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Journal Articles Journal of Computational Acoustics Year : 2012

The Variational Theory of Complex Rays for three-dimensional Helmholtz problems

Abstract

This article proposes an extension of the Variational Theory of Complex Rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective \emph{a priori} selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry.
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Dates and versions

hal-00714312 , version 1 (04-07-2012)

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Louis Kovalevsky, Pierre Ladevèze, Hervé Riou, Marc Bonnet. The Variational Theory of Complex Rays for three-dimensional Helmholtz problems. Journal of Computational Acoustics, 2012, 20, 125021 (25 p.). ⟨10.1142/S0218396X1250021X⟩. ⟨hal-00714312⟩
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