RUI: Low Mach Number Flows in an Infinite Domain

小行星9321728 Navier-Stokes方程是洋流、天气模式、喷气发动机噪音、物体通过流体运动产生的波浪以及许多其他物理现象建模的核心。 Navier-Stokes方程可用于模拟可压缩、轻微可压缩和不可压缩的流体流动。 方程是足够复杂的数值，而不是解析解的方法必须采用。 每种类型流量的数值计算（例如，可压缩与不可压缩）存在其自身的特殊困难。 在这个项目中，重点是在一个无限区域中的轻微可压缩Navier-Stokes方程的解的有效确定。 这些解决方案代表低马赫数流动，是关键的声音传播的建模。 在微可压缩流的情况下，至少有两个时间尺度存在于解决方案。 两个或更多个时间尺度的存在通常使得难以实现有效的数值计算。 然而，在这个项目中，多个时间尺度的存在实际上是有利的。 最近的研究表明，包含多个时间尺度的某些解可以扩展为更简单的解的总和（即， 基本上包含一个时间尺度的解决方案）。 在这个项目的分析部分，这个总和的解决方案的一般行为进行检查。 这个项目的目标是开发，实施和分析一个数值求解器，利用这些解决方案的行为的理解。 这个新的实现的效率和精度将与现有的数值方案进行比较。 该求解器有望在效率、准确性和易用性方面优于现有的求解器。

9321728 de Pillis The Navier-Stokes equations are central to the modeling of ocean currents, weather patterns, jet engine noise, waves generated by the movement of an object through a fluid, and many other physical phenomena. The Navier-Stokes equations can be used to model compressible, slightly compressible, and incompressible fluid flow. The equations are complicated enough that numerical as opposed to analytical solution methods must be employed. The numerical calculation of each type of flow (e.g., compressible versus incompressible) presents its own particular difficulties. In this project, the focus is on the efficient determination of the solutions to the slightly compressible Navier-Stokes equations in an infinite domain. These solutions represent low Mach number flow, and are pivotal to the modeling of sound propagation. In the case of slightly compressible flow, at least two time scales are present in the solutions. The presence of the two or more time scales generally makes efficient numerical calculations difficult to achieve. In this project, however, the presence of multiple time scales is actually used advantageously. Recent research has shown how certain solutions containing multiple time scales can be expanded into a sum of simpler solutions (i.e., solutions containing essentially one time scale). In the analytic portion of this project, the general behavior of this sum of solutions is examined. The goal of this project is to develop, implement and analyze a numerical solver which makes use of this understanding of the behavior of these solutions. The efficiency and accuracy of this new implementation will be compared with that of existing numerical schemes. This solver is expected to be an improvement over existing solvers in efficiency, accuracy and ease of use.