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; 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.

首席研究人员将继续他对控制飞机发电和传播的声学方程的数值解决方案的研究。 具体而言，他将研究两个主要问题领域：数值代码的开发和实施，这些代码可以在存在涡度的情况下解决声学方程，以及在无界域中流动问题的物理正确和数值一致的边界条件的摆姿势。 在发动机或起落架等尖锐边缘附近产生的涡度为常规数值代码带来了困难，因此主要研究人员正在开发有限的元素代码，该代码避免了许多与涡度有关的问题。 关于适当的边界条件的摆姿势，必须在人工接口上设置边界条件，以便在无限域中的问题中计算问题。 降落和起飞过程中飞机噪音的问题引起了许多社区和地方政府的关注。 这个问题的一个明显解决方案是设计飞机的发动机和外表面以最小的噪声水平运行。 正如人们可以想象的那样，这是一个复杂的现象，因此数学家和空气动力学家通常会使用更简单的方程式建模一组方程组，然后在数值上求解近似方程。 但是，这也可能很棘手，因为飞机会产生涡度，这会影响噪声模式，并且通常会击败常规数值方案。 主要研究者正在研究可以以计算有效的方式处理流动域的涡度和无限制的数值算法。