Boundary Element Analysis of Single and Multidomain Problems in Acoustics.

A numerical technique based on the boundary element method for the solution of single-domain linear interior acoustic boundary value problems governed by the Helmholtz equation for time-harmonic acoustic waved has been developed. A boundary element computer code is developed to study the acoustic fields in an enclosed acoustic region. The development of the method is general, but the area of application is broad. The specific applications considered are the prediction of acoustic behavior in an acoustical cavity and transmission loss of various expansion-type mufflers and acoustical silencers. The method is shown to be accurate in studying the acoustic response in an enclosed cavity and is particularly useful in predicting the transmission loss of an acoustical filter in the frequency region where the one-dimensional plane-wave theory is invalid. The validity and the usefulness of the technique is demonstrated using comparisons with experimental, analytical and other numerical results. Both axisymmetric and fully three-dimensional geometries are considered in the study. The analysis capability and applicability of the boundary element method are also extended to multidomain problems in which the interior acoustic region can be divided into a few subdomains. The formulation of the multidomain boundary element procedure is the same as that for the single-domain boundary element procedure in which the interior boundary integral equation is applied to each subdomain. The solution at the interface between each subdomain is coupled by the continuity constraints. The overall system of equations is assembled using the algebraic equations obtained from each subdomain. The acoustic variables on the boundary, as well as at the interface between each subdomain, is obtained by solving the resulting algebraic system of equations. A variety of acoustic cavities and muffler configurations can be analyzed best by means of this procedure for which the conventional single-domain boundary element procedure would encounter numerical difficulty if used. The multidomain boundary element procedure is further extended to include analysis of the coupled interior/exterior acoustic problems. Such problems may include the acoustic transmission-radiation problems. The formulation of these problems is handled in a way similar to the interior multidomain formulation except it utilizes both the interior and exterior boundary integral equations. The interior boundary integral equation is applied to a finite internal region, while the exterior boundary integral equation is applied to an infinite external region. The solution at the interface between the interior and exterior regions is coupled together by the continuity constraint equations. Thus, the problem can be solved as a continuous field problem to obtain a solution at any point either in the interior or the exterior domain.