[RajaHannan]

Hello.I am currently doing research on Lid Driven Cavity problem...My teacher has provided me with this code that solves NS equation and uses Artificial compressibilty Method for pressure calculation. The section that computes pressure is given below...

For 81x81 grid: nx=81 and ny=81

intially: p(1:nx,1:ny)=0.5;
p1 = p;
for i=2:nx-1
for j=2:ny-1
p(i,j)= p1(i,j) - dt*b*(0.5/dx*(u(i+1,j)-u(i-1,j))+0.5/dy*(v(i,j+1)-v(i,j-1)));
end
end

p(1,:) = p(2,:);
p(nx,:) = p(nx-1,:);
p(:,1) = p(:,2);
p(:,ny) = p(:,ny-1);

Why do we have to put pressure of the boundary nodes and the penultimate nodes equal to each other for a Lid Driven Cavity problem?