Developing efficient finite element techniques for atmospheric sound propagation

Abstract

Applying the finite element method to problems in atmospheric sound propagation is challenging because the use of a standard approach, such as meshing the entire domain, quickly delivers a prohibitive problem size. The finite element method does, however, offer many advantages such as the ability to accommodate continuous variations in fluid properties, as well as scattering from obstacles of complex geometry. This means the method is ideally placed to provide benchmark solutions for more popular approaches. Accordingly, ideas for developing more efficient versions of the finite element method suitable for atmospheric sound propagation are explored here for two dimensional problems. These are based on the use of one dimensional normal mode expansions, and then mapping these on to two dimensional solutions for non-uniform obstacles. The normal mode solution for a range independent inhomogenous moving fluid is presented, and numerical mode matching techniques are introduced to demonstrate the inclusion of a point source. The extension of these mode matching methods to accommodate scattering from obstacles is then discussed, and the conditions necessary to deliver efficient finite element solutions are reviewed.