Mathematical Sciences: Numerical Solution of Stiff Ordinary Differential Equations and the Navier-Stokes Equation

本研究属于数值分析领域， 流体动力学的数学理论。 部分工作将 研究刚性常微分方程组， 有界区间 这种方程出现在研究近 无粘性流体流动问题，半导体物理， 反应扩散现象 数值方法来解决这些问题 非线性方程将基于延拓和 线性化 二维不可压Navier-Stokes方程 还将考虑空间维度。 将对结果进行测试 在最小的尺度上。 这项决议是必要的 在高雷诺数的流动问题中。 这项工作的结果将直接关系到 均匀湍流的数值模拟 他们还将 导致更好的流体流动算法的发展 问题和增加的物理洞察力的机制， 稳定和过渡。

This research lies in the areas of numerical analysis and the mathematical theory of fluid dynamics. Part of the work will examine stiff systems of ordinary differential equations on a bounded interval. Such equations arise in the study of nearly inviscid fluid flow problems, semiconductor physics, and reaction-diffusion phenomena. Numerical methods to solve these nonlinear equations will be developed based on continuation and linearization. The incompressible Navier-Stokes equations in two space dimensions will also be considered. Results will be tested at the level of the smallest scales. This resolution is needed in flow problems with high Reynolds numbers. Results of this work will be immediately relevant to the numerical simulation of homogeneous turbulence. They will also lead to the development of better algorithms for fluid flow problems and increased physical insight into the mechanisms of stability and transition.