Modeling and computation for non-equilibrium gas dynamics: Beyond single relaxation time kinetic models

Abstract

Many kinetic relaxation models have been proposed for the study of rarefied flows. Based on the single relaxation time model, a discrete velocity method-based unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the discretized space directly on account of accumulating flow evolution from particle transport and collision within a time step. Under the UGKS framework, a unified gas-kinetic wave-particle (UGKWP) method has been further developed for non-equilibrium flow simulation, where the time evolution of the gas distribution function is composed of analytical wave and individual particles. In the highly rarefied regime, the flow evolution is mainly described by the particle transport and collision. Because of the use of single relaxation time for particle collision, there is a noticeable discrepancy between the UGKWP solution and the full Boltzmann or direct simulation Monte Carlo (DSMC) result, such as the temperature distribution inside a shock layer at high Mach numbers. In this Letter, a modification of the particle collision time according to the particle velocity will be implemented in the UGKWP. As a result, the new model greatly improves the performance of the UGKWP in the capturing of non-equilibrium flows. There is an excellent match between UGKWP and DSMC or Boltzmann solution in the highly rarefied regime. In the continuum flow regime, due to the absence of particles, the modification of the particle collision time will not take effect and the UGKWP will get back to the hydrodynamic Navier–Stokes flow solver with correct dissipative coefficients at small cell Knudsen numbers.