Boundary Conditions

What boundary conditions to use in a CAA simulation should be given a good deal of thought. In previous chapters, a variety of numerical boundary conditions was discussed. So, for a given aeroacoustic phenomenon, more than one type of boundary condition may be used. For example, for a radiation boundary, one may use radiation boundary conditions based on asymptotic solution. An equally good, and maybe even better boundary condition, is to use the perfectly matched layer (PML) absorbing boundary condition.

Sometimes, the choice of which numerical boundary condition to use is severely limited, unless some new way to enforce the radiation boundary condition is found. For instance, to compute the noise and flow of an imperfectly expanded supersonic jet, an external boundary condition must be imposed that allows the ambient pres­sure, pa, to be specified. At the nozzle exit, the static pressure of the jet, pexit, is specified by the nozzle flow. Now, the enforcement of the nozzle exit boundary condition p = pexit is relatively straightforward. At the external boundary of the computational domain, the boundary condition must perform two different roles. It must allow the outgoing acoustic waves to exit with little reflection. At the same time, it must require the mean static pressure of the numerical solution to take on the valuepa. Most known absorbing boundary conditions do not have this capability. Among all the boundary conditions discussed in this book, it seems that only the asymptotic radiation boundary condition, discussed in Chapter 6 and Chapter 9, is capable of performing the dual functions.

Although it has been mentioned before, it is worthwhile to reemphasize that the external boundary conditions of a CAA simulation must exert the same influence on the computation as in the physical problem. This includes waves generated outside the computational domain, but propagated into the domain as incident waves. The same is true with mean flow and entrainment flow. It is not possible to anticipate what boundary condition requirement one might encounter. Thus, it is necessary to be creative when computing unusual aeroacoustic phenomena.