RKDG methods with WENO type limiters and conservative interfacial procedure for one-dimensional compressible multi-medium flow simulations

Abstract

In this paper, we continue on studying the Runge–Kutta discontinuous Galerkin (RKDG) methods to solve compressible multi-medium flow with conservative treatment of the moving material interface. Comparing with the paper by J. Qiu, T.G. Liu and B.C. Khoo [J. Comput. Phys. 222 (2007) 353–373], we adopt the HLLC flux instead of Lax-Friedrichs numerical flux, the finite volume weighted essentially nonoscillatory (WENO) and Hermite WENO (HWENO) reconstructions as limiter instead of TVB limiter for RKDG. The HLLC flux is based on the approximate Riemann solver with little numerical viscosity and can resolve the contact discontinuity and shear wave very well. For limiter procedure, first we use the KXRCF indicator to identify the troubled cell, then apply WENO or HWENO method to reconstruct the polynomial in the troubled cell, while maintaining the cell average. This limiter procedure is more accurate and less problem dependent than the TVB limiter. Numerical results in one dimension for multi-medium flows such as gas–gas and gas–water are provided to illustrate the capability of these procedures.