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maxwell.f90
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maxwell.f90
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module Maxwell
use zone
implicit none
integer, private :: i, j
real(kind=prec), private :: dex_dx, dey_dy
real(kind=prec), private :: dex_dy, dey_dx
real(kind=prec), private :: dbz_dx, dbz_dy
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine faraday( tm )
type( mesh_fields ) :: tm
!*** On utilise l'equation de Faraday sur un demi pas
!*** de temps pour le calcul du champ magnetique Bz
!*** a l'instant n puis n+1/2 apres deplacement des
!*** particules
do i=0,nx-1
do j=0,ny-1
dex_dy = (tm%ex(i,j+1)-tm%ex(i,j)) / hy(j)
dey_dx = (tm%ey(i+1,j)-tm%ey(i,j)) / hx(i)
tm%bz(i,j) = tm%bz(i,j) + 0.5 * dt * (dex_dy - dey_dx)
end do
end do
end subroutine faraday
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine ampere( tm )
type( mesh_fields ) :: tm
!*** Calcul du champ electrique E au temps n+1
!*** sur les points internes du maillage
!*** Ex aux points (i+1/2,j)
!*** Ey aux points (i,j+1/2)
do i=0,nx-1
do j=1,ny-1
dbz_dy = (tm%bz(i,j)-tm%bz(i,j-1)) / hhy(j)
tm%ex(i,j) = tm%ex(i,j) + csq * dt * dbz_dy - dt * tm%jx(i,j)/e0
end do
end do
do i=1,nx-1
do j=0,ny-1
dbz_dx = (tm%bz(i,j)-tm%bz(i-1,j)) / hhx(i)
tm%ey(i,j) = tm%ey(i,j) - csq * dt * dbz_dx - dt * tm%jy(i,j)/e0
end do
end do
end subroutine ampere
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine conditions_limites( tm, time )
type( mesh_fields ) :: tm
real(kind=prec) :: a11,a12,a21,a22,b1,b2,dis
real(kind=prec) :: time, alpha, omega
integer :: mm=1 !parametre du cas entran
select case ( bcname )
case ("period")
do i=0,nx-1
dbz_dy = (tm%bz(i,0)-tm%bz(i,ny-1)) / hhy(0)
tm%ex(i,0) = tm%ex(i,0) + csq * dt * dbz_dy - dt * tm%jx(i,0)/e0
tm%ex(i,ny) = tm%ex(i,0)
end do
do j=0,ny-1
dbz_dx = (tm%bz(0,j)-tm%bz(nx-1,j)) / hhx(0)
tm%ey(0,j) = tm%ey(0,j) - csq * dt * dbz_dx - dt * tm%jy(0,j)/e0
tm%ey(nx,j) = tm%ey(0,j)
end do
case ("silver")
!Frontiere Ouest : Ey + c Bz = 0
do j=0,ny-1
a11 = 1
a12 = -csq*dt/hx(0)
a21 = 1
a22 = c
b1 = tm%ey(0,j) - csq*dt/hx(0) * tm%bz(0,j) - dt * tm%jy(0,j)/e0
b2 = - tm%ey(0,j) - c*tm%bz(0,j)
dis = a11*a22-a21*a12
tm%ey(0,j) = (b1*a22-b2*a12) / dis
end do
!Frontiere Est : -Ey + c Bz = 0
do j=0,ny-1
a11 = 1
a12 = csq*dt/hx(nx-1)
a21 = 1
a22 = -c
b1 = tm%ey(nx,j) + csq*dt/hx(nx-1) * tm%bz(nx-1,j) - dt * tm%jy(nx,j)/e0
b2 = - tm%ey(nx,j) + c*tm%bz(nx-1,j)
dis = a11*a22-a21*a12
tm%ey(nx,j) = (b1*a22-b2*a12) / dis
end do
!Frontiere Sud : -Ex + c Bz = 0
do i=0,nx-1
a11 = 1
a12 = csq*dt/hy(0)
a21 = 1
a22 = -c
b1 = tm%ex(i,0) + csq*dt/hy(0) * tm%bz(i,0) - dt * tm%jx(i,0)/e0
b2 = - tm%ex(i,0) + c*tm%bz(i,0)
dis = a11*a22-a21*a12
tm%ex(i,0) = (b1*a22-b2*a12) / dis
end do
!Frontiere Nord : Ex + c Bz = 0
do i=0,nx-1
a11 = 1
a12 = -csq*dt/hy(ny-1)
a21 = 1
a22 = c
b1 = tm%ex(i,ny) - csq*dt/hy(ny-1) * tm%bz(i,ny-1) - dt * tm%jx(i,ny)/e0
b2 = - tm%ex(i,ny) - c*tm%bz(i,ny-1)
dis = a11*a22-a21*a12
tm%ex(i,ny) = (b1*a22-b2*a12) / dis
end do
case("conduc")
!Frontieres Nord et Sud : Ex = 0
do i=0,nx-1
tm%ex(i,0) = 0.
tm%ex(i,ny) = 0.
end do
!Frontieres Est et Ouest : Ey = 0
do j=0,ny-1
tm%ey(0,j) = 0.
tm%ey(nx,j) = 0.
end do
case ("entran")
!Frontieres Nord et Sud : Ex = 0
do i=0,nx-1
tm%ex(i,0) = 0.
tm%ex(i,ny) = 0.
end do
!Frontiere Ouest : Ey + Bz = donnees !!!onde entrant et non S-M
alpha = 2*mm*pi/dimx
omega = alpha
do j=0,ny-1
a11 = 1
a12 = -csq*dt/hx(0)
a21 = 1
a22 = c
b1 = tm%ey(0,j) - csq*dt/hx(0) * tm%bz(0,j) - dt * tm%jy(0,j)/e0
b2 = - tm%ey(0,j) - c*tm%bz(0,j) + 4*cos(omega*(time+0.5*dt))
dis = a11*a22-a21*a12
tm%ey(0,j) = (b1*a22-b2*a12) / dis
end do
!Frontiere Est : -Ey + Bz = 0
do j=0,ny-1
a11 = 1
a12 = csq*dt/hx(nx-1)
a21 = 1
a22 = -c
b1 = tm%ey(nx,j) + csq*dt/hx(nx-1) * tm%bz(nx-1,j) - dt * tm%jy(nx,j)/e0
b2 = - tm%ey(nx,j) + c*tm%bz(nx-1,j)
dis = a11*a22-a21*a12
tm%ey(nx,j) = (b1*a22-b2*a12) / dis
end do
case ("Eincom")
!Frontieres Nord et Sud : Ex = 0
do i=0,nx-1
tm%ex(i,0) = 0.
tm%ex(i,ny) = 0.
end do
!Frontiere Ouest : Ey + c Bz = 0
alpha = 2*mm*pi/dimx
do j=0,ny-1
a11 = 1
a12 = -csq*dt/hx(0)
a21 = 1
a22 = c
b1 = tm%ey(0,j) - csq*dt/hx(0) * tm%bz(0,j) - dt * tm%jy(0,j)/e0
b2 = - tm%ey(0,j) - c*tm%bz(0,j)
dis = a11*a22-a21*a12
tm%ey(0,j) = (b1*a22-b2*a12) / dis
end do
!Frontiere Est : -Ey + c Bz = donnee
do j=0,ny-1
a11 = 1
a12 = csq*dt/hx(nx-1)
a21 = 1
a22 = -c
b1 = tm%ey(nx,j) + csq*dt/hx(nx-1) * tm%bz(nx-1,j) - dt * tm%jy(nx,j)/e0
b2 = - tm%ey(nx,j) + c*tm%bz(nx-1,j) + 4*cos(alpha*(time+0.5*dt+dimx))
dis = a11*a22-a21*a12
tm%ey(nx,j) = (b1*a22-b2*a12) / dis
end do
case ("Sincom")
!Frontieres Est et Ouest : Ey = 0
do j=0,ny-1
tm%ey(0,j) = 0.
tm%ey(nx,j) = 0.
end do
!Frontiere Sud : -Ex + c Bz = donnee
alpha = 2*mm*pi/dimy
do i=0,nx-1
a11 = 1
a12 = csq*dt/hy(0)
a21 = 1
a22 = -c
b1 = tm%ex(i,0) + csq*dt/hy(0) * tm%bz(i,0) - dt * tm%jx(i,0)/e0
b2 = - tm%ex(i,0) + c*tm%bz(i,0) + 4*cos(alpha*(time+0.5*dt))
dis = a11*a22-a21*a12
tm%ex(i,0) = (b1*a22-b2*a12) / dis
end do
!Frontiere Nord : Ex + c Bz = 0
do i=0,nx-1
a11 = 1
a12 = -csq*dt/hy(ny-1)
a21 = 1
a22 = c
b1 = tm%ex(i,ny) - csq*dt/hy(ny-1) * tm%bz(i,ny-1) - dt * tm%jx(i,ny)/e0
b2 = - tm%ex(i,ny) - c*tm%bz(i,ny-1)
dis = a11*a22-a21*a12
tm%ex(i,ny) = (b1*a22-b2*a12) / dis
end do
case ("Nincom")
!Frontieres Est et Ouest : Ey = 0
do j=0,ny-1
tm%ey(0,j) = 0.
tm%ey(nx,j) = 0.
end do
!Frontiere Sud : -Ex + c Bz = 0
alpha = 2*mm*pi/dimy
do i=0,nx-1
a11 = 1
a12 = csq*dt/hy(0)
a21 = 1
a22 = -c
b1 = tm%ex(i,0) + csq*dt/hy(0) * tm%bz(i,0) - dt * tm%jx(i,0)/e0
b2 = - tm%ex(i,0) + c*tm%bz(i,0)
dis = a11*a22-a21*a12
tm%ex(i,0) = (b1*a22-b2*a12) / dis
end do
!Frontiere Nord : Ex + c Bz = donnee
do i=0,nx-1
a11 = 1
a12 = -csq*dt/hy(ny-1)
a21 = 1
a22 = c
b1 = tm%ex(i,ny) - csq*dt/hy(ny-1) * tm%bz(i,ny-1) - dt * tm%jx(i,ny)/e0
b2 = - tm%ex(i,ny) - c*tm%bz(i,ny-1) + 4*cos(alpha*(time+0.5*dt+dimy))
dis = a11*a22-a21*a12
tm%ex(i,ny) = (b1*a22-b2*a12) / dis
end do
case("faisce")
!Frontiere Sud : -Ex + c Bz = 0 Silver Muller
do i=0,nx-1
a11 = 1
a12 = csq*dt/hy(0)
a21 = 1
a22 = -c
b1 = tm%ex(i,0) + csq*dt/hy(0) * tm%bz(i,0) - dt * tm%jx(i,0)/e0
b2 = - tm%ex(i,0) + c*tm%bz(i,0)
dis = a11*a22-a21*a12
tm%ex(i,0) = (b1*a22-b2*a12) / dis
end do
!Frontiere Nord : Ex + c Bz = 0 Silver Muller
do i=0,nx-1
a11 = 1
a12 = -csq*dt/hy(ny-1)
a21 = 1
a22 = c
b1 = tm%ex(i,ny) - csq*dt/hy(ny-1) * tm%bz(i,ny-1) - dt * tm%jx(i,ny)/e0
b2 = - tm%ex(i,ny) - c*tm%bz(i,ny-1)
dis = a11*a22-a21*a12
tm%ex(i,ny) = (b1*a22-b2*a12) / dis
end do
!** Est et Ouest : conducteur parfait **
do j = 0, ny-1
tm%ey(nx,j) = 0.d0
tm%ey(0,j) = 0.d0
end do
end select
end subroutine conditions_limites
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine decalage( tm, tm1 )
type(mesh_fields) :: tm, tm1
!*** Calcul des composantes des champs
!*** sur les noeuds du maillage de rho
!*** par interpolation lineaire
do i=1,nx-1
do j=1,ny-1
tm1%ex(i,j) = ( hx(i)*tm%ex(i-1,j) + hx(i-1)*tm%ex(i,j) ) &
& / (hx(i)+hx(i-1))
tm1%ey(i,j) = ( hy(j)*tm%ey(i,j-1) + hy(j-1)*tm%ey(i,j) ) &
& / (hy(j)+hy(j-1))
tm1%bz(i,j) = ( ( hx(i)*tm%bz(i-1,j-1) + hx(i-1)*tm%bz(i,j-1) ) &
& * hy(j) + ( hx(i)*tm%bz(i-1,j) + hx(i-1)*tm%bz(i,j) ) &
& * hy(j-1) ) / ( (hx(i)+hx(i-1)) * (hy(j)+hy(j-1)) )
end do
end do
if (bcname == 'period') then
do i=1,nx-1 !Sud et Nord
tm1%ex(i,0) = ( hx(i)*tm%ex(i-1,0) + hx(i-1)*tm%ex(i,0) ) &
& / (hx(i)+hx(i-1))
tm1%ey(i,0) = ( hy(0)*tm%ey(i,ny-1) + hy(ny-1)*tm%ey(i,0) ) &
& / (hy(0)+hy(ny-1))
tm1%bz(i,0) = ( ( hx(i)*tm%bz(i-1,ny-1) + hx(i-1)*tm%bz(i,ny-1) ) &
& * hy(0) + ( hx(i)*tm%bz(i-1,0) + hx(i-1)*tm%bz(i,0) ) &
& * hy(ny-1) ) / ( (hx(i)+hx(i-1)) * (hy(0)+hy(ny-1)) )
tm1%ex(i,ny) = tm1%ex(i,0)
tm1%ey(i,ny) = tm1%ey(i,0)
tm1%bz(i,ny) = tm1%bz(i,0)
end do
do j=1,ny-1 !Ouest et Est
tm1%ex(0,j) = ( hx(0)*tm%ex(nx-1,j) + hx(nx-1)*tm%ex(0,j) ) &
& / (hx(0)+hx(nx-1))
tm1%ey(0,j) = ( hy(j)*tm%ey(0,j-1) + hy(j-1)*tm%ey(0,j) ) &
& / (hy(j)+hy(j-1))
tm1%bz(0,j) = ( ( hx(0)*tm%bz(nx-1,j-1) + hx(nx-1)*tm%bz(0,j-1) ) &
& * hy(j) + ( hx(0)*tm%bz(nx-1,j) + hx(nx-1)*tm%bz(0,j) ) &
& * hy(j-1) ) / ( (hx(0)+hx(nx-1)) * (hy(j)+hy(j-1)) )
tm1%ex(nx,j) = tm1%ex(0,j)
tm1%ey(nx,j) = tm1%ey(0,j)
tm1%bz(nx,j) = tm1%bz(0,j)
end do
!Coins
tm1%ex(0,0) = ( hx(0)*tm%ex(nx-1,0) + hx(nx-1)*tm%ex(0,0) ) &
& / (hx(0)+hx(nx-1))
tm1%ey(0,0) = ( hy(0)*tm%ey(0,ny-1) + hy(ny-1)*tm%ey(0,0) ) &
& / (hy(0)+hy(ny-1))
tm1%bz(0,0) = ( ( hx(0)*tm%bz(nx-1,ny-1) + hx(nx-1)*tm%bz(0,ny-1) ) &
& * hy(0) + ( hx(0)*tm%bz(nx-1,0) + hx(nx-1)*tm%bz(0,0) ) &
& * hy(ny-1) ) / ( (hx(0)+hx(nx-1)) * (hy(0)+hy(ny-1)) )
tm1%ex(nx,0) = tm1%ex(0,0)
tm1%ex(nx,ny) = tm1%ex(0,0)
tm1%ex(0,ny) = tm1%ex(0,0)
tm1%ey(nx,0) = tm1%ey(0,0)
tm1%ey(nx,ny) = tm1%ey(0,0)
tm1%ey(0,ny) = tm1%ey(0,0)
tm1%bz(nx,0) = tm1%bz(0,0)
tm1%bz(nx,ny) = tm1%bz(0,0)
tm1%bz(0,ny) = tm1%bz(0,0)
else
do i=1,nx-1
! Sud
tm1%ex(i,0) = ( hx(i)*tm%ex(i-1,0) + hx(i-1)*tm%ex(i,0) ) &
& / (hx(i)+hx(i-1))
tm1%ey(i,0) = ( -hy(0)*tm%ey(i,1) + (hy(1)+2*hy(0))*tm%ey(i,0) ) &
& / (hy(0)+hy(1))
tm1%bz(i,0) = ( ( -hy(0)*tm%bz(i-1,1) + (2*hy(0)+hy(1))*tm%bz(i-1,0) ) &
& * hx(i-1) + ( -hy(0)*tm%bz(i,1) + (2*hy(0)+hy(1))*tm%bz(i,0) ) &
& * hx(i) ) / ( (hx(i-1)+hx(i)) * (hy(0)+hy(1)) )
! Nord
tm1%ex(i,ny) = ( hx(i)*tm%ex(i-1,ny) + hx(i-1)*tm%ex(i,ny) ) &
& / (hx(i)+hx(i-1))
tm1%ey(i,ny) = ( -hy(ny-1)*tm%ey(i,ny-2) + (hy(ny-2)+2*hy(ny-1)) &
& *tm%ey(i,ny-1) ) / (hy(ny-1)+hy(ny-2))
tm1%bz(i,ny) = ( ( -hy(ny-1)*tm%bz(i-1,ny-2) + (2*hy(ny-1)+hy(ny-2)) &
& *tm%bz(i-1,ny-1) ) * hx(i-1) + ( -hy(ny-1)*tm%bz(i,ny-2) &
& + (2*hy(ny-1)+hy(ny-2))*tm%bz(i,ny-1) ) * hx(i) ) &
& / ( (hx(i-1)+hx(i)) * (hy(ny-1)+hy(ny-2)) )
end do
do j=1,ny-1
! Ouest
tm1%ex(0,j) = ( -hx(0)*tm%ex(1,j) + (2*hx(0)+hx(1))*tm%ex(0,j) ) &
& / (hx(0)+hx(1))
tm1%ey(0,j) = ( hy(j)*tm%ey(0,j-1) + hy(j-1)*tm%ey(0,j) ) &
& / (hy(j)+hy(j-1))
tm1%bz(0,j) = ( ( -hx(0)*tm%bz(1,j-1) + (2*hx(0)+hx(1))*tm%bz(0,j-1) ) &
& * hy(j) + ( -hx(0)*tm%bz(1,j) + (2*hx(0)+hx(1))*tm%bz(0,j) ) &
& * hy(j-1) ) / ( (hx(0)+hx(1)) * (hy(j)+hy(j-1)) )
! Est
tm1%ex(nx,j) = ( -hx(nx-1)*tm%ex(nx-2,j) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%ex(nx-1,j) ) / (hx(nx-1)+hx(nx-2))
tm1%ey(nx,j) = ( hy(j)*tm%ey(nx,j-1) + hy(j-1)*tm%ey(nx,j) ) &
& / (hy(j)+hy(j-1))
tm1%bz(nx,j) = ( ( -hx(nx-1)*tm%bz(nx-2,j-1) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%bz(nx-1,j-1) ) * hy(j) + ( -hx(nx-1)*tm%bz(nx-2,j) &
& + (2*hx(nx-1)+hx(nx-2))*tm%bz(nx-1,j) ) * hy(j-1) ) &
& / ( (hx(nx-1)+hx(nx-2)) * (hy(j)+hy(j-1)) )
end do
! Coin SW
tm1%ex(0,0) = ( -hx(0)*tm%ex(1,0) + (2*hx(0)+hx(1))*tm%ex(0,0) ) &
& / (hx(0)+hx(1))
tm1%ey(0,0) = ( -hy(0)*tm%ey(0,1) + (hy(1)+2*hy(0))*tm%ey(0,0) ) &
& / (hy(0)+hy(1))
tm1%bz(0,0) = ( ( -hx(0)*tm%bz(1,0) + (2*hx(0)+hx(1))*tm%bz(0,0) ) &
& * (2*hy(0)+hy(1)) + ( -hx(0)*tm%bz(1,1) + (2*hx(0)+hx(1)) &
& *tm%bz(0,1) ) * (-hy(0)) ) / ( (hx(0)+hx(1)) * (hy(0)+hy(1)) )
! Coin NW
tm1%ex(0,ny) = ( -hx(0)*tm%ex(1,ny) + (2*hx(0)+hx(1))*tm%ex(0,ny) ) &
& / (hx(0)+hx(1))
tm1%ey(0,ny) = ( -hy(ny-1)*tm%ey(0,ny-2) + (hy(ny-2)+2*hy(ny-1)) &
& *tm%ey(0,ny-1) ) / (hy(ny-1)+hy(ny-2))
tm1%bz(0,ny) = ( ( -hx(0)*tm%bz(1,ny-1) + (2*hx(0)+hx(1))*tm%bz(0,ny-1) ) &
& * (2*hy(ny-1)+hy(ny-2)) + ( -hx(0)*tm%bz(1,ny-2) &
& + (2*hx(0)+hx(1)) *tm%bz(0,ny-2) ) * (-hy(ny-1)) ) &
& / ( (hx(0)+hx(1)) * (hy(ny-1)+hy(ny-2)) )
! Coin SE
tm1%ex(nx,0) = ( -hx(nx-1)*tm%ex(nx-2,0) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%ex(nx-1,0) ) / (hx(nx-1)+hx(nx-2))
tm1%ey(nx,0) = ( -hy(0)*tm%ey(nx,1) + (hy(1)+2*hy(0))*tm%ey(nx,0) ) &
& / (hy(0)+hy(1))
tm1%bz(nx,0) = ( ( -hx(nx-1)*tm%bz(nx-2,0) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%bz(nx-1,0) ) * (2*hy(0)+hy(1)) + ( -hx(nx-1)*tm%bz(nx-2,1) &
& + (2*hx(nx-1)+hx(nx-2)) *tm%bz(nx-1,1) ) * (-hy(0)) ) &
& / ( (hx(nx-1)+hx(nx-2)) * (hy(0)+hy(1)) )
! Coin NE
tm1%ex(nx,ny) = ( -hx(nx-1)*tm%ex(nx-2,ny) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%ex(nx-1,ny) ) / (hx(nx-1)+hx(nx-2))
tm1%ey(nx,ny) = ( -hy(ny-1)*tm%ey(nx,ny-2) + (hy(ny-2)+2*hy(ny-1)) &
& *tm%ey(nx,ny-1) ) / (hy(ny-1)+hy(ny-2))
tm1%bz(nx,0) = ( ( -hx(nx-1)*tm%bz(nx-2,ny-1) + (2*hx(nx-1)+hx(nx-2)) &
& *tm%bz(nx-1,ny-1) ) * (2*hy(ny-1)+hy(ny-2)) &
& + ( -hx(nx-1)*tm%bz(nx-2,ny-2) &
& + (2*hx(nx-1)+hx(nx-2)) *tm%bz(nx-1,ny-2) ) * (-hy(ny-1)) ) &
& / ( (hx(nx-1)+hx(nx-2)) * (hy(ny-1)+hy(ny-2)) )
end if
end subroutine decalage
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
end module Maxwell