J.M. Zhao, L.H. Liu. A Conservative Stabilization Scheme of Spectral / Finite Element Method for Solving Radiative Transfer Equation. The 7th International Symposium on Heat Transfer (ISHT 7). October 26-29, 2008, Beijing, China, 2008. download

Abstract: Based on a recently proposed stabilization scheme of spectral element method (SEM) for solving radiative transfer equation, namely, adaptive isotropical diffusion (AISO) scheme, which can effectively mitigate the ray effects in the solution of radiative transfer equation, a conservative adaptive isotropical diffusion (CAISO) scheme that satisfies radiation energy equation is developed, as such, overcomes the drawback of AISO scheme which can not strictly preserve the radiative energy per unit volume. In the CAISO scheme, besides an artificially added isotropical diffusion term, a new compensate term is designed and added to recover the energy loss caused by the artifical diffusion term, hence the energy equation is exactly satisfied. A SEM based on the CAISO scheme (CAISO-SEM) is presented. The performances of the CAISO-SEM for solving radiative transfer equation are verified by benchmark problems. The CAISO scheme inherited the advantages of AISO scheme, such as, easy and efficient to be implemented under the spectral or finite element method framework, and very good performance in mitigating the ‘wiggles’ in both low and high order spatial approximation. Numerical experiments show that the CAISO-SEM is stable, high order accurate and effective to solve radiative transfer in simple and complex geometry, and also robust to mitigate ray effects of different origins.