Bonnet-Ben Dhia, A. S.; Mercier, J. F.; Millot, F.; Pernet, S. A low-Mach number model for time-harmonic acoustics in arbitrary flows. (English) Zbl 1407.76139 J. Comput. Appl. Math. 234, No. 6, 1868-1875 (2010). Summary: This paper concerns the finite element simulation of the diffraction of a time-harmonic acoustic wave in the presence of an arbitrary mean flow. Considering the equation for the perturbation of displacement (due to Galbrun), we derive a low-Mach number formulation of the problem which is proved to be of Fredholm type and is therefore well suited for discretization by classical Lagrange finite elements. Numerical experiments are done in the case of a potential flow for which an exact approach is available, and a good agreement is observed. Cited in 2 Documents MSC: 76Q05 Hydro- and aero-acoustics 76M10 Finite element methods applied to problems in fluid mechanics 35Q35 PDEs in connection with fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs Keywords:aeroacoustics; scattering of sound in flows; low-Mach number model; Galbrun’s equation; Fredholm alternative; finite elements PDF BibTeX XML Cite \textit{A. S. Bonnet-Ben Dhia} et al., J. Comput. Appl. Math. 234, No. 6, 1868--1875 (2010; Zbl 1407.76139) Full Text: DOI References: [1] J.P. Coyette, Manuel Théorique ACTRAN, Free Field Technologies, Louvain-la-Neuve, Belgique, 2001 [2] S. Duprey, Etude mathématique et numérique de la propagation acoustique d’un turboréacteur. Ph.D. Thesis, Ecole Doctorale IAEM Lorraine Université Henri Poincaré-Nancy I, 2006 [3] Treyssede, F.; Gabard, G.; Tahar, M.B., A mixed finite element method for acoustic wave propagation in moving fluids based on an eulerian – lagrangian description, J. acoust. soc. am., 113, 705-716, (2003) [4] Bécache, E.; Bonnet-Ben Dhia, A.-S.; Legendre, G., Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow, SIAM J. numer. anal., 44, 1191-1217, (2006) · Zbl 1126.76051 [5] A.S. Bonnet-Ben Dhia, E.M. Duclairoir, J.F. Mercier, Acoustic propagation in a flow: Numerical simulation of the time-harmonic regime, in: Proceedings du CANUM 2006, ESAIM Procs., vol. 22, 2007 · Zbl 1133.76047 [6] E. M. Duclairoir, Rayonnement acoustique dans un écoulement cisaillé: Une méthode d’éléments finis pour la simulation du régime harmonique. Ph.D. Thesis, Ecole Doctorale de l’Ecole Polytechnique, 2007 [7] Poirée, B., LES équations de l’acoustique linéaire et non linéaire dans un écoulement de fluide parfait, Acustica, 57, 5-25, (1985) · Zbl 0634.76080 [8] Bonnet-Ben Dhia, A.S.; Duclairoir, E.M.; Legendre, G.; Mercier, J.F., Time-harmonic acoustic propagation in the presence of a shear flow, J. comput. appl. math., (2007) · Zbl 1112.76068 [9] Peake, N., On applications of high-frequency asymptotics in aeroacoustics, Phil. trans. R. soc. lond. A, 362, 673-693, (2004) · Zbl 1083.76056 [10] Agarwal, A.; Dowling, A.P., Low-frequency acoustic shielding by the silent aircraft airframe, Aiaa j., 45, 2, 358-365, (2007) [11] Costabel, M., A coercive bilinear form for maxwell’s equations, J. math. anal. appl., 157, 527-541, (1991) · Zbl 0738.35095 [12] Panton, R.L., Incompressible flow, (1995), John Wiley and Sons, Inc. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.