Numerical Methods for Wave Propagation Problems: Efficient Resolution of Multiple Scales

波传播问题的数值方法：多尺度的有效解决

• 批准号: 0610067
• 负责人: Thomas Hagstrom
• 金额: $ 15万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0610067&HistoricalAwards=false
• 关键词: Numerical; Methods; Wave; Propagation; Problems

The focus of our research will be the detailed study of questions we deem crucial to the development of reliable, efficient, and general computational tools for wave propagation problems. These, in turn, can have long-term impacts on numerous fields in science and engineering. Precisely we will:(i) Further develop accurate methods for truncating the computational domain near regions where full approximations are required, extending the range of application of the successful methods we have previously constructed to inhomogeneous and anisotropic media as well as to multiscale computations; (ii) Construct and analyze novel high-resolution approximation schemes enabling accurate simulations with near-optimal degrees-of-freedom per wavelength, mild time-step stability restrictions, and easy coupling with grid grid generation software to efficiently treat problems in complex geometry; (iii) Apply our methods to difficult problems in aeroacoustics; (iv) Collaborate with other computational scientists who are building andmaintaining high-quality software for simulating waves. Wave propagation phenomena are ubiquitous in nature. Although waves may be produced by physical processes ranging from electric currents to turbulent flows to massive earthquakes, their basic features allow a unified mathematical description. From the perspective of simulations on modern computers, it is reasonable to hope that generally applicable tools can be constructed which will be useful in answering important questions throughout the basic and applied sciences. The challenge in the computational analysis of waves is that almost all problems of interest exhibit widely varying spatial scales. This is a consequence of the fundamental fact that waves propagate long distances relative to their characteristic dimension, the wavelength. We thus will work to develop methods which allow us to avoid the direct computation of the wave field everywhere along its path, concentrating computational resources only where they are needed. In addition to our work on basic techniques with broad applications, we plan focused studies on problems related to the generation of sound by jets and its propagation into the environment. We believe that the fundamental studies we will carry out can motivate the development of better sound suppression technologies for commercial and military aircraft.

我们研究的重点将是对我们认为对波浪传播问题的可靠，高效和一般计算工具至关重要的问题的详细研究。反过来，这些可能会对科学和工程领域的众多领域产生长期影响。确切地说，我们将：（i）进一步开发准确的方法来截断需要完全近似值的区域附近的计算域，从而扩展了我们以前已经构建到不均匀和各向异性媒体的成功方法的应用范围，以及对多尺度计算的应用； （ii）构建和分析新型的高分辨率近似方案，实现了每次波长，轻度的时间阶段稳定性限制以及与网格网格生成软件的易于耦合，以有效地处理复杂的几何形状问题； （iii）将我们的方法应用于航空声学中的困难问题； （iv）与正在建立和制造高质量软件的其他计算科学家合作，以模拟波浪。波传播现象本质上是普遍存在的。尽管波浪可能是通过从电流到湍流再到巨大地震的物理过程产生的，但它们的基本特征允许统一的数学描述。从现代计算机上的仿真的角度来看，有理由希望可以构建通常适用的工具，这将在回答整个基础科学和应用科学的重要问题上很有用。波浪计算分析的挑战在于，几乎所有感兴趣的问题都表现出广泛变化的空间量表。这是基本事实的结果，即波浪相对于其特征维度（波长）传播长距离。因此，我们将努力开发方法，使我们能够避免在其路径沿途的波浪场直接计算，仅在需要的地方集中计算资源。除了我们在具有广泛应用的基本技术方面的工作外，我们还计划针对与喷气机产生的问题及其传播到环境有关的问题。我们认为，我们将进行的基本研究可以激发为商用和军用飞机提供更好的声音抑制技术的发展。