A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios

Abstract

A low-dissipation method for calculating multi-component gas dynamics flows with variable specific heat ratio that is capable of accurately simulating flows which contain both high- and low-Mach number features is proposed. The technique combines features from the double-flux multi-component model, nonlinear error-controlled WENO, adaptive TVD slope limiters, rotated Riemann solvers, and adaptive mesh refinement to obtain a method that is both robust and accurate. Success of the technique is demonstrated using an extensive series of numerical experiments including premixed deflagrations, Chapman–Jouget detonations, re-shocked Richtmyer–Meshkov instability, shock-wave and hydrogen gas column interaction, and multi-dimensional detonations. This technique is relatively straight-forward to implement using an existing compressible Navier–Stokes solver based on Godunov’s method.