Executive Summary : | The design of thermal protection systems for hypersonic vehicles requires accurate aero-thermal predictions. Computational Fluid Dynamics (CFD) methods are often used, but shock-capturing methods often lead to unphysical solutions, such as "carbuncle" phenomena. The Simple Low-dissipation AUSM (Advection Upstream Splitting Method) and its extension SLAU2 convective scheme have gained popularity due to their ability to improve robustness for strong shocks. However, SLAU2 still struggles with heat flux prediction accuracy. This project aims to test the hypothesis regarding the addition of appropriate numerical dissipation, check the effectiveness of the improvement for other AUSM family schemes, test the method for challenging blunt-body problems, and re-calibrate the advantages of the shock-capturing method with modern shock-fitting methods for accurate and robust prediction of hypersonic heating. Shock-fitting approaches do not suffer from shock anomalies problems but have not been traditionally popular due to their associated algorithmic difficulties. The project also aims to preserve the all-speed computational feature of the SLAU2 scheme, ensuring that the proposed modification does not alter the scheme's ability to provide low dissipation required for low-speed computation. The project aims to offer the hypersonic community a robust and accurate modification to SLAU2 and other AUSM family schemes for improved heat flux prediction for both two and three-dimensional blunt body problems. It will also improve the understanding of the advantages of AUSM family-based shock-capturing methods over the shock-fitting method with recent advancements. |