# Diffusion Problems code in Fortran

! 0<=x<=1, 0<=y<=1

! with boundary conditions phi=xy

!* implicit none integer, parameter :: nx=25, ny=25 integer :: i,j,iterations real :: x,y,z,dx,dy,omega real, dimension(1:nx,1:ny) :: AE,AW,AN,AS,AP,SP,SU real, dimension(0:nx+1,0:ny+1) :: phi !*
dx=1./float(nx); dy=1./float(ny)

! initialize SU and SP to interior cell values of zero
SU=0; SP=0
phi=0.0

! initialize AE,AW,AN,AS,AP over all cells to
! the values over the interior cells
AE=1.; AW=1.; AN=1.; AS=1.
!
! set wall boundary values (overwrite initialization values)
! west boundary
SU(1,:)=0.
SP(1,:)=-2.

! east boundary
SP(NX,:)=-2.
do j=1,NY
SU(NX,j)=2.( (dy/2.) + dyfloat(j-1) )
end do

! south boundary
SU(:,1)=0.
SP(:,1)=-2.

! north boundary
SP(:,NY)=-2.
do i=1,NX
SU(i,NY)=2.( (dx/2.) + dxfloat(i-1) )
end do

! corner cell boundary values(overwrite values from boundaries above)
! southwest
AW(1,1)=0.
SU(1,1)=0.
SP(1,1)=-4.
! northwest
AW(1,ny)=0.
SU(1,ny)=2.(dx/2.) SP(1,ny)=-4. ! southeast AS(nx,1)=0. !cut links AE(nx,1)=0. SU(nx,1)=2.(dy/2.)
SP(nx,1)=-4.
! northeast
AE(nx,ny)=0.
SU(nx,ny)=2.((dx/2.) + dxfloat(nx-1)) + 2.((dy/2.) + dyfloat(ny-1))
SP(nx,ny)=-4.

AP=AE+AW+AN+AS-SP

!
! ITERATIVE SOLVER
omega=1.7
do iterations=1,500 !fix number of iterations at 500
do i=1,nx
do j=1,ny
phi(i,j)=phi(i,j) + omega/AP(i,j)(AE(i,j)phi(i+1,j)+AW(i,j)phi(i-1,j)+ & AN(i,j)phi(i,j+1)+AS(i,j)phi(i,j-1)+ & SU(i,j)-AP(i,j)phi(i,j))
end do
end do
end do
!
! comma separated DATA FILE FOR PARAVIEW
open(unit=10,file=’results.csv’)
write(10,)’x coord, y coord, z coord, phi’ do i=1,nx do j=1,ny x=dx/2+float(i-1)dx
y=dy/2+float(j-1)dy z=0. write(10,)x,’,’,y,’,’,z,’,’,phi(i,j)
end do; end do

! west boundary values
do j=1,ny
y=dy/2+float(j-1)dy write(10,)0.0,’,’,y,’,’,0.0,’,’,0.0
end do;
! east boundary values
do j=1,ny
y=dy/2+float(j-1)dy write(10,)1.0,’,’,y,’,’,0.0,’,’,y
end do;
! south boundary values
do i=1,nx
x=dx/2+float(i-1)dx write(10,)x,’,’,0.0,’,’,0.0,’,’,0.0
end do;
! north boundary values
do i=1,nx
x=dx/2+float(i-1)dx write(10,)x,’,’,1.0,’,’,0.0,’,’,x
end do;
! corners
write(10,)0.0,’,’,0.0,’,’,0.0,’,’,0.0 !southwest write(10,)0.0,’,’,1.0,’,’,0.0,’,’,0.0 !northwest
write(10,)1.0,’,’,0.0,’,’,0.0,’,’,0.0 !southeast write(10,)1.0,’,’,1.0,’,’,0.0,’,’,1.0 !northeast

end