RUI: Low Mach Number Flows in an Infinite Domain

[321728 . de Pillis]纳维-斯托克斯方程对于洋流、天气模式、喷气发动机噪声、物体在流体中运动产生的波以及许多其他物理现象的建模至关重要。Navier-Stokes方程可以用来模拟可压缩、微压缩和不可压缩的流体流动。这些方程非常复杂，必须采用数值解法而不是解析解法。每种流动类型（例如，可压缩与不可压缩）的数值计算都有其特定的困难。在这个项目中，重点是在无限域中微压缩Navier-Stokes方程解的有效确定。这些解表示低马赫数流，是声音传播建模的关键。在微可压缩流的情况下，解中至少存在两个时间尺度。两个或更多时间尺度的存在通常使有效的数值计算难以实现。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，某些包含多个时间尺度的解决方案可以扩展为更简单的解决方案的总和（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，这个解和的一般行为被检查。这个项目的目标是开发、实现和分析一个数值求解器，它利用了对这些解的行为的理解。将与现有数值格式的效率和精度进行比较。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.