Stability and convergence in fluid flow problems

Abstract

The general convergence and stability theory for finite-difference approximations to fluid flow problems is described. The methods of analysis are outlined and applied to a typical problem. Simple models are then used to consider the behaviour of common difference schemes under practical conditions of finite mesh intervals. Practical stability limits, mode propagation and conservation properties, and nonlinear instabilities are particular characteristics considered. The leapfrog method when used with appropriate safeguards emerges as the most generally suitable basic method.