Numerical dispersion analysis of the convected Helmholtz equation

TL;DR

This paper analyzes how numerical schemes for the convected Helmholtz equation introduce dispersion errors, focusing on the effects of Mach number and frequency, and verifies findings through numerical experiments.

Contribution

It provides a detailed dispersion analysis for conforming and nonconforming quadrilateral finite element schemes applied to the convected Helmholtz equation, highlighting the influence of Mach number and frequency.

Findings

Dispersion relations depend on Mach number and frequency.

Numerical experiments confirm the relationship between dispersion errors and computational inaccuracies.

Analysis guides improved finite element scheme design for wave problems.

Abstract

We present the numerical dispersion effects in solving the convected Helmholtz equation by the conforming and nonconforming quadrilateral finite elements. Particularly, we evaluate the dispersion relations for the numerical schemes. The dispersive behaviors are analyzed by focusing on the Mach number and the angular frequency. Numerical experiments are conducted to verify the relations between the numerical dispersions and the computational errors.