pressure correction method
 

Hi all,
I am writing a 2D matlab code based on pressure correction method for lid driven cavity flow problem. When I frame the pressure poisson matrix {grad^2 P'=0} with neumann pressure boundary condition {dp'/dn=0} at all the 4 walls, what I observed is that the determinant [A] of AX=B becomes zero. I would be greatful if anyone can tell me how do I get out of this problem.

Thank you,
Ravi

The pressure is determined only to a constant with Neumann boundary conditions.

You're free to pin the pressure at one node to solve the matrix problem.

If you solve the pressure equation by relaxation you will get a solution. But only the pressure gradients will be unique - the overall level will depend on your initial guess for the pressure field.

Yes , you are right. We can not obatain a solution if we adopte the direct method to solve the Ax=B, we should use the iteration method.
in the incompressible flow, we only care about the pressure difference in the flow field.

Finally I am able to solve the lid driven problem by fixing one of the node's pressure correction value=0. Thanks for your suggestions :o.

Dear friends,

Thanks, I have written my staggered grid incompressible code using SIMPLE algorithm. Now that i want write it using a collocated grid. Is it direct or should i do some major changes ? Please help me in this regard.

cheers

jyo

no major changes are needed. momentum interpolation should be introduced. the coefficient of the U , V and W should be changed at that of the scalar equations.

momentum interpolation
 

Hi,

Momentum interpolation u mean to say row*u*u or row*u*v for u momentum eqn. (finding the value between the two nodes) and scalar equation u mean to say the pressure correction equation ?

cheers

jyothish

MIM is used to caculate the interface flux and source term of the pressure correction equations.
please refer to some CFD book.
Ferziger J.H., Peric M. Computational methods for fluid dynamics

MIM is used to caculate the interface flux and source term of the pressure correction equations.
please refer to some CFD book.
Ferziger J.H., Peric M. Computational methods for fluid dynamics

Hi friends, I, too, am working on this very same problem, and would really appreciate it if someone would be willing to provide their code to me.

Feel free to post it here or send it to me in a PM.

Thanks a lot! I really want to improve what I have by looking at others. :)