Generalised SIMPLE-Based Pressure Correction Method for Unstructured Co-located Grids

摘要

This paper reports on the SIMPLE-like solution algorithm which 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-centred finite-volume method using co-located storage of flow variables on unstructured grids. The convergence acceleration is an outcome of the novel treatment of the pressure correction equation which accounts for two commonly neglected terms appearing in a general pressure correction equation. These terms, namely neighbour and non-orthogonal corrections, represent velocity corrections from neighbouring cells and the cell-face pressure correction gradient associated with the grid non-orthogonality, respectively. Reminiscent of the PISO method, both neighbour and non-orthogonal corrections are taken into account by performing two or more correction steps. However, the full inclusion of neighbours 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 pseudo unsteady term into discretised velocity correction equations. Using this term, the contribution of neighbour corrections is under-relaxed, enabling 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.