Computational Aeroacoustics (CAA) is a relatively young research area. It began in earnest fewer than twenty years ago. During this time, CAA algorithms have developed rapidly. These methods soon found applications in many areas of aeroacoustics.

The objective of CAA is not simply to develop computational methods, but also to use these methods to solve real practical aeroacoustics problems. It is also a goal of CAA to perform numerical simulation of aeroacoustic phenomena. By analyzing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. Hence, CAA offers a way to obtain a better understanding of the physics of a problem.

Computational Aeroacoustics is not the same as Computational Fluid Dynamics (CFD). In fact, CAA faces a different set of computational challenges, because aeroacoustics problems are intrinsically different from standard aerodynamics and fluid mechanics problems. By definition, aeroacoustics problems are time dependent, whereas aerodynamics and fluid mechanics problems are, in general, time independent or involve only low-frequency unsteadiness.

Computationally, there are two general ways to treat problems with complex geometry. One way is to use unstructured grids. The other is to use overset grids. Overset grids are formed by overlapping structured grids. In this chapter, the basic idea of overset grids methodology and its implementation are discussed.

Basic Concept of Overset Grids

To illustrate the basic idea of overset grids, consider the problem of computing the scattering of acoustic waves by a solid cylinder in two dimensions. In the space around the cylinder, the coordinates of choice for computing the solution is the cylindrical polar coordinates centered at the axis of the cylinder. This coordinate system provides a set of body-fitted coordinates and, hence, a body-fitted mesh when discretized around the cylinder. One significant advantage of using a body-fitted grid is the relative ease in enforcing the no-through-flow wall boundary condition using the ghost point method or other methods. Away from the cylinder, acoustic waves propagate with no preferred direction. The natural coordinate system to use is the Cartesian coordinates. Therefore, to take into account the advantages stated, one may use a polar mesh around the cylinder and a Cartesian mesh away from the cylinder with an overlapping mesh region. The overlapping mesh region is for data transfer from one set of grids to the other and vice versa.

Many aeroacoustics problems involve multiple length and time scales. This should not be difficult to understand. For, in addition to the intrinsic sizes and scales of the noise sources, the acoustic wavelength is an inherent length scale of the problem. In many instances, the length scale of the noise source differs greatly from the acoustic wavelength. This leads to a large disparity in length scales as in classical multiscales problems. For example, in supersonic jet noise, Mach wave radiation is generated by the instability waves of the jet flow. The instability waves are supported by the thin shear layer of the jet. In the region near the nozzle exit, the averaged shear layer thickness is about 0.1D, where D is the jet diameter. The acoustic wavelength, on the other hand, is two or more jet diameters long. Thus, there is an order of magnitude difference between those characteristic lengths. In sound scattering problems, the length scale of the surface geometry of the scatterers may be much smaller than the acoustic wavelength. This occurs very often in edge scattering and diffraction problems. A concrete example is the radiation of fan noise from a jet engine inlet. The acoustic wavelength could be much longer than the radius of the lip of the engine inlet. To obtain an accurate numerical solution of the inlet diffraction problem, a fine mesh is needed around the lip region. Oftentimes, an aeroacoustics problem becomes a multiscales problem because of the change in the physics governing the different parts of the computational domain. An example is the shedding of vortices at the edge of a resonator or a sharp edge of a solid body induced by high-intensity incident sound waves. Away from the solid surface, the fluid is nearly inviscid, but close to the wall, the viscosity effect dominates. The oscillatory motion of the incident sound waves induces a very thin Stokes layer on the solid surface. The Stokes layer rolls up at the corner of a solid surface to form vortices that shed periodically. To simulate the vortex shedding process, therefore, it is necessary to use very fine mesh close to the solid surface and around the corner to resolve the Stokes layer. But away from the solid surface, a coarse mesh with 7 mesh points per acoustic wavelength is all that is needed to capture the sound waves accurately using the 7-point stencil dispersion-relation-preserving (DRP) scheme.