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A formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical acoustics, first-order, and multiple-order edge diffraction components. An existing secondary-source model for edge diffraction from finite edges is extended to handle multiple diffraction of all orders. It is shown that the multiple-order diffraction component can be found via the solution to an integral equation formulated on pairs of edge points. This gives what can be called an edge source signal. In a subsequent step, this edge source signal is propagated to yield a multiple-order diffracted field, taking all diffraction orders into account. Numerical experiments demonstrate accurate response for frequencies down to 0 for thin plates and a cube. No problems with irregular frequencies, as happen with the Kirchhoff-Helmholtz integral equation, are observed for this formulation. For the axisymmetric scattering from a circular disc, a highly effective symmetric formulation results, and results agree with reference solutions across the entire frequency range.

The scattering of sound by convex bodies with rigid surfaces can be modeled accurately without any wavenumber restriction using an edge source integral equation (ESIE) [A. Asheim and U. P. Svensson, J. Acoust. Soc. Am. 133 (2013) 3681-3691]. This edge diffraction-based approach has known limitations for non-convex scattering geometries, and the most challenging case might be an aperture in a thin screen. For such apertures, the ESIE predicts that only first-order diffraction occurs because the ESIE has no inclusion of the so-called slope diffraction effect. This effect occurs when the diffraction wave vanishes but its derivative is different from zero. This paper focuses on the low-frequency sound transmission through apertures in screens, as well as into ducts. A reference solution is established with a boundary element (BE) method for the particle velocity field in the aperture, which illustrates the singular behavior near the edges. The field in the aperture is also computed with first-order diffractio...

For the problem of edge diffraction from an edge of finite length a frequency-domain solution, obtained from an analytical time-domain solution, has been presented by Svensson et al. [Acta. Acust. Acust. 95, 568-572]. This formulation takes the form of a Fourier-type integral whose evaluation is expensive in the high frequency range. This paper demonstrates that by using tailored highly oscillatory quadrature methods based on asymptotic properties of the integral, accurate approximations in the high frequency case can be obtained with little computational effort.

In computer simulations of sound in enclosures, diffraction components can be added to geometrical acoustics ones for increased accuracy. A computational problem with diffraction is the large number of higher-order terms that is generated. A recent frequency-domain edge source integral equation (ESIE) efficiently handles the sum of all higher-order diffraction for rigid, external scattering objects, while computing first-order diffraction separately. Here, a time-domain formulation of the same ESIE is presented. An initial version handles higher-order diffraction for separate scattering objects, such as stage ceiling reflectors, and the extension to general geometries is outlined. With this approach, in a first step an incident transient sound field is computed at discretized edge points, including the outgoing directivity. In a second step, the effects of diffraction of arbitrarily high order is handled by solving the IE iteratively, yielding the complete edge source time signals. In a third step, the edge source signals are propagated to receiver points. Numerical issues will be discussed, including discretization strategies and how to handle shadow zone boundary singularities.

A new integral equation for the scattering from rigid, or pressure-release, convex polyhedra and disks is presented. It is based on edge diffraction as a complement to the geometrical acoustics components, and uses directional edge sources as unknowns in the frequency-domain integral equation. Comparisons with reference results show that the new method gives correct results down to 0 Hz in spite of being a geometrically based method [Asheim & Svensson, Report TW610, KU Leuven, Dept. of Computer Science, 2012]. The two-dimensional unknowns are solved for all edges, straight or curved, of the scattering object, but this reduces to a one-dimensional unknown for certain geometries such as axisymmetric scattering from a circular thin disk, or plane-wave incidence onto a polygonal cylinder. The general integral equation can be solved with the regular Nystrom technique, iteratively or by direct inversion. The scattered field is computed in a post-processing stage, and is added to the geometrical acoustics and fi...