[rayan-dc]

Dear all,

I am trying to implement the SIMPLE method for steady state incompressible flow in lid-driven cavity using by Matlab. i solve the problem with methode of patankars book .
but i have a problem in solving pressure corection equations. the unknown just Pprim . the other variables is known. please any one can help me to solve this equations . Pprim is n*m matrix which n & m input by user

PHP Code:

for i=3:2:m-3
    for j=3:2:n-3
    ((dX(2,3))+(dY(3,2)))*Pprim(2,2)=((dX(2,3)*Pprim(2,4))+(dY(3,2)*Pprim(4,2))+(-us(2,3))+(-vs(3,2)))%left down
    ((dX(n-1,3))+(dY(n-2,2)))*Pprim(n-1,2)=dX(n-1,3)*Pprim(n-1,4))+(dY(n-2,2)*Pprim(n-3,2))+(-us(n-1,3))+(vs(n-2,2)-uinf))%left up
    ((dX(2,m-2))+(dY(3,m-1)))*Pprim(2,m-1)=(dX(2,m-2)*Pprim(2,m-3))+(dY(3,m-1)*Pprim(4,m-1))+((us(2,m-2)))+(-(vs(3,m-1)))%right down
    (dX(n-1,m-2))+(dY(n-2,m-1)))*Pprim(n-1,m-1)=(dX(n-1,m-2)*Pprim(n-1,m-3))+(dY(n-2,m-1)*Pprim(n-3,m-1))+((us(n-1,m-2)))+(vs(n-2,m-1)))%right up
    (((dX(2,j+2)+dX(2,j)))+(dY(3,j+1)))*Pprim(2,j+1)=dX(2,j+2)*Pprim(2,j+3))+(dX(2,j)*Pprim(2,j-1))+(dY(3,j+1)*Pprim(4,j+1))+((us(2,j)-us(2,j+2)))+(-(vs(3,j+1)))%down
    ((dX(n-1,j+2)+dX(n-1,j))+(dY(n-2,j+1)))*Pprim(n-1,j+1)=dX(n-1,j+2)*Pprim(n-1,j+3))+(dX(n-1,j)*Pprim(n-1,j-1))+(dY(n-2,j+1)*Pprim(n-3,j+1))+((us(n-1,j)-us(n-1,j+2)))+(vs(n-2,j+1))%up
    ((dX(i+1,3))+(dY(i+2,2)+dY(i,2)))*Pprim(i+1,2)=dX(i+1,3)*Pprim(i+1,4))+(dY(i+2,2)*Pprim(i+3,2))+(dY(i,2)*Pprim(i-1,2))+(-us(i+1,3)))+(vs(i,2)-(vs(i+2,2)))%left
    ((dX(i+1,m-2))+(dY(i+2,m-1)+dY(i,m-1)))*Pprim(i+1,m-1)=(dX(i+1,m-2)*Pprim(i+1,m-3))+(dY(i+2,m-1)*Pprim(i+3,m-1))+(dY(i,m-1)*Pprim(i-1,m-1))+((us(i+1,m-2)))+(vs(i,m-1)-(vs(i+2,m-1)))%right
    ((dX(i+1,j+2)+dX(i+1,j))+(dY(i+2,j+1)+dY(i,j+1)))*Pprim(i+1,j+1)=dX(i+1,j+2)*Pprim(i+1,j+3))+(dX(i+1,j)*Pprim(i+1,j-1))+(dY(i+2,j+1)*Pprim(i+3,j+1))+(dY(i,j+1)*Pprim(i-1,j+1))+((us(i+1,j)-us(i+1,j+2)))+(vs(i,j+1)-(vs(i+2,j+1)))% inside control volume
         end
end