Evaluating the Accuracy and Robustness of the Rotated-RoeM Scheme in Hypersonic Flow Computations

This talk presents the development and extension of the Rotated-RoeM flux scheme for accurately resolving strong shock waves in hypersonic flows using a compact stencil approach. The Roe scheme suffers from shock instability issues when applied to hypersonic flow. To address this, the rotated hybrid concept is introduced, effectively mitigating shock instabilities while maintaining computational efficiency on unstructured grids. Additionally, a Mach-number-based weighting function is implemented to distinguish between boundary layer flow and shock instability regions. This scheme is further extended to solve hypersonic equilibrium flow, demonstrating its versatility. Numerical analyses confirm its effectiveness in capturing multi-dimensional shock waves, resolving thermal boundary layers, and accurately predicting heat transfer rates in hypersonic flows.