Assessment of Limiting Processes of Numerical Schemes on Hypersonic Aeroheating Predictions

Abstract

This paper deals with a systematic assessment study on the performance of conventional MUSCL slope limiters and recently developed multidimensional limiting processes in the context of aeroheating predictions of hypersonic flows. Three test cases are considered: 1) the flow () around a cylindrical leading-edge configuration, 2) the flow () around a biconic configuration, and 3) the flow () around a double-ellipsoid configuration. Through the careful comparisons between one another and with the available experimental data, numerical results are presented to demonstrate the behaviors of different limiting processes in hypersonic aeroheating predictions. It is found that the medium dissipative van Leer slope limiter could be the best compromise between accuracy and robustness of all the MUSCL slope limiters considered, whereas the multidimensional limiting processes can numerically behave better than all the MUSCL slope limiters, whether in accuracy or in robustness. The results indicate that, within the total variation diminishing framework, the multidimensional limiting processes can be identified with the double minmod slope limiter in dissipation, and can come up to the minmod slope limiter and/or the van Albada slope limiter in robustness. In addition, the multidimensional limiting and enhanced multidimensional limiting processes could compare with the conventional total variation diminishing MUSCL approach in overall computational cost. Therefore, the multidimensional limiting processes should be preferred to predict hypersonic aeroheating issues accurately with better performance. On the other hand, it is noteworthy that the postprocessing method for calculating surface heat flux proposed in this study is proven to largely reduce the grid dependence of aeroheating predictions.