Study of Shock Structures Using the Unified Gas-Kinetic Wave-Particle Method with Various BGK Models

Abstract

Recently, the unified gas-kinetic wave-particle (UGKWP) method was proposed to describe rarefied flows efficiently in all Knudsen numbers. However, the initial UGKWP method with the Bhatnagar–Gross–Krook (BGK) model has its own limitations due to the unit Prandtl number. To further improve its performance in non-equilibrium flows, the UGKWP method is extended for the ellipsoidal statistical model (ESBGK) and Shakhov model (SBGK) in this paper. The numerical results of shock structures of the above BGK-type models show that the SBGK model fits the reference data best except the asymmetry parameter, and the ESBGK model comes the second. Meanwhile, in order to overcome the deficiency of negative probability density function (PDF) in SBGK, the UGKWP method with positive-preserving Shakhov PDF is also constructed. It weakens the early rising of temperature phenomenon that existed in the SBGK model, and improves the performance in predicting the stress and heat flux evidently at high Mach numbers.