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.

It is only approximately divergence free on projection method because divergence of gradient is not Laplacian in the solver for efficient pressure solver.

Thanks Kim, but will this not be a problem if mass is not conserved?

So, when you deal with mass advection, you use divergence free velocity field, look at the papers about projection methods.

Hi,

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

Oscar.

I'm solving the pressure Poisson equation

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.