High-quality boundary conditions are an essential part of computational aeroacoustics (CAA). Because a computational domain is necessarily finite in size, numerical boundary conditions play several diverse roles in numerical simulation. First and foremost, they must assist any outgoing disturbances to leave the computational domain with little or no reflection. The alternative is to use a perfectly absorbing layer as a numerical boundary treatment. Such a layer absorbs all outgoing disturbances without reflection as in the case of an anechoic chamber. In addition, if the problem to be simulated involves incoming disturbances, then these disturbances must be generated by the boundary conditions prescribed at the outer boundary of the computational domain. Furthermore, if there are flows that are originated from outside the computational domain, they must be reproduced by the boundary treatment as well. In this chapter, methods to construct numerical boundary conditions that perform these various functions are discussed.
Boundaries with Incoming Disturbances
In many aeroacoustics problems, there are disturbances that enter the computational domain through the outer boundary. For example, in computing the scattering characteristics of an object, acoustic waves must be allowed to pass through the boundary of a computational domain in a specified direction and intensity. The scattering phenomenon produces scattered waves. These waves are radiated in all directions. They propagate to the far field as outgoing waves through the boundary of the computational domain. In this case, the boundary condition of the computational domain must take on the responsibility of generating the incoming sound and, at the same time, they also serve as radiation boundary conditions for the scattered waves. To handle the dual role, a split-variable method has been developed. The essence of this method is discussed below.