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 new October 11, 2008 17:55

some question on matrix in FVM

I am new to CFD and ask some simple questions. when NS equations is solved over unstructured grid based on SIMPLE coupling method, matrices for the discretized momentum and pressure correction equations are symmetrical or non-symmetrical? When we may have symmetrical or non-symmetrical matrices?

 New October 14, 2008 23:58

Re: some question on matrix in FVM

Re: some question on matrix in FVM

pressure can be symm.

but mom. can be unsym. due to usung upwinding (if you use central schemes, not feasible for convective terms, you mom. can be symm. too)

 New October 15, 2008 03:00

Re: some question on matrix in FVM

Than you very much. Here is my understanding of your replies, symm has nothing to with mesh topology, right? I mean for hybrid grids containing mixing elements such as hex, tetra, and prism, and for grids containing hex only, pressure equations are both symm. This sounds a little strange. For hybrid grids, different volumes may have different unknown variable, e.g. 5 for a tetra and y for a hexa. it seems symm is not about how many unknown variables a discretised equation for a control volume has. How should I to understand symm?

Re: some question on matrix in FVM

> symm has nothing to with mesh topology, right?

yes,

first (you use simple method )i assume you mean incompressible flow; pressure eq. is resulted fro discritization of Poisson equation

like this Del^P = rhs

in fact a steady diffusion equation for which the best schemes are central schems, so each quantity has same share from each cell and so system of eq. will be symm. but we should be careful for boundary cells, but it is possible to apply bc so system will be symmetric

> How should I to understand symm?

try to derive your system on a small uniform cartesin grid, then you will see how momentum eq. will be obviously unsymmetric and how it would be possible to have symm. pressure eq.

assume neighbour cells A and B, and a shared face between them, assume flow direction is from cell A to B, so using first order upwind method (consider just convectie terms), momentum equation of cell B has a contribution from cell A, but cell A does not have any contribution from cell B which leads to unsymmetric system of equation

 new October 15, 2008 04:40

Re: some question on matrix in FVM

thx

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