SIMPLE Algorithm for 2D Lid Driven Cavity Flow

Hello Everyone,

I am an aerospace engineering student taking a CFD course at my university. We briefly covered the SIMPLE algorithm and I would like to code it in MATLAB. I have been trying to follow the steps in the method 1. staggered grid 2. guess pressure, velocity field 3. solve momentum equations 4. solve for the pressure correction 5. solve for the velocity correction 6. update the pressure and velocity field with an under relaxation factor for convergence 7. repeat until solution converges

I have attempted coding this algorithm for while and can't seem to get it right.

I am asking for help with my code. I use three matrices to account for the staggered grid, and try to solve the momentum and continuity equation with a jacobi iteration technique. I cannot figure out why my code won't converge. I have attached two attempts of my code one uses strictly central differencing and the other (Untitled) uses alpha/beta_plus/minus factors to uses central or first order upwind.

I would really appreciate it if someone could take a look at my code and try to help me, or any advice regarding coding SIMPLE will be greatly appreciated. Thank you.

[ce lee]

Hi there, I would like to ask a questino regarding on the code if you don't mind. In the coding, u preallocate u- and v- velocities, why is it u_star = zeros(ny,nx-1) and not u_star = zeros(ny,nx)?

[Naeem Ullah]

kamirot, Sir, if you kindly upload your review work I want to read it. Thank you