Computational and Analytical Problems in Fluid Mechanics

本课题包括流体力学分析与计算方法三个子课题。Krasny、Borgers和Harabetian教授将作为一个小组相互合作。他们将解决以下问题：涡片演化的计算。这个项目是关于扩展所谓的漩涡团法来计算漩涡片的演变。一个计划中的应用是确定在周期性扰动涡片中形成的螺旋的结构。2. 快速椭圆求解器在局部细化网格。本研究将领域分解方法与McCormick开发的FAC算法相结合。这些方法将在流体力学应用中出现的拉普拉斯方程的Neumann问题上进行测试。3. 守恒律系统的数值和解析问题。讨论了小粘性扰动、粘性消失法和接触不连续面不可压缩极限的问题。在这项资助下进行的研究将有可能应用于空气动力学和燃烧研究，并将广泛依赖与非线性偏微分方程相关的计算工具。

This project consists of three subprojects on analytical and computational methods in fluid mechanics. Professors Krasny, Borgers and Harabetian will work in collaboration with each other as a group. They will attack the following problems: 1. Computation of vortex sheet evolution. This project is concerned with extending the so-called vortex blob method for computing vortex sheet evolution. One planned application is to determine the structure of the spiral which forms in a periodically perturbed vortex sheet. 2. Fast elliptic solver on locally refined meshes. This research will combine domain decomposition methods with the FAC algorithm developed by McCormick. These methods will be tested on Neumann problems for Laplace's equation on regions arising in fluid dynamics applications. 3. Numerical and analytical problems for systems of conservation laws. Problems with small viscous perturbations, with vanishing viscosity method, and with the incompressible limit of a contact discontinuity are going to be considered. Research performed under this grant will have potential applications to studies of aerodynamics and combustion, and will rely extensively on computational tools related to nonlinear partial differential equations.