Mathematical Sciences: Analysis & Calculation of Solutions to the Acoustics Equations

数学科学：分析

• 批准号: 9002768
• 负责人: Noel Walkington
• 金额: $ 4.35万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002768&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; & Calculation

The principal investigator will continue his research into the numerical solution of the acoustic equations that govern the generation and propagation of noise by aircraft. Specifically he will study two major problem areas: the development and implementation of numerical codes that can resolve the acoustic equations in the presence of vorticity, and the posing of physically correct and numerically consistent boundary conditions for flow problems in unbounded domains. The vorticity that is generated near sharp edges like the engines or the landing gear creates difficulties for conventional numerical codes, and so the principal investigator is developing a finite element code that obviates many of the problems associated with vorticity. With regard to the posing of proper boundary conditions it is necessary to set boundary conditions on an artificial interface, in order to make the computations for a problem in an infinite domain tractable. The problem of aircraft noise during landings and takeoffs is of growing concern to many communities and local governments. One obvious solution of this problem is to design airplanes whose engines and exterior surfaces operate at minimal noise levels. As one can imagine easily this is a complicated phenomenon, and so mathematicians and aerodynamicists often resort to modelling the complex sets of equations with simpler ones, and then solving the approximate equations numerically. However this can be tricky too, since aircraft generate vorticity, which influences the noise pattern and which often defeats conventional numerical schemes. The principal investigator is working on numerical algorithms that can handle the vorticity and the unboundedness of the flow domain in a computationally efficient manner.

首席研究员将继续研究控制飞机噪声产生和传播的声学方程的数值解。 具体来说，他将研究两个主要问题领域：开发和实施能够在存在涡量的情况下求解声学方程的数值代码，以及为无界域中的流动问题提出物理正确且数值一致的边界条件。 在发动机或起落架等尖锐边缘附近产生的涡量给传统的数字代码带来了困难，因此主要研究人员正在开发一种有限元代码，以消除与涡量相关的许多问题。 关于适当边界条件的提出，有必要在人工界面上设置边界条件，以便使无限域中的问题的计算易于处理。 飞机着陆和起飞过程中的噪音问题越来越受到许多社区和地方政府的关注。 这个问题的一个明显的解决方案是设计发动机和外表面以最低噪音水平运行的飞机。 人们可以很容易地想象到这是一种复杂的现象，因此数学家和空气动力学家经常求助于用更简单的方程组对复杂的方程组进行建模，然后对近似方程进行数值求解。 然而，这也可能很棘手，因为飞机会产生涡度，这会影响噪声模式，并且通常会破坏传统的数值方案。 首席研究员正在研究能够以计算有效的方式处理流域的涡度和无界性的数值算法。