Two New Second Order Radiative Transfer Equations and Their Solution by Meshless Method with Applications to Strongly Inhomogeneous Media

Details Two New Second Order Radiative Transfer Equations and Their Solution by Meshless Method with Applications to Strongly Inhomogeneous Media Two New Second Order Radiative Transfer Equations and Their Solution by Meshless Method with Applications to Strongly Inhomogeneous Media

2011-05-06

arxiv.org/abs/1105.1207v3

Physics

Computational Physics

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Two new second order form of radiative transfer equations (named here LSORTE and MSORTE) are proposed to overcome the singularity problem of a previous proposed second order radiative transfer equation [proposed separately in J. Comput. Phys. 214 (2006) 12-40 (where it was termed SAAI) and in Numer. Heat Transfer B 51 (2007) 391-409 (where it was termed SORTE)] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. Both the LSORTE and the MSORTE contain a naturally introduced diffusion (or second order) term which will provide better numerical property than the classic first order radiative transfer equation (RTE). The feature of the LSORTE is that it leads to a formulation exactly the same as the least squares scheme discretization of the RTE when it is discretized by weighted residual approach with standard Galerkin scheme. A deficiency problem of the LSORTE in solving radiative transfer in media with strong inhomogeneity is reported and analyzed theoretically. Collocation meshless methods based on moving least square approximation are developed to solve the LSORTE and the MSORTE. Several critical test cases are taken to verify the performance of the presented methods. As for homogeneous media, the LSORTE and the MSORTE show comparable performance when solved by the meshless method, while the MSORTE shows better accuracy in solving radiative transfer in media with strong inhomogeneity.

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