The finite volume FLIC method and its stability analysis (Q1905606)

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 analyzed by directly using two-dimensional Euler equations instead of a linear model equation. This direct approach to the analysis of nonlinear stability is based on the Taylor expansion of the discretized Euler equations. The exact forms of numerical viscosity or truncation errors are derived and discussed.