2 research outputs found
An Implicit Unified Gas-kinetic Scheme for Unsteady Flow in All Knudsen Regimes
The unified gas-kinetic scheme (UGKS) is a direct modeling method for
multiple scale transports. The modeling scale of the scheme is the mesh size
and time step, and the ratios of the mesh size over particle mean free path or
the time step over particle collision time determine the local evolution regime
of flow physics. For unsteady flow computation, due to the CFL condition the
time step in the explicit UGKS is limited by the smallest cell size in the
computational domain. As a result, for a largely stretched non-uniform mesh the
global time step becomes very small and the ratio of the time step over local
particle collision time may get a very small value. Under such a circumstance,
the physics in explicit UGKS may be constrained by the kinetic scale physics
only. The multiscale UGKS reduces into a single scale discrete velocity method
where the free transport is used for the flux evaluation. In order to keep the
advantages of UGKS and improve the efficiency for unsteady flow computation,
the restriction from global CFL condition on the time step has to be removed.
In this paper, we develop an implicit UGKS (IUGKS) for unsteady flow by
alternatively solving the macroscopic and microscopic governing equations
within a step iteratively. In order to preserve the coherent flow evolution and
multiscale nature, the numerical flux is still evaluated by the explicit UGKS
with the local CFL condition. Therefore, the multiscale property of the UGKS
modeling is preserved over non-uniform meshes. Many numerical examples are
included to validate the scheme for both continuum and rarefied flows. The
IUGKS presents reasonably good results with second order accuracy for unsteady
flow computation and the efficiency has been improved by dozen of times in
comparison with the explicit UGKS
The first decade of unified gas kinetic scheme
In 2010, the unified gas kinetic scheme (UGKS) was proposed by Xu et al . (A
unified gas-kinetic scheme for continuum and rarefied flows, Journal of
Computational Physics, 2010). In the past decade, many numerical techniques
have been developed to improve the capability of the UGKS in the aspects of
efficiency increment, memory reduction, and physical modeling. The methodology
of the direct modeling of the UGKS on discretization scale provides a general
framework for construction of multiscale method for multiscale transport
processes. This paper reviews the development and extension of the UGKS in its
first decade