Mathematical Sciences: Advanced Numerical Methods for Modeling Fluid Interfaces

数学科学：流体界面建模的高级数值方法

• 批准号: 9104472
• 负责人: Elbridge Puckett
• 金额: $ 6.61万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1994-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104472&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Advanced; Numerical; Methods

This research is concerned with the design and development of numerical methods for modeling fluid interfaces and the application of these methods to the study of fundamental problems in fluid mechanics. An important goal of this work is to develop accurate and efficient algorithms for modeling three dimensional problems. The interface tracking algorithms considered are generally of the volume-of-fluid type. Some generalizations of this type of algorithm, based on conservative shock tracking ideas, are also considered. These algorithms will be used, in conjunction with adaptive mesh refinement and high order numerical methods for approximating solutions of the compressible Euler equations, to study shock wave refraction and the Richtmyer-Meshkov instability. In addition, they will also be used with a second order projection method to study the Rayleigh- Taylor instability in incompressible flow. Studies of fluid dynamics have a long and honorable history, with many applications in engineering, earth and ocean sciences, among others.

本研究涉及流体界面建模数值方法的设计和开发以及这些方法在流体力学基本问题研究中的应用。 这项工作的一个重要目标是开发准确有效的算法来建模三维问题。 所考虑的界面跟踪算法通常是流体体积类型的。 还考虑了基于保守冲击跟踪思想的此类算法的一些概括。 这些算法将与自适应网格细化和用于逼近可压缩欧拉方程解的高阶数值方法结合使用，以研究冲击波折射和 Richtmyer-Meshkov 不稳定性。 此外，它们还将与二阶投影方法一起用于研究不可压缩流中的瑞利-泰勒不稳定性。 流体动力学研究有着悠久而光荣的历史，在工程、地球和海洋科学等领域有许多应用。