Treatment of Sharp Edges {\&} Corners in the Acoustic Boundary Element Method under Neumann Boundary Condition
Zai You Yan

doi:10.3970/cmes.2006.013.081
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 13, No. 2, pp. 81-90, 2006
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Keywords Boundary element method, Sharp edge, Sharp corner, Normal velocity, Normal vector, Helmholtz integral equation
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 numerical implementation. Then the normal velocity is transformed 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 three cases of interior acoustic problems for which analytical solutions can be found and one classical exterior acoustic radiation problem. Curvilinear quadrilateral isoparametric elements are applied in the computation. It is found that the numerical results agree with corresponding analytical solutions quite well.
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