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A new second order form of radiative transfer equation (named MSORTE) isproposed, which overcomes the singularity problem of a previously proposedsecond order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40(where it was termed SAAI), Numer. Heat Transfer B 51 (2007) 391-409] indealing with inhomogeneous media where some locations have very small/zeroextinction coefficient. The MSORTE contains a naturally introduced diffusion(or second order) term which provides better numerical property than theclassic first order radiative transfer equation (RTE). The stability andconvergence characteristics of the MSORTE discretized by central differencescheme is analyzed theoretically, and the better numerical stability of thesecond order form radiative transfer equations than the RTE when discretized bythe central difference type method is proved. A collocation meshless method isdeveloped based on the MSORTE to solve radiative transfer in inhomogeneousmedia. Several critical test cases are taken to verify the performance of thepresented method. The collocation meshless method based on the MSORTE isdemonstrated to be capable of stably and accurately solve radiative transfer instrongly inhomogeneous media, media with void region and even withdiscontinuous extinction coefficient.

A Second Order Radiative Transfer Equation and Its Solution by Meshless Method with Application to Strongly Inhomogeneous Media