A Newly Improved WENO Scheme and its Application to the Simulation of Richtmyer-Meshkov Instability

Abstract

This paper investigates the use of a newly improved fifth-order weighted ENO scheme on the simulation of 2D Richtmyer-Meshkov instability. The new scheme, which we called WENO-Z-P, arises from the WENO-Z scheme of Borges et al. WENO-Z-P scheme achieves fifth-order accuracy near the first-order and second-order critical points and possesses higher resolution. We obtain an amazing high-resolution result of two-dimensional Richtmyer-Meshkov instability by WENO-Z-P scheme. More numerous small vortices are found in the shear layer with higher contrast and clarity. We can conclude that the accuracy lose near the second-order critical points play a significant role.The accuracy lose near the second-order critical points deeply drop the resolution of numerical scheme.