A Quasi-Conservative Alternative WENO Finite Difference Scheme for Solving Compressible Multicomponent Flows

Abstract

We construct a quasi-conservative alternative WENO finite difference scheme respectively coupled with the global Lax-Friedrichs (AWENO-GLF) and the contact restored Harten-Lax-van Leer approximate Riemann solver (AWENO-HLLC) for solving compressible multicomponent flows. The mass equation, the momentum equation, and the energy equation are discretized by a fully conservative AWENO-GLF or AWENO-HLLC finite difference scheme from which a consistent nonconservative discretization of the topological equation is derived according to the velocity and pressure equilibrium principle proposed by Agrall (J Comput Phys 125:150–160, 1996). We prove that, coupling with the constructed scheme, WENO interpolations with common weights for conservative variables or standard WENO interpolations with independent weights for primitive quantities can maintain velocity and pressure equilibrium. Numerical examples demonstrate that AWENO-HLLC scheme is not only less dissipative but also less oscillatory than classical WENO-GLF scheme for compressible multicomponent flows.