I developed a matlab code solving the lid-driven cavity problem using a staggered grid and it worked fine. I'm facing a problem with developing a collocated grid code for solving the ACM but it doesn't work well.
My boundary conditions are the following:
for the upper wall: u=1, v=0 and dp/dy=0, hence, p(i,ny)=p(i,ny-1)
for the right and left walls: u=0, v=0, and dp/dx=0
for the bottom wall: u=0, v=0, and dp/dy=0
the convergence history is constant just after few iterations while the divergence free term is relatively high. I chose the compressibility constant to be 4.5, dt=0.001, dx=1/50 and dy=1/50.
Can anyone recommend me some resources or any advices for making the square lid-driven cavity works on a collocated grid?
Dear Ahmed Essa ,
Look the link, maybe useful.
Article Artificial compressibility method on half-staggered grid for...
Regards,
Shafagat
Related to your query, I would like to suggest you to follow these lectures :https://www.youtube.com/watch?v=FO3IDwShGMA
https://www.youtube.com/watch?v=OOILoJ1zuiw
https://www.youtube.com/watch?v=yBpZn0fok6E
+ follow the other lectures in the same way.
Dear Ahmed Essa
These links seems to be helpful, have a look:
1. https://iopscience.iop.org/article/10.1088/1742-6596/1978/1/012027/pdf
2. https://www.mdpi.com/2077-1312/8/8/590/pdf
3. https://www.youtube.com/watch?v=FO3IDwShGMA
Kind Regards
Qamar Ul Islam
Thank you for your responses. I found what I was looking for in the textbook of Ferizger. I really appreciate your help.
Qamar Ul Islam Muhammad Ali and Shafagat Mahmudova