# Solve Pressure Correction.f90 - Solution of pressure-correction equation and correction of U,V and P

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!Sample program for solving Lid-driven cavity flow test using SIMPLE-algorithm
! solution of pressure-correction quation and correction U,V, and P
!Copyright (C) 2016  Michail Kiričkov, Kaunas University for Technology

!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 Solve_Pressure_Correction
include 'icomm_1.f90'
integer test
DpU(2:NXmax,2:NYmax) = 1./Ap(2:NXmax,2:NYmax,1)
DpV(2:NXmax,2:NYmax) = 1./Ap(2:NXmax,2:NYmax,2)
!This is 1./AP coefficient involved in the derivation of the pressure equation
!and correction velocities. Check for simple algorithm in dedicated books.
!AP is the central coefficent there is one for U momentum equation
!    --> APU and one for V-momentum APV.
! in fact for this code APU(i,j) = AP(i,j,1)
! APV(i,j) = AP(i,j,2)
! because he works with vector componnents style
!*****************************************************************************
! vertical  faces East - e
Do 101 I=1,NXmax
Do 101 J=1,NYmax-1
DXc_e = 0.
S_e   = 0.
VOL_e = 0.
APU_e = 0.
Ul_e  = 0.
DPl_e = 0.
DPx_e = 0.
U_e   = 0.
If(i.ne.NXmax)then
!this is the distance between node P and node E
DXc_e = Xc(i+1,j+1) - Xc(i,j+1)
!This is the east surface S_e
S_e   =  Y(i  ,j+1) -  Y(i,j  )
VOL_e = DXc_e * S_e
!-------------------------------------------------------------
!this is the iterpolation of 1/APU at east location
APU_e =       0.5 * (   DpU(i,j+1)   +   DpU(i+1,j+1)   )
!this is the interpolation of velocity U on east location
Ul_e  =       0.5 * (     F(i,j+1,1) +     F(i+1,j+1,1) )
! the same for interpolation of DPx
DPl_e =       0.5 * ( DPx_c(i,j+1)   + DPx_c(i+1,j+1)   )
! this is the gradient of pressure at east location usint central difference
DPx_e =             ( F(i+1,j+1,4) - F(i,j+1,4) ) / DXc_e
! This is the interpolated velocity using at east location
!         using the interpolation of Rhie and Chow
U_e   = Ul_e  + APU_e * VOL_e * ( DPl_e - DPx_e)
!--------------------------------------------------------------
Con_we(i,j) =   U_e  * S_e ! this is the convective flux.
End If
Con_we(1,j) = 0.
Con_we(NXmax,j) = 0.
101 continue
!********************************************************************
! horisontal  faces
Do 102 I=1,NXmax-1
Do 102 J=1,NYmax
DYc_n = 0.
S_n   = 0.
VOL_n = 0.
APV_n = 0.
Vl_n  = 0.
DPl_n = 0.
DPy_n = 0.
V_n   = 0.
If((j.ne.NYmax))then
DYc_n = Yc(i+1,j+1) - Yc(i+1,j)
S_n   =  X(i+1,j  ) -  X(i  ,j)
VOL_n = DYc_n * S_n
!-----------------------------------------------------------
APV_n =       0.5 * (   DpV(i+1,j)   +   DpV(i+1,j+1)   )
Vl_n  =       0.5 * (     F(i+1,j,2) +     F(i+1,j+1,2) )
DPl_n =       0.5 * ( DPy_c(i+1,j)   + DPy_c(i+1,j+1)   )
DPy_n = ( F(i+1,j+1,4) - F(i+1,j,4) ) / DYc_n
V_n   = Vl_n  + APV_n * VOL_n * ( DPl_n - DPy_n )
!-----------------------------------------------------------
Con_ns(i,j) =   V_n  * S_n
End If
Con_ns(i,1) = 0.
Con_ns(i,NYmax) = 0.
102 continue
Summ = 0.
Do 200 I=2,NXmax
Do 200 J=2,NYmax
S_e   =  Y(i  ,j) -  Y(i,j-1)
S_n   =  X(i  ,j) -    X(i-1,j)
An(i,j) = 0.5 * (   DpV(i,j)   +   DpV(i,j+1)   )  * S_n * S_n
As(i,j) = 0.5 * (   DpV(i,j)   +   DpV(i,j-1)   )  * S_n * S_n
Ae(i,j) = 0.5 * (   DpU(i,j)   +   DpU(i+1,j)   )  * S_e * S_e
Aw(i,j) = 0.5 * (   DpU(i,j)   +   DpU(i-1,j)   )  * S_e * S_e
Ap(i,j,3) = (An(i,j) + As(i,j) + Ae(i,j) +	Aw(i,j))
Sp(i,j,3) = -1. * ( Con_ns(i-1,j) - Con_ns(i-1,j-1) &
+ Con_we(i,j-1) - Con_we(i-1,j-1) )
Summ = Summ + Sp(i,j,3) !
200 continue
write(*,*)'Sum',summ
write(*,*)'solve PP'
niter = 0
20 continue
call Convergence_Criteria(3,Res_sum_before,niter)
niter= niter + 1
Call TDMA_1(3)
call Convergence_Criteria(3,Res_sum_After,niter)

if((abs(Res_sum_before-Res_sum_After).Ge.1.0E-10) &
.and.(niter.le.1500).and.(abs(Res_sum_After).ge.1.0E-06))go to 20
write(*,*)'Pressure correction Res_sum_before-Res_sum_After' &
,Res_sum_before-Res_sum_After,niter
!  pressure correction
Do 301 I=2,NXmax
Do 301 J=2,NYmax
F(i,j,4) = F(i,j,4) + 0.2 *   F(i,j,3)
301 continue
!  velocities and pressure correction
Do 302 I=2,NXmax
Do 302 J=2,NYmax
DY = Y(i,j)-Y(i,j-1)
DX = X(i,j)-X(i-1,j)
PPe = 0.5 * ( F(i,j,3) + F(i+1,j,3) )
PPw = 0.5 * ( F(i,j,3) + F(i-1,j,3) )
PPn = 0.5 * ( F(i,j,3) + F(i,j+1,3) )
PPs = 0.5 * ( F(i,j,3) + F(i,j-1,3) )
F(i,j,1) = F(i,j,1) + (PPw - PPe)  * DpU(i,j)  * Dy
F(i,j,2) = F(i,j,2) + (PPs - PPn)  * DpV(i,j)  * Dx
302 continue
!**********************************************************************
Do 501 I=1,NXmaxC
F(i,1,4) = F(i,2,4)            !
F(i,NYmaxC,4) = F(i,NYmaxC-1,4)!
501 continue

Do 502 J=1,NYmaxC
F(1,j,4) = F(2,j,4)             !
F(NXmaxC,j,4) = F(NXmaxC-1,j,4) !
502 continue
F(:,:,4) = F(:,:,4) - F(3,4,4)
999 continue

Return
End

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