A relaxation model for numerical approximations of the multidimensional pressureless gas dynamics system

Abstract

Relaxation models for the pressureless gas dynamics (PGD) equations attempt to satisfy the strictly hyperbolic conservation law in order to employ the well-posed approximated Riemann solvers. In this study, a new type of relaxation model is proposed to resolve two shortcomings of the existing relaxation models: the constant propagation speed of sound, and the collapse of delta shock waves in multidimensional problems. The proposed model seeks a strictly hyperbolic system of equations without any special consideration for the proper values of the propagation speed of sound. Numerical tests showed that the proposed model can accurately describe the behavior of the PGD equations, in particular, the occurrence of delta shock waves and vacuum states in a multidimensional problem. (C) 2020 Elsevier Ltd. All rights reserved.