Incompressible Finite difference Formulation

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 October 18, 2004, 14:22 Incompressible Finite difference Formulation #1 agg Guest   Posts: n/a Hello, My question specifically concerns the satisfaction of divergence (del dot u) for a finite difference formulation of incompresible flow. I use pressure projection method (non-staggered mesh). Could anyone with experience please guide me on this? Is it possible to satisfy divergence on a non-staggered grid without any tricks involved? Thanks in advance.

 October 18, 2004, 14:27 Re: Incompressible Finite difference Formulation #2 Junseok Kim Guest   Posts: n/a It is only approximately divergence free on projection method because divergence of gradient is not Laplacian in the solver for efficient pressure solver.

 October 18, 2004, 14:51 Re: Incompressible Finite difference Formulation #3 agg Guest   Posts: n/a Thanks Kim, but will this not be a problem if mass is not conserved?

 October 18, 2004, 15:40 Re: Incompressible Finite difference Formulation #4 Junseok Kim Guest   Posts: n/a So, when you deal with mass advection, you use divergence free velocity field, look at the papers about projection methods.

 October 21, 2004, 14:37 Re: Incompressible Finite difference Formulation #5 Oscar Link Guest   Posts: n/a Hi, Are you solving the poisson equation or are you trying some pressure-correction method like the artificial compressibility? Oscar.

 October 22, 2004, 00:29 Re: Incompressible Finite difference Formulation #6 agg Guest   Posts: n/a I'm solving the pressure Poisson equation

 November 1, 2004, 11:22 Re: Incompressible Finite difference Formulation #7 Oscar Link Guest   Posts: n/a You can assume that your solution will satisfy the mass continuity (div(u)=0). For this, a non-staggered grid is better than a staggered one. Probably you will get some spurious oscillations also called wiggles. Staggering help to avoid this problem, but it is not absolute necessary.

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