Effective Technique to Improve Shock Anomalies and Heating Prediction for Hypersonic Flows

A technique of combining characteristic decomposition in the reconstruction to improve hypersonic flow computations was reported. The governing equations are the compressible Euler or Navier–Stokes equations, which are solved using upwind schemes in the finite volume discretization framework. If not stated otherwise in the following, the inviscid numerical fluxes are calculated by the Roe scheme using Muller’s entropy fix. For viscous flux computation, a second-order central difference is employed. To thoroughly cover the effects of characteristic decomposition for the reconstruction process, two common reconstruction strategies at different spatial accuracies are considered. Three test cases are carried out to examine the performance of the current characteristic reconstruction in improving shock anomalies. By designing the eigenvector matrices from the characteristic transformation and by applying limiting strategies based on the type of characteristic variables, characteristic reconstruction for both the monotone upstream scheme for conservation law and weighted essentially nonoscillatory methods at different spatial accuracies was investigated. Typical numerical examples demonstrated that, in comparison with the primitive method, the current characteristic decomposition was effective in both suppressing shock anomalies and improving heating prediction accuracy. Furthermore, the characteristic method reduced the dependence of heating computation on the choice of both the cell Reynolds number and the numerical fluxes.