Abstract
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.
Highlights
Multiscale gas flows appear in many natural and industrial systems, such as nano/micro devices, aerospace vehicles, vacuum techniques, and unconventional natural gas exploitation
Kinetic schemes based on the Boltzmann or model equations have the potential to serve this purpose, but it is non-trivial to design a kinetic scheme which can capture the hydrodynamics without resolving the kinetic scale, i.e., exhibit the unified preserving (UP) properties
The discrete unified gas kinetic scheme (DUGKS) is one such kinetic scheme with the desired properties, and its merit lies in the reconstruction of the numerical flux at cell interfaces, which is based on the numerical solution of the kinetic equation itself
Summary
Multiscale gas flows appear in many natural and industrial systems, such as nano/micro devices, aerospace vehicles, vacuum techniques, and unconventional natural gas exploitation. In the continuum flow regime, the UP schemes should keep the same properties as the shock capturing schemes designed for the Navier-Stokes equations directly in the calculation of hydrodynamic wave structure, such as the boundary layer with the resolution of a few mesh points. From this perspective, the DSMC and classical explicit DVM are not good choices for multiscale flows in that the cell size and/or time step are required to be smaller than the mean-freepath and relaxation time, respectively, which is a severe limitation for near-continuum flow computation.
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