Information preservation optimization method based on the advection upstream splitting method in supersonic rarefied flow simulation

Abstract

Here, we propose an information preservation (IP) optimization approach for supersonic flow simulations. Based on the conversion of variables integrated in a half-space and analogical analysis, we obtained a relationship between the integrated variables, used in the governing equations of the preserved information, and the macroscopic variables used in Navier–Stokes equations. Computationally, the flux for the correlation terms is reconstructed using the Advection Upstream Splitting Method (AUSM) scheme, giving the IP method windward characteristics. Additionally, the pressure boundary treatment is modified to improve the stability and accuracy of the IP method in the simulation of rarefied supersonic flows driven by high pressures. The particle number threshold method is proposed to solve the “carbuncle point” problem, which is caused by insufficient local collisions. The IP optimization method combines the advantages of the AUSM scheme and low statistical scatter method. Thus, it can be used to investigate the real-time variations in a rarefied supersonic flow through simulations of the supersonic microscale jet flow and hypersonic macroscale nozzle flow. The results indicate that the real-time statistical accuracy of the IP optimization method is significantly higher than that of the direct-simulation Monte Carlo method, and the correctness and accuracy of this method are satisfactory as well. Therefore, the proposed method can unveil the mechanisms underlying the variations and unsteadiness in rarefied supersonic flows on different scales.