扩散方程的单元中心型有限体积格式研究

本项目面向Z箍缩(Z-pinch)驱动惯性约束聚变（ICF）研究的数值模拟需求，针对辐射磁流体力学方程组中的能量方程和磁场演化方程数值求解中的精度、效率与置信度等问题，研究极端物理条件下多边形和多面体网格上扩散方程的单元中心型有限体积格式，包括高精度保正加权算法、线性精确格式、单元泛函极小化格式以及相关的理论分析等内容，为相关应用程序的研制储备高置信度算法，为提升我国的Z-pinch驱动ICF数值模拟能力作出贡献。同时，本项目的研究成果也可用于激光驱动的ICF研究，与油藏模拟、地下污染物处理等实际应用问题的研究有很强的相关性。

This project aims to the increasing demand of numerical simulation in Z-pinch-driven inertial confinement fusion(ICF) research and focuses on the accuracy, efficiency and confidence issues for the numerical solution of the energy equation and magnetic evolution equation in radiation magnetohydrodynamics. The main concern is placed on the study of cell-centered finite volume schemes for diffusion equations on polygonal and polyhedral grids under extreme physical conditions. The contents include high accuracy and positivity-preserving weighted algorithm, the linearity preserving scheme, the cell functional minimization scheme and the related theoretical analysis, which will contribute to enhance our ability in numerical simulation for Z-pinch-driven ICF research. Meanwhile, this project can also contribute to laser-driven ICF research and has strong correlation to many practical problems such as reservoir simulation,underground pollutants handling and so on.