Simple Improvement of Momentum Interpolation Equation for Navier-Stoke Equation Solver on Unstructured Grid

Abstract

Problem statement: Pressure and velocity decoupling have been source of problem in solving Navier-Stokes and continuity equation particularly in complex collocated grid. The problem of pressure velocity decoupling is usually reduced by using momentum interpolation to calculate mass flux at face of control volume. Equation of momentum interpolation was derived by assumption that the face of cell is equidistant from two neighbor cell centers and face of cell is collinear with two neighbor cell centers. This assumption is not valid in many unstructured grid and cause significant error. Approach: In this article a simple improvement of momentum interpolation for using in unstructured grid was proposed. The improvement was done by added a correction term to original equation. Results: The method was compared with original method in Kovasznay’s flow and Laminar Poisseulli Flow. The method was found able to reduce error about 40% in both cases. Conclusion: The correction added to original momentum interpolation is able to reduce error in Navier-Stokes equation solver on unstructured grid.