Simulation of Viscous and Reactive Hypersonic Flows Behaviour in a Shock Tube Facility: TVD Schemes and Flux Limiters Application

Abstract

Work performed in this study concerns mainly the analysis and the wisely use of TVD type schemes (total variation diminishing) for numerical simulation of reactive flows, these schemes are first presented in scalar equation. Their extension to Euler equations for a reactive gas mixture is conducted through the approximate extended solver of Riemann problem. A comparative study of specific variants of TVD schemes has been made in the case of one-dimensional unsteady flow for an inert and reactive gas mixture, which represents the classical instance of a shock tube. The purpose of this investigation is to highlight the general behaviour (order of accuracy) and performance of TVD schemes with various flux limiters for the simulation of reactive flows and in particular, to make possible the capture of the shock wave together with waves expansion for choosing the appropriate scheme to apply eventually in simulation of hypersonic viscous flow in chemical non equilibrium.