Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case

Abstract

Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.