A General Method to Compute Numerical Dispersion Error

Abstract

This article presents a new spectral analysis approach for dispersion error and a methodology to numerically evaluate it. In practice, this new analysis allows the numerical study of dispersion errors on all types of mesh and for multiple dimensions. Nonetheless, when mesh uniformity and one-dimensionality assumptions are imposed as in the classical method, the results of this new technique coincide with those of the classic method. We establish the theoretical basis of the approach, derive a numerical methodology to evaluate dispersion errors and assess the method after a set of numerical tests on non-uniform stretched meshes.