| Abstract: | In this study, a general finite volume Fluid-in-cell method (FVFLIC) for solving the Navier—Stokes equations is introduced. The stability of the numerical method is then analysed by directly using two-dimensional Euler equations instead of a linear model equation. This direct approach to the analysis of non-linear stability is based on the Taylor expansion of the discretized Euler equations and some basic principals that have been used for analysing linear model equations. The exact forms of numerical viscosity or truncation errors are derived and discussed. The influences of the numerical viscosity as well as the artificial viscosity on numerical solutions are investigated. Results from this analysis can be used to construct appropriate artificial viscosity terms. Based on the above methodology, a stability criterion is proposed for the calculation of time steps for general three-dimensional computation using non-orthogonal grids. |
