Treatment of Sharp Edges & Corners in the Acoustic Boundary Element Method under Neumann Boundary Condition

Abstract

Boundary element method in acoustics for Neumann boundary condition problems including sharp edges & corners is investigated. In previous acoustic boundary element method, acoustic pressure and normal velocity are the two variables at sharp edges & corners. However, the normal velocity at sharp edges & corners is discontinuous due to the indefinite normal vector. To avoid the indefinite normal vector and the discontinuous normal velocity at sharp edges & corners, normal vector of elemental node is defined and applied in the numer- ical implementation. Then the normal velocity is trans- formed to velocity which is unique even at sharp edges & corners. Such treatments make sure that all variables in the acoustic boundary element method are definite. Computational efficiency and accuracy of the new model are demonstrated by threecases of interioracousticprob- lems for which analytical solutionscan be found and one classical exterior acoustic radiation problem. Curvilin- ear quadrilateral isoparametric elements are applied in the computation. It is found that the numerical results agree with corresponding analytical solutions quite well. keyword: Boundary element method, Sharp edge, Sharp corner, Normal velocity, Normal vector, Helmholtz integral equation