delta_b,delta_b2,delta_b3,eta_b
DOUBLE PRECISION :: T_b,T_b2,omega_b,sigma_b,delta_b4
DOUBLE PRECISION :: Crys
INTEGER :: i,Na
! Remplissage de f
DO i=1,N,1
IF1:IF (i .NE. 1) THEN
eta_b=(grav*(H(i,3)-H(i-1,3))+el*(P(i,3)-P(i-1,3)))/Dr
Bi=(ray(i-1)/(dist(i)*Dr))
h_b=0.5d0*(H(i,3)+H(i-1,3))
h_b2 = 0.5d0*(H(i,3)**2+H(i-1,3)**2)
delta_b=0.5d0*(BL(i,col)+BL(i-1,col))
delta_b2=0.5d0*(BL(i,col)**2+BL(i-1,col)**2)
delta_b3=0.5d0*(BL(i,col)**3+BL(i-1,col)**3)
delta_b4=0.5d0*(BL(i,col)**4+BL(i-1,col)**4)
T_b = 0.5d0*(T(i,col)+T(i-1,col))
T_b2 = 0.5d0*(T(i,col)**2+T(i-1,col)**2)
omega_b = -4.0d0/5.0d0*T_b*delta_b3*eta_b*nu/h_b + 0.8d0*T_b*&
& delta_b3*eta_b/h_b + 2*T_b*delta_b2*eta_b*nu - 2.0d0*T_b*&
& delta_b2*eta_b - 2*T_b*delta_b*eta_b*h_b*nu + 2.0d0*T_b*delta_b&
& *eta_b*h_b + T_b*eta_b*h_b2*nu - 1.0d0*T_b*eta_b*h_b2 - eta_b&
& *h_b2*nu
sigma_b = -8.0d0/15.0d0*T_b2*delta_b4*eta_b*nu/h_b2 +&
& 0.533333333333333d0*T_b2*delta_b4*eta_b/h_b2 + (54.0d0/&
& 35.0d0)*T_b2*delta_b3*eta_b*nu/h_b - 1.54285714285714d0*T_b2&
& *delta_b3*eta_b/h_b - 5.0d0/3.0d0*T_b2*delta_b2*eta_b*nu +&
& 1.66666666666667d0*T_b2*delta_b2*eta_b + (2.0d0/3.0d0)*T_b2&
& *delta_b*eta_b*h_b*nu - 0.666666666666667d0*T_b2*delta_b*eta_b*&
& h_b - 2.0d0/5.0d0*T_b*delta_b3*eta_b*nu/h_b + T_b*delta_b2*&
& eta_b*nu - 2.0d0/3.0d0*T_b*delta_b*eta_b*h_b*nu
ENDIF IF1
IF2: IF (i .NE. N) THEN
eta_a=(grav*(H(i+1,3)-H(i,3))+el*(P(i+1,3)-P(i,3)))/Dr
Ai=(ray(i)/(dist(i)*Dr))
h_a=0.5d0*(H(i+1,3)+H(i,3))
h_a2=0.5d0*(H(i+1,3)**2+H(i,3)**2)
delta_a=0.5d0*(BL(i+1,col)+BL(i,col))
delta_a2=0.5d0*(BL(i+1,col)**2+BL(i,col)**2)
delta_a3=0.5d0*(BL(i+1,col)**3+BL(i,col)**3)
delta_a4=0.5d0*(BL(i+1,col)**4+BL(i,col)**4)
T_a = 0.5d0*(T(i,col)+T(i+1,col))
T_a2 = 0.5d0*(T(i,col)**2+T(i+1,col)**2)
omega_a = -4.0d0/5.0d0*T_a*delta_a3*eta_a*nu/h_a + 0.8d0*T_a*&
& delta_a3*eta_a/h_a + 2*T_a*delta_a2*eta_a*nu - 2.0d0*T_a*&
& delta_a2*eta_a - 2*T_a*delta_a*eta_a*h_a*nu + 2.0d0*T_a*delta_a&
& *eta_a*h_a + T_a*eta_a*h_a2*nu - 1.0d0*T_a*eta_a*h_a2 - eta_a&
& *h_a2*nu
sigma_a = -8.0d0/15.0d0*T_a2*delta_a4*eta_a*nu/h_a2 +&
& 0.533333333333333d0*T_a2*delta_a4*eta_a/h_a2 + (54.0d0/&
& 35.0d0)*T_a2*delta_a3*eta_a*nu/h_a - 1.54285714285714d0*T_a2&
& *delta_a3*eta_a/h_a - 5.0d0/3.0d0*T_a2*delta_a2*eta_a*nu +&
& 1.66666666666667d0*T_a2*delta_a2*eta_a + (2.0d0/3.0d0)*T_a2&
& *delta_a*eta_a*h_a*nu - 0.666666666666667d0*T_a2*delta_a*eta_a*&
& h_a - 2.0d0/5.0d0*T_a*delta_a3*eta_a*nu/h_a + T_a*delta_a2*&
& eta_a*nu - 2.0d0/3.0d0*T_a*delta_a*eta_a*h_a*nu
END IF IF2
IF (i<6) THEN
Crys = psi*(H(i,3)-H(i,1))/Dt
ELSE
Crys = 0D0
ENDIF
IF4: IF (i==1) THEN
f(i) = -(Ai*Omega_a*Xi(i,col))&
&-(Ai*h_a*Sigma_a)&
&-4D0*Pe*T(i,col)/BL(i,col)+qa(i)+Crys
ELSEIF (i==N) THEN
f(i) = -(-Bi*Omega_b*Xi(i-1,col))&
&-(-Bi*h_b*Sigma_b)&
&-4D0*Pe*T(i,col)/BL(i,col)+qa(i)+Crys
ELSE
f(i) = -(Ai*Omega_a*Xi(i,col)-Bi*Omega_b*Xi(i-1,col))&
&-(Ai*h_a*Sigma_a-Bi*h_b*Sigma_b)&
&-4D0*Pe*T(i,col)/BL(i,col)+qa(i)+Crys
END IF IF4
END DO
END SUBROUTINE TEMPERATURE
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE JACOBIENNE TEMPERATURE
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE JACOBI_TEMPERATURE(a,b,c,N,H,BL,T,Ts,Xi,P,Dr,dist,ray,nu,Pe,delta0,el,grav,psi,Dt)
!*****************************************************************
! Give the jacobian coeficient a1,b1,c1
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:) , INTENT(INOUT) :: a,b,c
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H,BL,T,Ts,Xi,P
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: dist,ray
! Prametre du model
DOUBLE PRECISION ,INTENT(IN) :: Dr ,Dt
INTEGER ,INTENT(IN) :: N
! Nombre sans dimension
DOUBLE PRECISION ,INTENT(IN) :: nu,Pe,delta0,el,grav,psi
! Parametre pour le sous programme
DOUBLE PRECISION :: Ai
DOUBLE PRECISION :: h_a,h_a2,delta_a,delta_a2,delta_a3,eta_a
DOUBLE PRECISION :: T_a,T_a2,omega_a,sigma_a,delta_a4
DOUBLE PRECISION :: Bi
DOUBLE PRECISION :: h_b,h_b2,delta_b,delta_b2,delta_b3,eta_b
DOUBLE PRECISION :: T_b,T_b2,omega_b,sigma_b,delta_b4
INTEGER :: i,col
! Remplissage de la matrice Jacobienne
col=2
DO i=1,N,1
IF1:IF (i .NE. 1) THEN
eta_b=(grav*(H(i,3)-H(i-1,3))+el*(P(i,3)-P(i-1,3)))/Dr
Bi=(ray(i-1)/(dist(i)*Dr))
h_b=0.5d0*(H(i,3)+H(i-1,3))
h_b2 = 0.5d0*(H(i,3)**2+H(i-1,3)**2)
delta_b=0.5d0*(BL(i,col)+BL(i-1,col))
delta_b2=0.5d0*(BL(i,col)**2+BL(i-1,col)**2)
delta_b3=0.5d0*(BL(i,col)**3+BL(i-1,col)**3)
delta_b4=0.5d0*(BL(i,col)**4+BL(i-1,col)**4)
T_b = 0.5d0*(T(i,col)+T(i-1,col))
T_b2 = 0.5d0*(T(i,col)**2+T(i-1,col)**2)
omega_b = -4.0d0/5.0d0*T_b*delta_b3*eta_b*nu/h_b + 0.8d0*T_b*&
& delta_b3*eta_b/h_b + 2*T_b*delta_b2*eta_b*nu - 2.0d0*T_b*&
& delta_b2*eta_b - 2*T_b*delta_b*eta_b*h_b*nu + 2.0d0*T_b*delta_b&
& *eta_b*h_b + T_b*eta_b*h_b2*nu - 1.0d0*T_b*eta_b*h_b2 - eta_b&
& *h_b2*nu
ENDIF IF1
IF2: IF (i .NE. N) THEN
eta_a=(grav*(H(i+1,3)-H(i,3))+el*(P(i+1,3)-P(i,3)))/Dr
Ai=(ray(i)/(dist(i)*Dr))
h_a=0.5d0*(H(i+1,3)+H(i,3))
h_a2=0.5d0*(H(i+1,3)**2+H(i,3)**2)
delta_a=0.5d0*(BL(i+1,col)+BL(i,col))
delta_a2=0.5d0*(BL(i+1,col)**2+BL(i,col)**2)
delta_a3=0.5d0*(BL(i+1,col)**3+BL(i,col)**3)
delta_a4=0.5d0*(BL(i+1,col)**4+BL(i,col)**4)
T_a = 0.5d0*(T(i,col)+T(i+1,col))
T_a2 = 0.5d0*(T(i,col)**2+T(i+1,col)**2)
omega_a = -4.0d0/5.0d0*T_a*delta_a3*eta_a*nu/h_a + 0.8d0*T_a*&
& delta_a3*eta_a/h_a + 2*T_a*delta_a2*eta_a*nu - 2.0d0*T_a*&
& delta_a2*eta_a - 2*T_a*delta_a*eta_a*h_a*nu + 2.0d0*T_a*delta_a&
& *eta_a*h_a + T_a*eta_a*h_a2*nu - 1.0d0*T_a*eta_a*h_a2 - eta_a&
& *h_a2*nu
END IF IF2
IF3:IF (i==1) THEN
a(i)=0.d0
b(i)=-Ai*Omega_a
c(i)=0.d0
ELSEIF (i==N) THEN
a(i)=Bi*Omega_b
b(i)=0.d0
c(i)=0.d0
ELSE
a(i) = Bi*Omega_b
b(i) = -Ai*Omega_a
c(i)=0.d0
END IF IF3
ENDDO
END SUBROUTINE JACOBI_TEMPERATURE
END MODULE MODULE_THERMAL_INTE_NEWTON_BERCOVICI