Acoustic waves can usually be described by the wave equation (or the Helmholtz equation). This allowed for the development of flexible numerical analysis tools, such as the finite element method and the boundary element method, in which various acoustical problems with complicated geometries can be modeled. Acoustical applications exist that cannot be modeled by the wave equation because of the small length scales involved. In the derivation of the wave equation, boundary layer effects, located near walls, have been neglected. This simplification does not lead to noticeable errors as long as the geometry is large compared to the boundary layer size. The analysis tool presented in this paper is a finite element that takes the viscous and thermal effects, occurring in the boundary layers, into account. Previously developed tools for these types of acoustical problems were restricted to rather simple geometries. In contrast, the new tool can analyze complicated geometries. This is the major advantage of this new tool, and of the finite element method in general. This paper presents one example that requires the new tool to accurately analyze it. Other applications for which the finite element can be used are the acoustic wave behavior in, for example, MEMS applications.
|Journal||Journaal Nederlands Akoestisch Genootschap|
|Publication status||Published - May 2008|