Fast Algorithms for Models of Incompressible Flow

不可压缩流模型的快速算法

• 批准号: 0726017
• 负责人: Howard Elman
• 金额: $ 27万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0726017&HistoricalAwards=false
• 关键词: Fast; Algorithms; Models; Incompressible; Flow

FAST ALGORITHMS FOR MODELS OF INCOMPRESSIBLE FLOWHoward C. ElmanDepartment of Computer Science andInstitute for Advanced Computer StudiesUniversity of MarylandCollege Park, MD 20742This project concerns development, analysis and testing of efficient algorithms for solving systems of equations arising from models of flow of incompressible fluids. The development of such algorithms is of broad potential use for understanding scientific phenomena and constructing engineering tools involving fluid flows. Examples include biological flows such as blood flow in the heart or veins and arteries; dispersal of environmental pollutants in rivers or groundwater; design of microfluidics devices, which are used in diagnosis of diseases and identification of pathogens in fluids; and atmospheric and oceanic phenomena.Understanding such processes through purely experimental techniques is prohibitively expensive or impossible, whereas the use of modelling together with computational solution enables basic understanding of the physics by providing information about quantities such as flow rates, pressures, and concentrations of solvents. This research involves the development of fast computational algorithms that allows models to be resolved quickly and inexpensively by computer simulation.The research is focused on two classes of problems: algebraic eigenvalue problems that arise from analysis of the stability of solutions of the steady-state incompressible Navier-Stokes equations; and linear and nonlinear systems of equations that arise when thermal and chemical effects are coupled with models of incompressible flow. For both problem classes, discretization leads to the requirement to solve a sequence of large-scale linear systems of equations. We study efficient preconditioning techniques for these systems that take advantage of the structure of the problems. In addition to the impact on applied science, development of efficient solvers addresses fundamental mathematical and computational questions such as the impact of mathematical structure on algorithm development and the identification of stable flows in complex geometries.

不可压缩流体流动模型的快速算法在C.Elman计算机科学系和马里兰大学高级计算机研究所，MD 20742这个项目涉及高效算法的开发、分析和测试，用于求解由不可压缩流体流动模型产生的方程组。这种算法的发展在理解科学现象和构建涉及流体流动的工程工具方面具有广泛的潜在用途。例如生物流动，如心脏或静脉和动脉中的血液流动；环境污染物在河流或地下水中的扩散；用于诊断疾病和识别流体中病原体的微流体设备的设计；以及大气和海洋现象。通过纯粹的实验技术理解这些过程的成本高得令人望而却步，甚至不可能，而将建模与计算解结合使用，通过提供有关流量、压力和溶剂浓度等量的信息，使人们能够基本了解物理学。这项研究涉及到快速计算算法的发展，使得通过计算机模拟可以快速和廉价地求解模型。研究集中在两类问题：由稳态不可压缩Navier-Stokes方程的解的稳定性分析产生的代数特征值问题；以及当热和化学效应与不可压缩流动模型耦合时产生的线性和非线性方程组。对于这两类问题，离散化都需要求解一系列大规模的线性方程组。我们研究了这些系统的有效的预条件技术，利用问题的结构优势。除了对应用科学的影响外，高效求解器的开发还解决了基本的数学和计算问题，如数学结构对算法开发的影响和复杂几何形状中稳定流动的识别。