# Coeff 11.f90 - calculate the coefficients

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
```
```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
```

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

!-------------------------------- HLPA SCHEME---------------------------- ! go to 600

! 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