An efficient Wave Based Method for 2D acoustic problems containing corner singularities

作者：Deckers Elke^*; Bergen Bart; Van Genechten Bert; Vandepitte Dirk; Desmet Wim

来源：Computer Methods in Applied Mechanics and Engineering, 2012, 241: 286-301.

DOI：10.1016/j.cma.2012.06.009

• Helmholtz equation
• 2D acoustics
• Corner singularities
• Wave Based Method
• Trefftz

The Wave Based Method is an efficient alternative prediction technique based on a Trefftz approach which, as compared to element-based methods, can be applied in a wider frequency range at a reasonable cost. This paper discusses the use of this method for the particular case of 2D acoustic problems where singularities are present in the corners of the acoustic domain. The conventional set of expansion functions used to approximate the dynamic pressure field is extended with special purpose functions that incorporate the singular behaviour in the region around the singular corners. This enrichment comes with a beneficial convergence rate while only a small increase of computational effort is incurred. This is illustrated for various problem settings, including different combinations of both homogeneous and non-homogeneous boundary conditions and bounded as well as unbounded problems are considered.

• 出版日期2012