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| PROGRAM calor
implicit none
integer :: i,j,k
integer, parameter :: Nr=1000 !Nombre de maille
integer :: niter !Nombre d'itération en temps
integer :: flg1,flg2,flg3,flg4,flg5,flg6,flg7,flg8,flg9,flg10
real(kind=8), parameter :: L=1.0,PI=acos(-1.),visco=0.1
real(kind=8), dimension (0:Nr) :: Lk,Dk,Uk,Sigma !Elément de matrice
real(kind=8), dimension (0:Nr) :: SM,Tp
real(kind=8), dimension (0:Nr) :: x
real(kind=8), dimension (0:Nr) :: dx,dx12u,dx12b,x12u,x12b
real(kind=8) :: t,dt,Time,test
!Période simulée (s)
Time = 10.0
!Pas de temps (s)
dt = 1E-3
!Nb d'itérations nécessaire
niter=Time/dt
print*, 'dt=',dt
print*, 'niter=',niter
!Maillage
do j=0,Nr
x(j)=j*L/Nr !régulier
!x(j) = L*(j**2)/(Nr**2) !irrégulier
!x(j) = L*(j**4)/(Nr**4) !irrégulier
enddo
!Intervalles et coordonnées demi-mailles
do j=1,Nr-1
x12u(j)=0.5*(x(j)+x(j+1))
x12b(j)=0.5*(x(j-1)+x(j))
dx12u(j)=x(j+1)-x(j)
dx12b(j)=x(j)-x(j-1)
!dx(j)=0.5*(dx12u(j)+dx12b(j))
!dx(j)=x(j+1)-x(j)
dx(j)=x12u(j)-x12b(j)
enddo
!Initialisation
Tp(:) = 0.0
SM(:) = Tp(:)
!flags pour sauvegarde des profils de température à différents instants
flg1=0;flg2=0;flg3=0;flg4=0;flg5=0;flg6=0;flg7=0;flg8=0;flg9=0;flg10=0
t = 0.0
!résolution du système sur j=1,Nr-1 (hors CL (points 0 et Nr))
do while(t .LE. Time)
t=t+dt
!Coef de la matrice tridiagonale
Lk(:) = 0.0
Dk(:) = 0.0
Uk(:) = 0.0
do j=1,Nr-1
!Discrétisation de l'équation
!Cylindrique 1D sur r (axie-symétrie)
!Sigma(j) = visco*dt/(x(j)*dx(j))
!Lk(j) = -Sigma(j)*(x12b(j)/(dx12b(j)))
!Dk(j) = 1+Sigma(j)*(x12u(j)/(dx12u(j)) + x12b(j)/(dx12b(j)))
!Uk(j) = -Sigma(j)*(x12u(j)/(dx12u(j)))
!Cartésien en 1D sur x
Sigma(j) = visco*dt/dx(j)
Lk(j) = -Sigma(j)/dx12b(j)
Dk(j) = 1+Sigma(j)*(1/dx12u(j) + 1/dx12b(j))
Uk(j) = -Sigma(j)/dx12u(j)
!Condition pour que l'algo TDMA soit pertinent
test = Dk(j)-(abs(Lk(j))+abs(Uk(j)))
if (test .LT. 0) then
print*, "Matrice non digonale-dominante!"
print*, "j",j,"Lk=",Lk(j),"Dk",Dk(j),"Uk",Uk(j),test
endif
enddo
!Conditions aux limites (ici Dirichlet)
Tp(Nr) = 0.0
Tp(0) = 20.0
SM = Tp
!Si CL de Dirichlet non-nulles, modif du second membre du système d'équation nécéssaire:
SM(1) = Tp(1) - Lk(1)*Tp(0)
SM(Nr-1) = Tp(Nr-1) - Uk(Nr-1)*Tp(Nr)
!Résolution du système
call TDMA(Nr,Lk,Dk,Uk,SM,Tp)
!Sauvegarde des profils
if(int(t*100).EQ.1 .AND. flg1.NE.1) then
flg1=1
print*, "0.1s",t
open(12,file="01s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.2 .AND. flg2.NE.1) then
flg2=1
print*, "02s",t
open(12,file="02s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.3 .AND. flg3.NE.1) then
flg3=1
print*, "0.3s",t
open(12,file="03s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.4 .AND. flg4.NE.1) then
flg4=1
print*, "0.4s",t
open(12,file="04s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.5 .AND. flg5.NE.1) then
flg5=1
print*, "05s",t
open(12,file="05s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.6 .AND. flg6.NE.1) then
flg6=1
print*, "06s",t
open(12,file="06s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.1 .AND. flg7.NE.1) then
flg7=1
print*, "07s",t
open(12,file="07s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.8 .AND. flg8.NE.1) then
flg8=1
print*, "08s",t
open(12,file="08s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.500 .AND. flg9.NE.1) then
flg9=1
print*, "09s",t
open(12,file="09s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
if(int(t*100).EQ.1000 .AND. flg10.NE.1) then
flg10=1
print*, "1s",t
open(12,file="1s.txt",status="unknown")
do j=0,Nr
write(12,*) x(j),Tp(j)
enddo
close(12)
endif
enddo
END PROGRAM calor
SUBROUTINE TDMA(N,A,B,C,D,X)
integer, intent(in) :: N
real(kind=8), dimension(0:N) :: A,B,C,D
real(kind=8), dimension(0:N) :: X
real(kind=8) :: xmult
integer :: i
do i = 2,N-1
xmult = A(i)/B(i-1)
B(i) = B(i) - xmult*C(i-1)
D(i) = D(i) - xmult*D(i-1)
end do
X(N-1) = D(N-1)/B(N-1)
do i = N-2,1,-1
X(i) = (D(i) - C(i)*X(i+1))/B(i)
end do
END SUBROUTINE TDMA |
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