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Incompressible Finite difference Formulation

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Old   October 18, 2004, 14:22
Default Incompressible Finite difference Formulation
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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.

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Old   October 18, 2004, 14:27
Default Re: Incompressible Finite difference Formulation
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Junseok Kim
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It is only approximately divergence free on projection method because divergence of gradient is not Laplacian in the solver for efficient pressure solver.

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Old   October 18, 2004, 14:51
Default Re: Incompressible Finite difference Formulation
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Thanks Kim, but will this not be a problem if mass is not conserved?
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Old   October 18, 2004, 15:40
Default Re: Incompressible Finite difference Formulation
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Junseok Kim
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So, when you deal with mass advection, you use divergence free velocity field, look at the papers about projection methods.

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Old   October 21, 2004, 14:37
Default Re: Incompressible Finite difference Formulation
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Oscar Link
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Hi,

Are you solving the poisson equation or are you trying some pressure-correction method like the artificial compressibility?

Oscar.
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Old   October 22, 2004, 00:29
Default Re: Incompressible Finite difference Formulation
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I'm solving the pressure Poisson equation
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Old   November 1, 2004, 11:22
Default Re: Incompressible Finite difference Formulation
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Oscar Link
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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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