Generalized SIMPLE-Based Pressure Correction Method for Unstructured Colocated Grids

Abstract

This paper reports on the SIMPLE-like solution algorithm that significantly improves velocity–pressure coupling, leading to the accelerated convergence. The algorithm is applicable to both incompressible and compressible flows. It is implemented within the framework of a cell centered finite volume method using colocated storage of flow variables on unstructured grids. The convergence acceleration is an outcome of the novel treatment of the pressure correction equation that accounts for two commonly neglected terms appearing in a general pressure correction equation. These terms, namely, the neighbor and nonorthogonal corrections, represent velocity corrections from neighboring cells and the cell-face pressure correction gradient associated with the grid nonorthogonality, respectively. Reminiscent of the PISO method, both neighbor and nonorthogonal corrections are taken into account by performing two or more correction steps. However, the full inclusion of neighbor velocity corrections can prevent the solution convergence. Following an analogy between time marching and a steady-state iterative approach, this problem has been resolved by introducing a pseudounsteady term into discretized velocity correction equations. Using this term, the contribution of neighbor corrections is underrelaxed, enabling a satisfactory convergence rate. The algorithm is applied to several benchmark test cases, covering laminar and turbulent, as well as incompressible and compressible, flows. For all test cases, the convergence rate can be significantly improved by performing two or more pressure correction steps. An optimal number of pressure corrections exists for which a meaningful reduction of computing time is possible.