论文部分内容阅读
The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photons mean-free path and its interaction with the material.In the small mean free path limit,the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction among radiation and material.In the optical thin limit,the particle free transport mechanism will emerge.In this paper,we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme(AP-UGKS)for the grey radiative transfer equations,where the radiation transport equation is coupled with the material thermal energy equation.The current work is based on the UGKS framework for the rarefied gas dynamics [K.Xu and J.Huang,J.Comput.Phys.229(2010),7747-7764],and is an extension of a recent work [L.Mieussens,J.Comput.Phys.253(2013),138-156] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional grey radiative system.The newly developed scheme has the asymptotic preserving(AP)property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photons mean free path,and the scheme can capture the exact solution in the optical thin regime as well.The current scheme is a finite volume method,which is distinguishable from the standard SN-method for radiation transfer equations with ordered computational cells.Numerical tests are presented to validate the current approach.