辐射扩散问题的节点型有限体积格式研究

本项目面向惯性约束聚变（ICF）研究的数值模拟需求，针对辐射流体力学方程组中的三温能量方程数值求解中的精度、效率与置信度等问题，研究极端物理和几何条件下多边形/多面体网格上扩散方程的节点型有限体积格式，包括节点型保对称线性精确格式、节点型保正格式、一般网格条件下Q1型有限体积元的理论分析、节点型扩散格式在三温能量方程求解中的应用等内容，为相关应用程序的研制探索新的数值模拟途径，为提升我国的ICF数值模拟能力作出贡献。同时，本项目的研究成果也可应用于油藏模拟、地下污染物处理等实际应用问题。

For the increasing demand of numerical simulation in inertial confinement fusion (ICF) research, this project focuses on the accuracy, efficiency and confidence issues for the numerical solution of the three temperature energy equations in radiation hydrodynamics. It aims to the study of vertex-centered finite volume schemes for diffusion equations on polygonal/polyhedral meshes under extreme physical and geometric conditions. The contents include the symmetric vertex-centered and linearity-preserving schemes, the vertex-centered and positivity-preserving schemes, the analysis of Q1 finite volume element method on general quadrilateral meshes, the application of vertex-centered schemes in the numerical solution of three temperature energy equations and so on. This project will contribute to enhance our ability in numerical simulation for ICF research. Meanwhile, it can also contribute to many practical applications such as reservoir simulation, underground pollutants handling and so on.