In this talk, we will present a positivity-preserving finite volume scheme for radiation diffusion problem. The scheme first introduces the cell-centered and cell-vertex unknowns in the flux discretization, then obtains the two-point nonlinear flux approximation by the convex combination. Different from most existing scheme: 1) we do not need either the convex decomposition stencil of the co-normal vector or the usual assumption of the non-negativity of cell-vertex unknowns by introducing two additional positive parameters in the flux discretization; 2) a new second-order cell-vertex elimination algorithm is developed for anisotropic diffusion tensor. These two features make our scheme more efficient and accurate, especially in 3D Lagrangian meshes. Several numerical examples are performed to show the second-order accuracy, the efficiency and the positivity-preserving property.

谢辉, 博士, 北京应用物理与计算数学研究所助理研究员。2006.9-2010.7南京师范大学数学科学学院获学士学位。2010.9-2015.7中科院数学院计算数学所获理学博士学位。2015.7-2017.4北京应用物理与计算数学研究所做博士后。2017.5至今在九所从事激光惯性约束聚变的数值模拟方法研究和程序研制工作。主要研究兴趣包括三维保物理约束的有限体积格式设计及高效扩散解法器研制等, 相关研究成果发表于Multiscale Model. Simul.以及Commun. Comput. Phys. 参与国家重大科技专项, 曾于2015年获中国计算数学学会优秀青年论文二等奖。