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rusanov.f90
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module rusanov
use numerics
use flow
use omp_lib
!------------------------------Systeme----------------------------------
REAL(rp), dimension(:), allocatable :: X_sys
REAL(rp), dimension(:,:), allocatable :: u_prevs, u_nexts
REAL(rp) :: a,b, dx_sys, tm, dt_sys
INTEGER :: ns
!-----------------------------------------------------------------------
contains
!------------------------Initialisation---------------------------------
subroutine init_syst(space_number,final_time)
real(rp) , intent(in) :: final_time
integer, intent(in) :: space_number
Ns=space_number
Tm=final_time
!--------------------------Allocation----------------------------------
allocate(u_prevs(Ns,3), u_nexts(Ns,3), X_sys(Ns))
!----------------------------Constantes--------------------------------
a=-1._rp
b=5._rp
dx_sys=(b-a)/Ns
!-----------------Initialisation donnée intiale-------------------------
Do i=1,Ns
X_sys(i)=a+i*dx_sys ! espace
u_prevs(i,1)=init_dam(x_sys(i))! hauteur
u_prevs(i,2)=1._rp/(un+abs(x_sys(i)))! u vitesse
u_prevs(i,3)=5._rp ! temperature
END DO
end subroutine init_syst
function init_dam(xx) !donnee initiale
real(rp) , intent(in):: xx
real(rp) :: init_dam
if ( xx < 0._rp ) then
init_dam=un
else
init_dam=zero
end if
return
end function init_dam
!---------------------------Valeurs propres-----------------------------
function eigen_min(Ug,Ud)
real(rp) , dimension(3), intent(in) :: Ug, Ud
real(rp) ::lam_g , lam_d, eigen_min
lam_g=min( Ug(1)-sqrt(grv*Ug(3)*Ug(1)),Ug(2), Ug(2)+sqrt(grv*Ug(3)*Ug(1)))
lam_d=min( Ud(1)-sqrt(grv*Ud(3)*Ud(1)),Ud(2), Ud(2)+sqrt(grv*Ud(3)*Ud(1)))
eigen_min=min(lam_g , lam_d)
return
end function eigen_min
function eigen_max(Ug,Ud)
real(rp) , dimension(3), intent(in) :: Ug, Ud
real(rp) ::lam_g , lam_d, eigen_max
lam_g=max( Ug(1)-sqrt(grv*Ug(3)*Ug(1)),Ug(2), Ug(2)+sqrt(grv*Ug(3)*Ug(1)))
lam_d=max( Ud(1)-sqrt(grv*Ud(3)*Ud(1)),Ud(2), Ud(2)+sqrt(grv*Ud(3)*Ud(1)))
eigen_max=max(lam_g , lam_d)
return
end function eigen_max
function eigen_sys(Ug,Ud)
real(rp) , dimension(3), intent(in) :: Ug, Ud
real(rp) ::lam_g , lam_d, eigen_sys
lam_g=max( abs(Ug(1)-sqrt(grv*Ug(3)*Ug(1))),abs(Ug(2)), abs(Ug(2)+sqrt(grv*Ug(3)*Ug(1))))
lam_d=max( abs(Ud(1)-sqrt(grv*Ud(3)*Ud(1))),abs(Ud(2)), abs(Ud(2)+sqrt(grv*Ud(3)*Ud(1))))
eigen_sys=max(lam_g , lam_d)
return
end function eigen_sys
!-----------------------------Flux--------------------------------------
subroutine F_sys(X,Y)
real(rp) , dimension(3), intent(in) :: X
real(rp) , dimension(3), intent(out) :: Y
Y(1)=X(2)*X(1)
Y(2)=X(2)**2+0.5*grv*X(2)*X(3)*X(1)**2
Y(3)=X(2)*X(3)*X(1)
end subroutine F_sys
subroutine rusanov_flow(Ug,Ud,F)
real(rp) , dimension(3), intent(in) :: Ug, Ud
real(rp) , dimension(3), intent(out) :: F
real(rp) , dimension(3) :: Fg , Fd
real(rp) :: cc
cc=eigen_sys(Ug,Ud)
call F_sys(Ug,Fg)
call F_sys(Ud,Fd)
F(1)= 0.5_rp*(Fg(1)+Fd(1))-cc*( Ud(1)-Ug(1))*0.5_rp
F(2)= 0.5_rp*(Fg(2)+Fd(2)) -cc*( Ud(2)-Ug(2))*0.5_rp
F(3)= 0.5_rp*(Fg(3)+Fd(3))-cc*(Ud(3)-Ug(3))*0.5_rp
end subroutine
!----------------------------------------------------------------------
subroutine HLL_flow(Ug,Ud,F)
real(rp) , dimension(3), intent(in) :: Ug, Ud
real(rp) , dimension(3), intent(out) :: F
real(rp) , dimension(3) :: Fg , Fd
real(rp) :: lam_min,lam_max
!--------------------min/max des valeurs propres------------------------
lam_min=eigen_min(Ug,Ud)
lam_max=eigen_max(Ug,Ud)
!--------------------Calcul de F---------------------------------------
call F_sys(Ug,Fg)
call F_sys(Ud,Fd)
!----------------Flux en fonction Val. propores-------------------------
if (lam_min < zero .and. zero <lam_max ) then
F=(lam_max*Fg-lam_min*Fd +(Ud-Ug)*(lam_min*lam_max))/(lam_max-lam_min)
else if (lam_max < zero) then
F=Fd
else if ( zero < lam_min) then
F=Fg
end if
end subroutine HLL_flow
!--------------------------Solveurs-------------------------------------
Subroutine RUS_Solve() ! Solveur basé sur Rusanov
!-----------------------------VARIABLES --------------------------------
integer :: i, cpt, step
real(rp) , dimension(:), allocatable:: tmp
real(rp) , dimension(:,:), allocatable:: Fluxx
real(rp) :: t
character(len=80) :: FileName
!-------------------------INITIALISATION--------------------------------
t=zero
!----------------------------ALLOCATION---------------------------------
allocate(Fluxx(Ns,3), tmp(Ns))
!------------------------BOUCLE EN TEMPS--------------------------------
cpt=0
step=1
DO WHILE (t<Tm )
!--------------------VECTEUR DE FLUX-----------------------------------
!$OMP PARALLEL
DO i=2,Ns-1
Call rusanov_flow(U_prevs(i,:),U_prevs(i+1,:),Fluxx(i,:))
tmp(i) =eigen_sys(U_prevs(i,:), U_prevs(i+1,:) )
END DO
!$OMP END PARALLEL
!----------------------------BORD---------------------------------------
Call rusanov_flow(U_prevs(Ns,:),U_prevs(1,:),Fluxx(1,:))
tmp(1) =eigen_sys(U_prevs(Ns,:), U_prevs(1,:) )
!-------------------Dt EN FONCTION DE LA CFL----------------------------
dt_sys=0.5_rp*dx_sys/maxval(tmp)
!----------------------ITERATION EN ESPACE------------------------------
!$OMP PARALLEL
DO i=2,Ns-1
U_nexts(i,:)=U_prevs(i,:)-dt_sys/dx_sys*(Fluxx(i,:)-Fluxx(i-1,:))
END DO
!$OMP END PARALLEL
U_nexts(1,:)=U_prevs(1,:)-dt_sys/dx_sys*(Fluxx(2,:)-Fluxx(1,:))
U_nexts(Ns,:)=U_prevs(Ns,:)-dt_sys/dx_sys*(Fluxx(1,:)-Fluxx(Ns-1,:))
U_prevs=U_nexts
!----------------------------------------------------------------------
t=t+dt_sys
step=step+1
if (mod(step,5)==0)then
write(FileName,'(A,I4.4,A)') 'resultat/hauteur_rus',cpt,'.txt'
CALL save_file(X_sys,U_nexts(:,1),FileName)
cpt=cpt+1
end if
END DO
!------------------------ Sauvegarde------------------------------------
CALL save_file(X_sys,U_nexts(:,1),'hauteur_rus.txt')
CALL save_file(X_sys,U_nexts(:,2),'vitesse_rus.txt')
CALL save_file(X_sys,U_nexts(:,3),'temperature_rus.txt')
end Subroutine RUS_Solve
Subroutine HLL_Solve() ! Solveur basé sur HLL
!-----------------------------VARIABLES ----------------------------
integer :: i,step, cpt
real(rp) , dimension(:), allocatable:: tmp
real(rp) , dimension(:,:), allocatable:: Fluxx
real(rp) :: t
character(len=80) :: FileName
!----------------INITIALISATION-----------------------------
t=zero
cpt=0
!-----------------ALLOCATION--------------------------------------------
allocate(Fluxx(Ns,3),tmp(Ns))
!----------------BOUCLE EN TEMPS----------------------------------------
step=1
write(FileName,'(A,I4.4,A)') 'resultat/hauteur_hll',cpt,'.txt'
CALL save_file(X_sys,U_prevs(:,1),FileName)
cpt=1
DO WHILE (t<Tm )
!----------------VECTEUR DE FLUX----------------------------------------
!$OMP PARALLEL
DO i=2,Ns-1
Call HLL_flow(U_prevs(i-1,:),U_prevs(i,:),Fluxx(i-1,:))
tmp(i) =eigen_sys(U_prevs(i-1,:), U_prevs(i+1,:) )
END DO
!$OMP END PARALLEL
!----------------------------BORD---------------------------------------
Call HLL_flow(U_prevs(Ns,:),U_prevs(1,:),Fluxx(1,:))
tmp(1) =eigen_sys(U_prevs(Ns,:), U_prevs(1,:) )
call HLL_flow(U_prevs(Ns-1,:),U_prevs(Ns,:),Fluxx(Ns-1,:))
tmp(Ns) =eigen_sys(U_prevs(Ns-1,:), U_prevs(Ns,:))
!---------------Dt EN FONCTION DE LA CFL-------------------------------
dt_sys=0.25_rp*dx_sys/maxval(tmp)
!----------------------ITERATION EN ESPACE ------------------------------
!$OMP PARALLEL
DO i=2,Ns-1
U_nexts(i,:)=U_prevs(i,:)-dt_sys/dx_sys*(Fluxx(i,:)-Fluxx(i-1,:))
END DO
!$OMP END PARALLEL
U_nexts(1,:)=U_prevs(1,:)-dt_sys/dx_sys*(Fluxx(2,:)-Fluxx(1,:))
U_nexts(Ns,:)=U_prevs(Ns-1,:)!-dt_sys/dx_sys*(Fluxx(Ns,:)-Fluxx(Ns-1,:))
U_prevs=U_nexts
t=t+dt_sys
step=step+1
! if (mod(step,50)==0)then
! write(FileName,'(A,I4.4,A)') 'resultat/hauteur_hll',cpt,'.txt'
! CALL save_file(X_sys,U_nexts(:,1),FileName)
! cpt=cpt+1
! end if
END DO
!-----------------------Sauvegarde-------------------------------------
!CALL save_file(X_sys,U_nexts(:,1),FileName)
CALL save_file(X_sys,U_nexts(:,1),'hauteur_hll.txt')
CALL save_file(X_sys,U_nexts(:,2),'vitesse_hll.txt')
!CALL save_file(X_sys,U_nexts(:,3),'temperature_hll.txt')
end Subroutine HLL_Solve
end module rusanov