Nonstandard High Order Multigrid Techniques with Applications to Laminar Diffusion Flame Simulations

非标准高阶多重网格技术及其在层流扩散火焰模拟中的应用

• 批准号: 9988165
• 负责人: Jun Zhang
• 金额: $ 25.4万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988165&HistoricalAwards=false
• 关键词: Nonstandard; Order; Multigrid; Techniques; Applications

This project will design efficient geometric multigrid methods using intermediate grids to solve convection diffusion problems discretized by high order compact schemes. The use of intermediate grids aims at reducing discrepancy between the solutions obtained on differentgrids. Symbolic computation packages will be used to derive a fourth order finite difference scheme on the intermediate grids. Special relaxation schemes and intergrid transfer operators will be developed.The nonstandard multigrid method with high order discretization schemes will be used in the numerical simulation of laminar diffusion flames. The use of intermediate grids is expected to alleviate the problem haunting existing multigrid methods in the flame simulation, in which the converged coarse grid correction is not in the convergence domain of the fine grid Newton iteration.This project requires both symbolic and numerical computation techniques. The successful development of a useful symbolic computation procedure will greatly promote the awareness and use of symbolic computation packages in numerical computation community.The results of this research project will make important contribution to the understanding of geometric multigrid solution of convectiondiffusion problems, and of the applications of high order compactschemes to realistic flow simulations. Efficient solution of such problems is central to many numerical simulations in computational fluid dynamics. The fast laminar diffusion flame code is useful in combustion and environment protection. Certain U.S. industries related to commercial burners, pollutant tracking, car and airplane manufacturing, combustion, can benefit from this research.

本项目将设计高效的几何多重网格方法，使用中间网格来求解由高阶紧致格式离散的对流扩散问题。使用中间网格的目的是减少在不同网格上得到的解之间的差异。使用符号计算程序在中间网格上推导出四阶有限差分格式。将开发特殊的松弛格式和网格间转移算子。层流扩散火焰的数值模拟将采用具有高精度离散格式的非标准多重网格方法。中间网格的使用有望缓解现有多重网格方法在火焰模拟中的问题，即收敛的粗网格校正不在细网格牛顿迭代的收敛域内。该项目需要符号和数值计算技术。一个实用的符号计算程序的成功开发将极大地促进符号计算包在数值计算界的认识和使用，本研究项目的成果将对理解对流扩散问题的几何多重网格解以及高阶紧致格式在实际流动模拟中的应用做出重要贡献。这类问题的有效解是计算流体力学中许多数值模拟的核心。快速层流扩散火焰程序在燃烧和环境保护中具有重要的应用价值。与商业燃烧器、污染物跟踪、汽车和飞机制造、燃烧相关的某些美国行业可以从这项研究中受益。