THE FINITE-VOLUME FLIC METHOD AND ITS STABILITY ANALYSIS

In this study, a general finite volume Fluid-in-cell method (FVFLIC) f or solving the Navier-Stokes equations is introduced. The stability of the numerical method is then analysed by directly using two-dimension al Euler equations instead of a linear model equation. This direct app roach to the analysis of non-linear stability is based on the Taylor e xpansion of the discretized Euler equations and some basic principals that have been used for analysing linear model equations. The exact fo rms of numerical viscosity or truncation errors are derived and discus sed. The influences of the numerical viscosity as well as the artifici al viscosity on numerical solutions are investigated. Results from thi s analysis can be used to construct appropriate artificial viscosity t erms. Based on the above methodology, a stability criterion is propose d for the calculation of time steps for general three-dimensional comp utation using non-orthogonal grids.