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ohm.f90
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subroutine ohm
!****************************************************************!
! COMPUTE: generalized Ohm's law !
! [2D version, no electron-inertia terms] !
! -------------------------------------------------------------- !
! original version: F. Califano, 2006 !
! MPI parallel version: M. Faganello/F. Valentini, 2008 !
! Anisotropic/FLR-MHD version: S. S. Cerri, 2011 !
!****************************************************************!
use parameter_mod
use box_mod
use deriv_mod
use fields_UJ_mod
use fields_DP_mod
use fields_EB_mod
use dom_distr_mod
IMPLICIT NONE
integer :: ix, iy, iz
REAL(dp),ALLOCATABLE :: zy(:), zx(:), zz(:)
REAL(dp),ALLOCATABLE :: AA(:,:,:), AB(:,:,:)
REAL(dp),ALLOCATABLE :: At(:,:,:)
REAL(dp),ALLOCATABLE :: bbx(:,:,:), bby(:,:,:), bbz(:,:,:)
REAL(dp),ALLOCATABLE :: Pdiag(:,:,:), Pmix(:,:,:)
!*******************************************!
! Computing: E = - u_s x B + eta*J !
! !
! [ ideal-MHD/or/Hall-MHD + resistivity ] !
!*******************************************!
if (hall_on .eq. 1) then
!case: Hall-MHD + resistivity
! E = - u_e x B + eta*J
Ex = Uez * By - Uey * Bz + eta*Jx
Ey = Uex * Bz - Uez * Bx + eta*Jy
Ez = Uey * Bx - Uex * By + eta*Jz
else
!case: ideal-MHD + resistivity
! E = - u_i x B + eta*J
Ex = Uz * By - Uy * Bz + eta*Jx !Ux = Uix when m_e = 0
Ey = Ux * Bz - Uz * Bx + eta*Jy !Uy = Uiy when m_e = 0
Ez = Uy * Bx - Ux * By + eta*Jz !Uz = Uiz when m_e = 0
endif
allocate(AA(nxl, ny, nz))
if (divPe_on .eq. 1) then
!***********************************************!
! Computing: - div(Pe)/n contribution !
! !
! [ Pe = pe_perp*I + (pe_para - pe_perp)*bb ] !
!***********************************************!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! !!!
!!! [ NOTICE: 3D version not yet released ] !!!
!!! !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
allocate(zy(ny))
allocate(zx(nx))
allocate(zz(nz))
allocate(AB(nxl, ny, nz))
allocate(At(nx, nyt, nz))
allocate(bbx(nxl, ny, nz))
allocate(bby(nxl, ny, nz))
allocate(bbz(nxl, ny, nz))
allocate(Pdiag(nxl, ny, nz))
allocate(Pmix(nxl, ny, nz))
!define useful quantities
AA = dsqrt( Bx**2 + By**2 + Bz**2 )
AA = 1.0d0 / AA
bbx = Bx * AA
bby = By * AA
bbz = Bz * AA
! further finite-m_e contributions:
! not available in this release
Pdiag = pe_perp ! + ...
Pmix = pe_para - pe_perp ! + ...
!-------------------------------------------!
! x-component: !
! !
! - {div[Pe]}_x = - d[Pe_xx]/dx !
! - d[Pe_yx]/dy !
! - d[Pe_zx]/dz !
! !
! (derivatives w.r.t z only in 3D version) !
!-------------------------------------------!
AA = Pdiag + Pmix*bbx*bbx
call traspdist( AA, At, 1 )
do iz = 1, nz
do iy = 1, nyt
call derx_1(At(:,iy,iz), zx)
At(:,iy,iz) = -zx
enddo
enddo
call traspdist( AB, At, -1 )
AA = Pmix*bbx*bby
do iz = 1, nz
do ix = 1, nxl
call dery_1(AA(ix,:,iz), zy)
AB(ix,:,iz) = AB(ix,:,iz) - zy
enddo
enddo
Ex = Ex + Dinv * AB
!-------------------------------------------!
! y-component: !
! !
! - {div[Pe]}_y = - d[Pe_xy]/dx !
! - d[Pe_yy]/dy !
! - d[Pe_zy]/dz !
! !
! (derivatives w.r.t z only in 3D version) !
!-------------------------------------------!
! AA = Pmix*bby*bbx -> same as above
call traspdist( AA, At, 1 )
do iz = 1, nz
do iy = 1, nyt
call derx_1(At(:,iy,iz), zx)
At(:,iy,iz) = -zx
enddo
enddo
call traspdist( AB, At, -1 )
AA = Pdiag + Pmix*bby*bby
do iz = 1, nz
do ix = 1, nxl
call dery_1(AA(ix,:,iz), zy)
AB(ix,:,iz) = AB(ix,:,iz) - zy
enddo
enddo
Ey = Ey + Dinv * AB
!-------------------------------------------!
! z-component: !
! !
! - {div[Pe]}_x = - d[Pe_xz]/dx !
! - d[Pe_yz]/dy !
! - d[Pe_zz]/dz !
! !
! (derivatives w.r.t z only in 3D version) !
!-------------------------------------------!
AA = Pmix*bbx*bbz
call traspdist( AA, At, 1 )
do iz = 1, nz
do iy = 1, nyt
call derx_1(At(:,iy,iz), zx)
At(:,iy,iz) = -zx
enddo
enddo
call traspdist( AB, At, -1 )
AA = Pmix*bby*bbz
do iz = 1, nz
do ix = 1, nxl
call dery_1(AA(ix,:,iz), zy)
AB(ix,:,iz) = AB(ix,:,iz) - zy
enddo
enddo
Ez = Ez + Dinv * AB
deallocate(bbx)
deallocate(bby)
deallocate(bbz)
deallocate(Pdiag)
deallocate(Pmix)
deallocate(AB)
deallocate(At)
deallocate(zy)
deallocate(zx)
deallocate(zz)
endif
if ( (hall_on .eq. 1) .or. (divPe_on .eq. 1)) then
!---------------------------------------------!
! smoothing -> ideal MHD at the x-boundaries !
!---------------------------------------------!
AA = Uz * By - Uy * Bz
do ix = 1, nxl
Ex(ix,:,:) = lambda(ixlg + ix - 1) * Ex(ix,:,:) + &
( 1.0d0 - lambda(ixlg + ix - 1) ) * AA(ix,:,:)
enddo
AA = Ux * Bz - Uz * Bx
do ix = 1, nxl
Ey(ix,:,:) = lambda(ixlg + ix - 1) * Ey(ix,:,:) + &
( 1.0d0 - lambda(ixlg + ix - 1) ) * AA(ix,:,:)
enddo
AA = Uy * Bx - Ux * By
do ix = 1, nxl
Ez(ix,:,:) = lambda(ixlg + ix - 1) * Ez(ix,:,:) + &
( 1.0d0 - lambda(ixlg + ix - 1) ) * AA(ix,:,:)
enddo
endif
deallocate(AA)
end subroutine