Numerical Simulations Using TVD Schemes of Two-Dimensional Supersonic Flow in Chemical Equilibrium

Abstract

A numerical scheme for the solution of both unsteady and steady-state, two-dimensional Euler equations considering gas in chemical equilibrium, is presented. Three alternatives of the Total Variation Diminishing (TVD) Harten-Yee scheme are implemented. One of them is a technique based on the adaptive use of different limiter functions in each wave of the inter-cell Riemann problem. With this technique, the undesirable effects of the artificial viscosity on the capture of contact discontinuities are reduced, without loss of robustness in nonlinear waves resolution. In order to verify the accuracy of the proposed scheme, results of the unsteady flow in cylindrical explosions, and of the steady-state solution of hypersonic flow over a blunt body, are presented. Finally, comparisons considering accuracy of results and convergence properties between the three Harten-Yee schemes are carried out.