Discrete unified gas-kinetic wave-particle method for flows in all flow regimes

This work proposes a discrete unified gas-kinetic wave-particle (DUGKWP) method for simulation of flows in all flow regimes. Unlike the discrete velocity method (DVM) and the direct simulation Monte Carlo (DSMC) method which solve the governing equations by either the deterministic method or the stochastic method, the DUGKWP combines the advantages of these two methods. In the DUGKWP, the information of microscopic particles as well as macroscopic flow variables are both evolved. Specifically, the microscopic particles are updated by the free-transport and resampling processes, while the macroscopic flow properties are evolved via solving the macroscopic governing equations of conservation laws with the finite volume method. According to the discrete characteristic solution to the Boltzmann-BGK equation utilized in the DUGKWP, in the highly rarefied flow regime, the motion of microscopic particles greatly determines the fluxes for the macroscopic governing equations. Conversely, for the continuum flow, no microscopic particle exists in the computational domain and the DUGKWP is degraded to the Navier-Stokes solver. Numerical studies validate that the DUGKWP can accurately predict the flow properties in all flow regimes. Furthermore, compared with the deterministic method, the DUGKWP enjoys superior efficiency with less memory consumption for both high-speed rarefied flows and flows close to the continuum regime.