A general method to compute numerical dispersion errors and its application to stretched meshes

TL;DR

This paper introduces a spectral analysis method for dispersion errors applicable to various mesh types and dimensions, providing a numerical evaluation approach that extends classical methods to non-uniform stretched meshes.

Contribution

It develops a general spectral analysis framework for dispersion errors and a numerical evaluation methodology applicable to complex, non-uniform meshes, expanding beyond classical assumptions.

Findings

The new analysis aligns with classical results under uniform, 1D conditions.

The methodology effectively evaluates dispersion errors on non-uniform stretched meshes.

Numerical tests validate the approach's accuracy and versatility.

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.