Analysis of Hypersonic Blunt-Body Flows Using a Total Variation Diminishing Scheme and the MacCormack Scheme.

摘要

An explicit second-order accurate, total variation diminishing (TVD) scheme and the MacCormack scheme are applied to the Euler equations in axisymmetric form to study hypersonic blunt body flows. The modified flux approach of Harten, with modification by Yee, for two-dimensional flows is extended to treat axisymmetric flows. Calculated flow properties for the steady state, blunt body problem such as shock standoff distance, bow shock shape, surface pressure distribution and entropy jump conditions are compared to theory, results from the MacCormack scheme, and experimental data for Mach numbers of 3.0, 4.03, 5.06, 6.03 and 8.1. Additionally, the TVD and MacCormack schemes are used to simulate numerically the unsteady shock impingement on a sphere. Results are compared to experimental data for a shock Mach number of 2.89. Analysis of the numerical simulations provide suitable ranges of values for the entropy correction parameter and the Courant (CFL) number. The high-resolution and robustness of the TVD scheme is clearly shown.