Mathematical Sciences: Finite Element Methods For Incompressible, Viscous Flows

数学科学：不可压缩粘性流的有限元方法

• 批准号: 9400057
• 负责人: William Layton
• 金额: $ 6万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400057&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Element; Methods

Layton The investigator studies solution algorithms for viscous, incompressible flows at high Reynolds number. This problem includes the interrelated difficulties of: boundary and interior layers, dominating and sensitive nonlinearities, highly nonsymmetric and possibly indefinite linear systems and the incompressibility constraint. Solution algorithms are studied for each of these difficulties from one aspect to another. (For example, it would not be satisfactory to simplify the linear system at the expense of increasing the difficult of resolving the nonlinearity.) The general approach is (1) higher order methods (2) point adaptivity and unstructured meshes, (3) stabilized finite element discretizations, (4) stabilized, multi-level, multi-step Newton methods for the nonlinearity, (5) robust (= uniform in Re), parallel, iterative solvers for the linear systems, and (6) full mathematical support for all algorithmic developments. Fluid flow problems at high Reynolds number arise in many technological and scientific applications, such as convection in the melted region in the solidification of materials, transport and dispersion of pollutants in air and groundwater and simulations of climatic changes. Since exact solution of these equations is impossible, computer based simulation of fluid flow problems is essential in accurately predicting, and ultimately controlling the quantities which are of interest. Accurate and reliable simulation of high Reynolds number flow problems is a very challenging scientific problem which is studied in this research. In large scale applications this involves the study of algorithms which are highly parallel.

莱顿 调查研究解决方案的算法粘性，不可压缩流在高雷诺数。 这个问题包括相互关联的困难：边界层和内层，主导和敏感的非线性，高度非对称和可能不确定的线性系统和不可压缩性约束。 从一个方面到另一个方面研究了每一个困难的解决算法。(For例如，以增加解决非线性问题的难度为代价来简化线性系统是不令人满意的。）一般的方法是（1）高阶方法（2）点自适应和非结构网格，（3）稳定的有限元离散化，（4）稳定的，多层次，多步牛顿法的非线性，（5）鲁棒的（=均匀Re），并行，迭代求解器的线性系统，和（6）所有的算法开发的完整的数学支持。 高雷诺数下的流体流动问题出现在许多技术和科学应用中，例如材料凝固过程中熔化区域的对流、空气和地下水中污染物的传输和扩散以及气候变化的模拟。 由于这些方程的精确解是不可能的，基于计算机的流体流动问题的模拟在准确预测和最终控制感兴趣的量方面是必不可少的。 准确可靠地模拟高雷诺数流动问题是一个非常具有挑战性的科学问题，这是本研究所要研究的。 在大规模应用中，这涉及到高度并行的算法的研究。