Novel Methods for Numerical Simulation of Wave Propagation in Inhomogeneous Media

非均匀介质中波传播数值模拟的新方法

• 批准号: 2110407
• 负责人: Lise-Marie Imbert-Gerard
• 金额: $ 33.48万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110407&HistoricalAwards=false
• 关键词: Novel; Methods; Numerical; Simulation; Wave; Novel; Methods; Numerical; Simulation; Wave

Many types of waves propagate through inhomogeneous media, such as light waves propagating in the air, where the particle density depends on the height of the atmospheric layers, acoustic waves propagating in the water, where the salinity depends on the ocean depth, or seismic waves propagating in the earth, where the density of geological layers varies depending on their sedimentation history. The scientific thrust of this project is devoted to the development of numerical simulation tools for wave propagation in anisotropic and inhomogeneous media. The principal application targeted is wave propagation in aeroacoustics to study the noise generated by a turbo-reactor in a flow, where the source of inhomogeneity and anisotropy is the non-uniform air flow around the engine. Yet the methods considered will also apply to other variable material properties such as permittivity or sound speed.This project is concerned with the further development of a class of Trefftz-like methods. Trefftz methods rely, in broad terms, on the idea of approximating solutions to partial differential equations using local basis functions, which are exact solutions of the governing equation, making explicit use of information about the ambient medium. Instead, the new methods rely on basis functions that are approximate solutions of the governing equation rather than exact solutions. The PI therefore refers to such methods as quasi-Trefftz methods. The goal of this project is two-fold: (1) investigate the properties of the quasi-Trefftz methods when using a high-order local basis; (2) investigate numerical integration techniques for the corresponding basis functions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

许多类型的波浪通过异质媒体传播，例如在空气中传播的光波，粒子密度取决于大气层的高度，在水中传播的声波，在水中，盐度取决于海洋深度或地震波在地球中传播的地震波，在地球的密度中，依赖于其泥沙的密度依赖于它们的密度依赖于它们的沉积物的历史。该项目的科学推力致力于开发各向异性和不均匀媒体中波传播的数值模拟工具。针对性的主要应用是航空声学中的波传播，以研究涡轮反应器在流动中产生的噪声，其中不均匀性和各向异性的来源是发动机周围的不均匀气流。然而，所考虑的方法也将适用于其他可变材料属性，例如介电常数或声速。该项目与类似Trefftz的方法的进一步开发有关。 TREFFTZ方法在广义上依赖于使用局部基础函数将解决方案近似偏微分方程的想法，这些函数是管理方程的确切解决方案，从而明确使用了有关环境介质的信息。取而代之的是，新方法依赖于近似管理方程的解决方案而不是精确解决方案的基础函数。因此，PI是指诸如准特夫兹方法之类的方法。该项目的目的是两个方面：（1）使用高阶局部基础时研究准特性方法的属性； （2）研究相应基础函数的数值集成技术。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准通过评估来获得支持的。