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

首席研究员将继续研究 声学方程的数值解， 飞机噪音的产生和传播。 他特别 将研究两个主要问题领域： 数字代码的实现，可以解决声学 方程中存在的涡度，并提出了 物理上正确和数值上一致的边界条件 在无界域中的流动问题。 这就是 在发动机或起落架等尖锐边缘附近产生 给传统的数字编码带来了困难， 首席研究员正在开发一个有限元代码 这就避免了许多与涡旋相关的问题。 关于适当边界条件的设定， 需要在人工界面上设置边界条件， 为了在无限大的情况下计算问题， 域可处理。 飞机在着陆和起飞时的噪音问题是 越来越多的社区和地方政府的关注。 一 这个问题的一个明显的解决办法是设计这样的飞机， 发动机和外表面以最小的噪音水平运行。 不难想象，这是一个复杂的现象， 所以数学家和空气动力学家经常求助于模型 复杂的方程组与简单的方程组，然后 数值求解近似方程。 然而，这可以 也很棘手，因为飞机会产生涡流， 影响了噪声模式，这往往会击败传统的 数值格式 首席研究员正在研究 数值算法，可以处理涡度和 计算效率高的流域的无界性 方式

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.