Progress of discrete unified gas-kinetic scheme for multiscale flows

Multiscale gas flows appear in many fields and have received particular attention in recent years.It is challenging to model and simulate such processes due to the large span of temporal and spatial scales.The discrete unified gas kinetic scheme(DUGKS)is a recently developed numerical approach for simulating multiscale flows based on kinetic models.The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux.Particularly,the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time,such that the particle transport and collision effects are coupled,accumulated,and evaluated in a numerical time step scale.Consequently,the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time.As a result,the DUGKS can capture the flow behaviors in all regimes without resolving the kinetic scale.Particularly,with the variation of the ratio between numerical mesh size scale and kinetic mean free path scale,the DUGKS can serve as a self-adaptive multiscale method.The DUGKS has been successfully applied to a number of flow problems with multiple flow regimes.This paper presents a brief review of the progress of this method.

An efficient algorithm of the unified stochastic particle Bhatnagar-Gross-Krook method for the simulation of multi-scale gas flows

The unified stochastic particle method based on the Bhatnagar-Gross-Krook model(USP-BGK)has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods,such as the direct simulation Monte Carlo(DSMC)method,for the simulation of multi-scale gas flows.However,running with extra virtual particles and space interpolation,the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes.In this work,the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes.As a result,the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.