Improving the performance of the physical influence scheme (PIS) for cell-centred finite volume method

One of the main difficulties in employing fully coupled algorithms for solving Navier-Stokes equations is the high computation cost of coefficient matrix determination and solving the linear equation system. Therefore, the number of required iterations and computational costs may be reduced by increasing the convergence rate. This article deals with the formulation and testing of an improved fully coupled algorithm based on physical influence scheme (PIS) for the solution of incompressible fluid flow on cell-centred grid. The discretisation of improved algorithm is investigated and fully clarified, by comparing the methodology with two similar schemes. For a better insight, two benchmark problems are solved. The first problem is a steady lid-driven cavity with different Reynolds numbers between 100 and 10000. The second problem is steady flow over a backward facing step for the specified Reynolds number of 800. The history of residuals for present and previous methods are compared, in order to demonstrate the performance of the new discretization scheme. It is worth mentioning, the presented method is based on nine cells discretization. Therefore, the computational costs and memory usage of the proposed method are almost the same as previous ones. The results indicate that, the improved method converges in fewer iterations in comparison with prior methods. The new scheme can be utilized for development of the computational fluid dynamics solvers based on cell-centred grid arrangement.