Title: The technique of MIEELDLD as a measure of the shock-capturing property of numerical methods for hyperbolic conservation laws

Authors: A.R. Appadu; S.N. Neossi Nguetchue

Addresses: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa ' Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Abstract: In this paper, we use some numerical methods namely Lax-Wendroff (LW), two-step Lax-Friedrichs (LF), two variants of composite methods made up of Lax-Wendroff and the two-step Lax-Friedrichs and Fromm's scheme to solve a 1D linear advection and 1D diffusionless Burger's equation, at some values of the Courant number. We then use two optimisation techniques based on both dispersion and dissipation and two optimisation techniques based on only dispersion and obtain the variation of the integrated errors vs. the CFL number. It is seen that out of the five techniques, only one is a good measure of the shock-capturing of property of numerical methods.

Keywords: composite methods; dispersion; dissipation; shock capturing properties; optimisation; hyperbolic conservation laws; damping; numerical methods; 1D linear advection equation; Lax-Wendroff; Lax-Friedrichs; Fromm; 1D diffusionless Burger equation; Courant number.

DOI: 10.1504/PCFD.2015.070441

Progress in Computational Fluid Dynamics, An International Journal, 2015 Vol.15 No.4, pp.247 - 264

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 06 Jul 2015 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article