Stability theory of time-marching methods

A relatively straightforward method for obtaining the local stability properties of multi-variable time-marching schemes for predicting compressible flows is developed. Applications of the method to several one-, two-, and three-dimensional examples are presented. An extension of the techniques used in the stability analysis to the prediction of ill-conditioning of steady state methods, in particular near sonic conditions, is also developed, and examples are given which show how to overcome the ill-conditioning problems.