Performance of the BEM solution in 3D acoustic wave scattering

Abstract

A fixed cylindrical circular cavity and a cylindrical circular column of fluid of infinite length submerged in a homogeneous fluid medium, and subjected to a pressure point source, for which closed form solutions are known, are used to assess the performance of constant, linear and quadratic boundary elements in the analysis of acoustic scattering. This aim is accomplished by evaluating the error committed by the boundary element method (BEM) for a wide range of frequencies and wave numbers. First, the position of dominant BEM errors in the frequency versus spatial wave number domains are identified and related to the natural modes of vibration of the cylindrical circular inclusion. Then, the errors that occur by using constant, linear and quadratic elements are compared when the inclusion is modelled with the same number of nodes (i.e. maintaining computational cost). Finally, the importance of the position of the nodal points inside discontinuous boundary elements is analysed.