Modified advection upstream splitting method: Revolutionizing accuracy and convergence speed in low-Mach flows

Abstract

The vital role of the numerical scheme is becoming increasingly critical as the use of computational fluid dynamics grows. To address the unfavorable effects experienced in low-speed flows when using the AUSM+M scheme (Improved Advection Upstream Splitting Method), the present paper presents an improved approach known as Modified-AUSM+M (M-AUSM+M). This novel method offers enhanced reliability in simulating low-Mach number flows, effectively mitigating the challenges associated with low-speed symptoms encountered in the original AUSM+M scheme. The novel scheme is facilitated by the parameter-free form of the pressure diffusion term in the mass flux and the low-dissipative form of the velocity diffusion term in the pressure flux. The impacts of these critical ingredients are then thoroughly evaluated, and the different characteristics are explored in terms of robustness and accuracy using a wide range of low-Mach test cases. The proposed scheme maintains a consistent correlation between accuracy and convergence speed. In addition, the recently devised technique demonstrates superior accuracy compared to AUSM+M and AUSM+UP schemes when dealing with low-Mach flows. Furthermore, the findings indicate an incredible reduction in iteration numbers, ranging from 30% to 80%, by employing the enhanced scheme in low-Mach domains. In the investigation of high-Mach test cases, the newly developed method preserves the accuracy achieved by AUSM+M in high-Mach flows.