一种求解二维辐射流体力学方程组的显隐式格式  

An IMEX Method for 2-D Radiation Hydrodynamics

作　　者：房尧立 王一 FANG Yaoli;WANG Yi(Graduate School of China Academy of Engineering Physics,Beijing 100094,China;Institute of Applied Physics and Computational Mathematics,Beijing 100094,China)

机构地区：[1]中国工程物理研究院研究生院,北京100094 [2]北京应用物理与计算数学研究所,北京100094

出　　处：《计算物理》2021年第4期401-417,共17页Chinese Journal of Computational Physics

摘　　要：构造一种求解二维辐射流体力学方程组的有限体积方法。相较于Euler方程组,辐射流体力学方程组的数值格式设计更为困难。不仅辐射压力与辐射能量的强非线性增加了数值计算的难度,而且求解强激波问题也是一大难点。与此同时,物质量以声速传播,辐射量以光速传播也增加了该系统求解的难度。为了克服这些难点,我们使用MUSCL-Hancock方法求解模型的双曲部分,利用TR/BDF2的变换格式求解其扩散部分。给出了灰非平衡扩散模型关于时间的渐近分析。最后,通过数值实验展现该格式的表现。We study a finite volume solver for radiation hydrodynamical models in two space dimensions. For nonlinearity of radiation pressure and radiation energy, it is not a trivial task to develop a numerical scheme for radiation hydrodynamics compared to Euler equations. The current strategy is that the convective part is solved by MUSCL-Hancock schemes, while the diffusive part is handled through an alternative form of TR/BDF2(trapezoidal rule with second order backward difference formula) method. An asymptotic analysis for the grey nonequilibrium diffusion model in time is presented. Numerical experiments are given to show performance of the IMEX scheme.

关 键 词：辐射流体力学 Godunov-type格式 MUSCL Hancock 二维空间维度 

分 类 号：O241.82[理学—计算数学]