Evaluation of non-singular BEM algorithms for potential problems

Abstract

Two non-singular boundary element method (BEM) algorithms for two-dimensional

Strongly singular and hypersingular integrals for aeroacoustic incident fields

“…The acoustic sources are extracted from the transient flow field data and then a wave equation, derived from Lighthill's acoustic analogy, is solved to predict the propagation of these acoustic sources. Gloerfelt et al [5] demonstrated that the surface distribution of for hypersingular integrals often results in oscillatory solutions with high errors [25]. He showed that the contribution of a stationary rigid body on the sound generated by unsteady flow is equivalent to a surface distribution of acoustic dipoles computed from the instantaneous pressure fluctuations on the body.…”

“…Curle [3] extended Lighthill's analogy to consider the effect of stationary boundaries present in the turbulent flow on the sound generation. For hypersingular BEM, discontinuous elements that satisfy the continuity requirement in the element interior, but are discontinuous across element boundaries, have been developed [25]. Powell [4] argued that forces acting on a rigid body due to the fluctuating hydrodynamic pressure cannot produce acoustic fluctuations as the boundary is fixed and cannot vibrate.…”

“…In the field of hypersingular BEM, some researchers have successfully applied a 'relaxed continuity' approach, whereby the C 1 continuity requirement to solve hypersingular boundary integrals is relaxed and the source field is instead approximated by a C 0 distribution [22][23][24]. However, using a relaxed continuity approach for hypersingular integrals often results in oscillatory solutions with high errors [25]. For hypersingular BEM, discontinuous elements that satisfy the continuity requirement in the element interior, but are discontinuous across element boundaries, have been developed [25].…”

“…However, using a relaxed continuity approach for hypersingular integrals often results in oscillatory solutions with high errors [25]. For hypersingular BEM, discontinuous elements that satisfy the continuity requirement in the element interior, but are discontinuous across element boundaries, have been developed [25].…”

A self-regularization technique in boundary element method for three-dimensional elastostatics

“…A strategy similar to the use of non-conforming element but with the same size of system matrix as in displacement-BIE, was used in two-dimensional elastodynamics by Gallego and Dominguez (1996). Ribeiro et al (2009) implemented this scheme for two-dimensional potential problems, and 3-D acoustic problems were treated in Liu and Chen (1999) using the scheme. and Dominguez et al (2 0 0 0 ) adopted this strategy for three-dimensional fracture problem where traction-BIE is only applied to elements on the crack surface while for the other elements in the problem, the displacement-BIE is applied.…”