On the stability analysis of the PISO algorithm on collocated grids

A Fourier stability analysis is performed on the standard PISO algorithm for collocated grids. The amplification matrices of the sequence are obtained for one-dimensional and two-dimensional incompressible flow problems and the error amplification is studied for different numerical conditions (i.e. mesh-Reynolds number, Courant number, number of PISO corrections). Stability features are also analyzed for steady state conditions and the performance is compared against the SIMPLE-family algorithms. The effect of the mesh orientation and aspect ratio on two-dimensional flow problems are also investigated. It is found that a grid with a higher refinement in one direction can produce an unstable behavior for small mesh-Reynolds numbers, while stability is ensured for the same conditions with a uniformly refined grid in both directions. The first situation can be corrected by enforcing the coupling between pressure and velocity through more PISO corrections.