[Woody27327]

I've been tasked with modelling this 2D incompressible viscous flow using these boundary conditions and for these values of U₁ and U₂ on a rectangular square grid with 193 by 129 grid points. I have been asked to model the steady-state flow at Re=200.


I’m not sure how I should go about this. Does anyone recommend a comprehensive guide or perhaps a similar example I’d be able to read through and reverse engineer?

[arungovindneelan]

U could refer this link
https://curiosityfluids.com/2016/03/...n-cavity-flow/

https://www.iist.ac.in/sites/default.../psi-omega.pdf

https://in.mathworks.com/matlabcentr...en-cavity-flow
and change that Boundary conditions as per ur requirement.

[selig5576]

There are two great books for this problem:

1. Computational Techniques for Fluid Dynamics 2: Specific Flow Problems, Fletcher
2. Computational Fluid Mechanics and Heat Transfer, Anderson

With that said most literature references will use SOR as the iterative solver for to find the streamfunction. I would avoid using such a method as it takes much longer for a convergence solution. BiCGStab or GMRES are more appropriate solvers .

[FMDenaro]

Originally Posted by selig5576

I would avoid using such a method as it takes much longer for a convergence solution. BiCGStab or GMRES are more appropriate solvers .

just a comment, out of the topic of this post...SOR can be slower in terms of number of iterations but if you consider the real computational time there is almost nothing fast as a SOR (that can be also easily parallelized) programmed for a standard second order discrete Laplace equation. You need to work on 3D problems with some hundreds of millions of nodes to see GMRES/BiCGStab being more convenient.

[selig5576]

Dr. Denaro,

I was speaking in terms of number of iterations for convergence, otherwise you are correct.