Development of an Implicit Physical Influence Upwinding Scheme for Cell-Centered Finite Volume Method

The main task in finite volume methods (FVM) is to estimate proper values on the cell faces based on the calculated values on the nodes or cell centers. In this way, upwinding schemes are the most successful schemes for estimation of values on the control volume faces. These schemes have been developed in FVM for various techniques with proper accuracy on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed to the cell-centered FVM in an implicit coupled solver and the results are compared with other two main branches of upwinding exponential differencing scheme (EDS) and skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated in lid-driven cavity flow at Re = 400-10000 and backward-facing step flow at Re = 800. Simulations show considerable difference between the of results EDS scheme with benchmarks, especially for lid-driven cavity flow at high Reynolds numbers which occurs due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results in backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in cavity flow can be related to its non-pressure sensitivity between cell face and upwind points which is critical for such vortex dominant flows. Instead, the PIS scheme by applying a momentum equation between the cell face and upwind points, is able to capture flow vortices properly and matching well with benchmarks.