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

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 twostep 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.