Mathematical Sciences: Numerical Solution of the Hele-Shaw Equations

数学科学：Hele-Shaw 方程的数值解

• 批准号: 8913482
• 负责人: Nathaniel Whitaker
• 金额: $ 4.72万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-02-01 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8913482&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Numerical; Solution; Hele

The proposed research involves the numerical solution of various free boundary value problems modelling flows of liquids in Hele-Shaw cells. Such Hele-Shaw flows, as they are called, are important in their own right, and they serve as very useful models of more complicated phenomena involving free boundaries. The proposed research will produce robust numerical schemes capable of handling many different types of nonlinear phenomena whose analytic resolution is currently impossible. The phenomenon of "fingering" of one fluid as it flows into another is a common, easily observed occurrence that is very difficult to describe quantitatively. The proposed research will suggest and evaluate different kinds of methods for studying numerically the set of mathematical equations that govern the evolution in time of an unstable finger. A successful numerical scheme for this particular problem will have much broader applicability to a host of problems in fluid dynamics.

拟议的研究涉及的数值解 模拟液体流动的各种自由边值问题 在黑尔-肖监狱里 这种黑尔-肖流，就像他们所说的， 它们本身就很重要， 涉及自由边界的更复杂现象的模型。 建议的研究将产生强大的数值方案 能够处理许多不同类型的非线性现象 其解析度目前是不可能的。 一种流体流入时的“指进”现象 另一种是常见的、容易观察到的现象，非常 很难定量描述。 拟议的研究将 建议并评估不同的学习方法 数值上的一组数学方程， 不稳定手指的时间演化。 一个成功的数字 针对这一特殊问题的方案将有更广泛的 适用于流体动力学中的许多问题。