A-posteriori diffusion analysis of higher-order numerical schemes for application to propagating linear waves

TL;DR

This paper introduces a new a-posteriori diffusion analysis technique for evaluating higher-order numerical schemes by examining energy content and stability in simulations of linear wave propagation.

Contribution

It presents a novel method for post-analysis of numerical schemes' diffusion and stability, applicable to complex wave simulations in electromagnetics and aeroacoustics.

Findings

Early detection of numerical instability.

Effective analysis of modern linear and nonlinear schemes.

Applicable to space-time coupled numerical methods.

Abstract

We propose a new technique for a-posteriori diffusion analysis of numerical schemes. The scalar linear advection equation with a broadband signal as initial conditions is numerically solved to simulate a traveling linear wave. A diffusion analysis is performed based on modal energy content and time evolution of total energy of the broadband signal. Onset of numerical instability can also be detected at an early stage using this technique. This technique is used for analyzing modern linear and nonlinear as well as space-time coupled numerical schemes. This analysis is particularly useful for analyzing numerical schemes used in simulation of traveling linear waves such as in computational electromagnetics (CEM) and computational aeroacoustics(CAA).