Unified gas-kinetic wave-particle methods V: Diatomic molecular flow

Abstract

In this paper, the unified gas-kinetic wave-particle (UGKWP) method is further developed for diatomic gas with the energy exchange between translational and rotational modes for flow study in all regimes. The multiscale transport mechanism in UGKWP is coming from the direct modelling in a discretized space, where the cell's Knudsen number, defined by the ratio of particle mean free path over the numerical cell size, determines the flow physics simulated by the wave particle method. The non-equilibrium distribution function in UGKWP is tracked by the discrete particle and analytical wave. The weights of distributed particle and wave in different regimes depend on cell's Knudsen number, where distinguishable macroscopic flow variables of particle and wave are updated inside each control volume. The UGKWP becomes a particle method in the highly rarefied flow regime and converges to the gas-kinetic scheme (GKS) for the Navier-Stokes solution in the continuum flow regime without particles. In comparison with discrete velocity method (DVM)-based unified gas-kinetic scheme (UGKS), the computational cost and memory requirement in UGKWP have been reduced by several orders of magnitude for the high speed and high temperature flow simulation, where the translational and rotational non-equilibrium can be captured accurately in the transition and rarefied regime. As a result, for the hypersonic flow around a flying vehicle, the computation can be conducted using a personal computer for the studies in all regimes. The UGKWP method for diatomic gas will be validated in various cases from one dimensional shock structure to three dimensional flow over a sphere, and the numerical solutions will be compared with the reference DSMC results and experimental measurements.