Discrete Unified Gas Kinetic Scheme Of Radiative Transfer

Thermal radiation is a basic way of heat transfer.So far many numerical methods have been developed for solving radiative transfer problems.However,for muti-scale radiation with strong changes in optical thickness,many methods will encounter problems of low efficiency or poor accuracy.Therefore,it is necessary to develop numerical methods which can efficiently and accurately solve multi-scale radiation problems.Discrete unified gas kinetic scheme(DUGKS),which was proposed recently,is one such multi-scale method.DUGKS has already gained great success for multi-scale gas flows.But DUGKS has not been well developed in thermal radiation.In this paper,the DUGKS method is extended for thermal radiation in the presence of a gray absorbing,emitting and scattering medium.The main work includes:(1)Based on RTE,a DUGKS is developed for radiative heat transfer in anisotropic scattering media.The anisotropic scattering phase is approximated by a finite series of the Legendre polynomials.Several one-and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS.The results show that the anisotropic scattering characteristics of participating media have a significant influence on the distribution of radiative heat flux,which cannot be ignored.(2)Multi-scale problems with large extinction coefficient difference are simulated by the developed DUGKS.Due to the AP characteristics of DUGKS,the grid size is not limited by the photon mean free path(MFP),and the difficulty of coupling between different methods is avoided.(3)A hybrid DUGKS is proposed to solve the combined transient conduction and radiation model within a gray absorbing,emitting and scattering medium.The DUGKS is used to solve the radiative transfer equation while a finite volume method(FVM)is used to solve the energy equation of transient conduction and radiation.The accuracy of the DUGKS-FVM is verified by several one-and two-dimensional tests.The results show that the proposed hybrid DUGKS provides a new method for solving the combination of transient conduction and radiation model.In summary,this paper extends the DUGKS to thermal radiation,and particularly focuses on the anisotropic scattering and multi-scale characteristics of participating media.In addition,a hybrid DUGKS method is proposed to solve the combination of transient conduction and radiation,which lays a foundation for future related research.