A Simple CIP Finite Volume Method for Incompressible Flows

Abstract

This paper presents a practical numerical method for incompressible flows by combining the concept of the CIP method and the finite volume formulation. The method, namely VSIAM3 (Volume/Surface Integrated Average based Multi-Moment Method), employs two integrated averages, i.e. Volume Integrated Average (VIA) and Surface Integrated Average (SIA) which are generically called integrated moments of the dependent variable herein. Using both VIA and SIA as the model variables, VSIAM3 is different from any existing conventional finite volume method and can be interpreted as the simplest finite volume method of the CIP type. Previous studies show that VSIAM3 has accurate numerical dispersion, compact mesh stencil and flexibility for various fluid problems. In this paper, the author will briefly introduce the general framework of VSIAM3 and its implementation to incompressible flows.