Numerical simulation of radiation transfer equations arises in many applications, including astrophysics, inertial confinement fusion, optical molecular imaging, shielding, and so on. The positivity-preserving and conservation-preserving properties are two important and challenging issues for the numerical solution of this kind of equations. In this talk, I will introduce our recent work on high order positivity-preserving and conservative discontinuous Galerkin (DG) schemes solving steady and unsteady radiation transfer equations. The properties such as positivity-preserving and high order accuracy are proven rigorously. One- and two-dimensional numerical results are provided to verify the designed characteristics of our schemes. 

成娟研究员是北京应用物理与计算数学研究所研究员，北京大学兼职教授。研究领域包括可压缩多物质流体流动的拉格朗日和任意拉格朗日—欧拉(ALE)方法，以及辐射输运方程的数值方法。目前担任国际著名期刊Journal of Computational Physics (JCP) 副主编、北京计算数学学会副理事长、中国工业与应用数学学会 (CSIAM) 大学数学建模竞赛工作委员会副主任委员。曾获航空航天工业部科技进步二等奖、中国工程物理研究院科技创新二等奖，多次在国内和国际会议上做特邀报告，包括 2019 年中国佛山举行的第 17 届 CSIAM 年会和俄罗斯新西伯利亚举办的纪念 Sergei K.Godunov 诞辰 90 周年的“数学及其应用”国际会议。