# Coeff 11.f90 - calculate the coefficients

```
!Sample program for solving Smith-Hutton Test using different schemes
!of covective terms approximation - Coefficients computing modul

!This program is free software; you can redistribute it and/or
!modify it under the terms of the GNU General Public License

!This program is distributed in the hope that it will be useful,
!but WITHOUT ANY WARRANTY; without even the implied warranty of
!MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!GNU General Public License for more details.

!You should have received a copy of the GNU General Public License
!along with this program; if not, write to the Free Software
!Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

!*********************************************************************
Subroutine Coef_1(nf)
include 'icomm_1.f90'

Dimension F_out(nx,ny),CheckFlux(nx,ny)
Character  Filename*10

!  calculation of fluxes
!  all geometry has rectangular 2D notation

Do 100 I= 2,NXmax
Do 100 J= 2,NYmax

Gam_e = ( Gam(i+1,j  ) + Gam(i  ,j  ) ) * 0.5
Gam_w = ( Gam(i-1,j  ) + Gam(i  ,j  ) ) * 0.5
Gam_s = ( Gam(i  ,j-1) + Gam(i  ,j  ) ) * 0.5
Gam_n = ( Gam(i  ,j+1) + Gam(i  ,j  ) ) * 0.5

Ro_e = ( Ro(i+1,j  ) + Ro(i  ,j  ) ) * 0.5
Ro_w = ( Ro(i-1,j  ) + Ro(i  ,j  ) ) * 0.5
Ro_s = ( Ro(i  ,j-1) + Ro(i  ,j  ) ) * 0.5
Ro_n = ( Ro(i  ,j+1) + Ro(i  ,j  ) ) * 0.5

Area_w = Y_xi(i-1,j-1)
Area_e = Y_xi(i  ,j-1)
Area_s = X_et(i-1,j-1)
Area_n = X_et(i-1,j  )

Del_e  = Del_X_et(i  ,j  )
Del_w  = Del_X_et(i-1,j  )
Del_n  = Del_Y_xi(i  ,j  )
Del_s  = Del_Y_xi(i  ,j-1)

! upwind differencing (all other will be included into the source term)

Con_e = Area_e *  ( F(i,j,1) + F(i+1,j  ,1) ) * 0.5
Con_w = Area_w *  ( F(i,j,1) + F(i-1,j  ,1) ) * 0.5
Con_s = Area_s *  ( F(i,j,2) + F(i  ,j-1,2) ) * 0.5
Con_n = Area_n *  ( F(i,j,2) + F(i  ,j+1,2) ) * 0.5

Diff_e = Area_e * Gam_e / Del_e
Diff_w = Area_w * Gam_w / Del_w
Diff_s = Area_s * Gam_s / Del_s
Diff_n = Area_n * Gam_n / Del_n

Flux_e = Area_e * Con_e * Ro_e
Flux_w = Area_w * Con_w * Ro_w
Flux_s = Area_s * Con_s * Ro_s
Flux_n = Area_n * Con_n * Ro_n

Aw(i,j) = Diff_w + max(     Con_w,0.)
Ae(i,j) = Diff_e + max(-1.* Con_e,0.)
As(i,j) = Diff_s + max(     Con_s,0.)
An(i,j) = Diff_n + max(-1.* Con_n,0.)

CheckFlux(i,j) =  Flux_e - Flux_w + Flux_s - Flux_n

Ap(i,j)= Aw(i,j) + Ae(i,j) + An(i,j) + As(i,j) + CheckFlux(i,j)

Sp(i,j)= 0.

!--------------------------------QUICK SCHEME-------------------------

go to 700 (now QUICK is "off")

if( (i.GT.2).AND.(i.LT.NXmax).and.(j.GT.4).AND.(j.LT.NYmax) ) then

if(Con_e.GT.0.)  Sp(i,j) = Sp(i,j) + Con_e * (-1.) * (-0.125 * F(i-1,j  ,nf) - 0.25 * F(i  ,j  ,nf) + 0.375 * F(i-1,j  ,nf) )

if(Con_w.GT.0.)  Sp(i,j) = Sp(i,j) + Con_w * (-1.) * (-0.125 * F(i-2,j  ,nf) - 0.25 * F(i-1,j  ,nf) + 0.375 * F(i-2,j  ,nf) )

if(Con_n.GT.0.)  Sp(i,j) = Sp(i,j) + Con_n * (-1.) * (-0.125 * F(i  ,j-1,nf) - 0.25 * F(i  ,j  ,nf) + 0.375 * F(i  ,j-1,nf) )

if(Con_s.GT.0.)  Sp(i,j) = Sp(i,j) + Con_s * (-1.) * (-0.125 * F(i  ,j-2,nf) - 0.25 * F(i  ,j-1,nf) + 0.375 * F(i  ,j-2,nf) )

if(Con_e.LT.0.)  Sp(i,j) = Sp(i,j) + Con_e * (-1.) * ( 0.375 * F(i  ,j  ,nf) - 0.25 * F(i+1,j  ,nf) - 0.125 * F(i+2,j  ,nf) )

if(Con_w.LT.0.)  Sp(i,j) = Sp(i,j) + Con_w * (-1.) * ( 0.375 * F(i-1,j  ,nf) - 0.25 * F(i  ,j  ,nf) - 0.125 * F(i+1,j  ,nf) )

if(Con_n.LT.0.)  Sp(i,j) = Sp(i,j) + Con_n * (-1.) * ( 0.375 * F(i  ,j  ,nf) - 0.25 * F(i  ,j+1,nf) - 0.125 * F(i  ,j+2,nf) )

! if(Con_s.LT.0.)  Sp(i,j) = Sp(i,j) + Con_s * (-1.) * ( 0.375 * F(i  ,j-1,nf) - 0.25 * F(i  ,j+0,nf) - 0.125 * F(i  ,j+1,nf) )

end if

700 continue

!-------------------------------- HLPA SCHEME----------------------------
go to 600 (now HLPA is "off")

! Subroutine HLPA(Uw,Fww,Fw,Fp,Fe,Delta_f)

if( (i.GT.2).AND.(i.LT.NXmax-0).and.(j.GT.2).AND.(j.LT.NYmax-0) ) then

!------------------ w face -------------------
Fww = F(i-2,j,nf)
Fw  = F(i-1,j,nf)
Fp  = F(i  ,j,nf)
Fe  = F(i+1,j,nf)

call  HLPA(Con_w,Fww,Fw,Fp,Fe,Delta_f)

Sp(i,j) = Sp(i,j) + Con_w * Delta_f

!------------------ e face--------------------

Fww = F(i-1,j,nf)
Fw  = F(i  ,j,nf)
Fp  = F(i+1,j,nf)
Fe  = F(i+2,j,nf)

call  HLPA(Con_e,Fww,Fw,Fp,Fe,Delta_f)

Sp(i,j) = Sp(i,j) + Con_e * Delta_f * (-1.)

!------------------ s face--------------------
Fww = F(i  ,j-2,nf)
Fw  = F(i  ,j-1,nf)
Fp  = F(i  ,j  ,nf)
Fe  = F(i  ,j+1,nf)

call  HLPA(Con_s,Fww,Fw,Fp,Fe,Delta_f)

Sp(i,j) = Sp(i,j) + Con_s * Delta_f

!------------------ n face--------------------

Fww = F(i  ,j-1,nf)
Fw  = F(i  ,j  ,nf)
Fp  = F(i  ,j+1,nf)
Fe  = F(i  ,j+2,nf)

call  HLPA(Con_n,Fww,Fw,Fp,Fe,Delta_f)

Sp(i,j) = Sp(i,j) + Con_n * Delta_f *(-1.)

end if

600 continue

!-------------------------------- HLPA SCHEME----------------------------

!------------------------------------------------------------------------

100 continue

!----------------------------------------------------------------
NImax = NXmaxp
NJmax = NYmaxp

F_out     = CheckFlux

Filename  ='0_Flx.txt'

Call  Out_array(F_out,NImax,NJmax,Filename)

!-------------------------------------------------------------------

Return
End

```