hi there,

i'm seeking informations and references discussing the issues related with the influence of the mesh skewness on the solution of a pressure poisson equation.

sincerely,

Frederic Felten

Mesh skewness reduces the diagonal dominance of the discrete Poisson operator which slows down convergence. ADI type preconditioners also become less effective.

Convergence rate aside, the accuracy might also drop when mesh is highly skewed. This results mainly from the way in which the face centered (in FV schemes) pressure gradients are computed using cell-centered pressure values. Usually a second order central-difference approximation is used and the accuracy might drop to first order for very high skewness (or even stretching). It is perhaps more appropriate to compute pressure gradients using multi-dimensional stencils (which could be non-symmetric unlike the central difference operators). I am not sure about the effects of directional biasing in this way of computing pressure gradients (since there is no physical basis for biased stencils here unlike upwinding for advective operators). However, the matrix corresponding the discrete Laplacian operator would still be symmetric.

Some the grid layout issues have been discussed in the introduction of the paper by Zang et al. (JCP, 1994 or 1995). You can find a concise discussion on the problems/advantages of the grid system (variable layout) used for incompressible flows. You might find some useful discussions in the papers they refer to as well.