Advancing high-speed flow simulations: SAUSM – an innovative hybrid numerical scheme for shock stability and accuracy

Abstract

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM[Formula: see text] scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM[Formula: see text] in smooth regions. The proposed SAUSM method combines AUSM[Formula: see text] and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM[Formula: see text] in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM’s proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM[Formula: see text], including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM[Formula: see text] when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research.