非规则网格上各向异性扩散问题的高性能计算方法

项目名称： 非规则网格上各向异性扩散问题的高性能计算方法

项目编号： No.11271054

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 崔霞

作者单位： 北京应用物理与计算数学研究所

项目金额： 68万元

中文摘要： 多维辐射磁流体力学问题中的扩散，通常具有非线性、间断、强耦合和强各向异性的特点，并需在大变形网格上求解；各向异性问题的求解与各向同性相比，在保持精度和物理性质等方面存在更大困难。本项目针对应用问题需求，开展具有上述特征的非规则网格上各向异性扩散问题的高性能计算方法研究。(1)从适应多物理耦合的角度出发，基于任意多边形网格，针对各向异性扩散问题，设计新的健壮的单元中心型有限体积格式，使之具有较高精度和保持守恒性等重要物理性质；(2)研究非线性扩散的非线性格式，设计与之匹配的具有超线性收敛速度的健壮的迭代方法，实现问题的高效求解；(3)进行离散格式的稳定性、收敛性和迭代法的收敛速度、精度等理论分析，研制程序模块，为多维辐射磁流体力学应用中的相关数值模拟提供高效高精度的扩散计算方法及其理论支持。项目的主要特色和创新在于：兼顾扩散的各向异性和网格的非规则性，设计高效计算方法，实现高性能数值模拟。

中文关键词： 各向异性扩散；非规则网格；有限体积方法；健壮性；高性能

英文摘要： Diffusion problems in multi-dimensional radiation magneto hydrodynamics are often characterized with nonlinearity, discontinuity, strong coupling and high anisotropy, and often need to be solved on severely deformed meshes. Compared with isotropic problems, there exist more difficulties on keeping perfect accuracy and embodying physical properties in the numerical solution of anisotropic diffusion problems. Aimed at meeting the needs of practical simulations, studies on the high performance computation methods for anisotropic diffusion problems with such characters on irregular meshes will be carried out in this project. The following contents are included. (1) For the purpose of being adaptive to multi-physical coupled procedures, new robust cell-centered finite volume schemes will be designed for the anisotropic diffusion problems on arbitrary polygonal meshes, which will have high accuracy and preserve the fundamental physical features such as conservation and so on. (2) Nonlinear schemes for nonlinear anisotropic diffusion problems will be studied, and robust iteration methods matching such nonlinear schemes and having superlinear convergent ratio will be designed to realize the efficient solution of the nonlinear problems. (3) Theoretical analysis will be made on the stability and convergence properties of

英文关键词： anisotropic diffusion；irregular meshes；finite volume method；robustness；high performance