Bonnet-Bendhia, A. S.; Dahi, L.; Luneville, E.; Pagneux, V. Acoustic diffraction by a plate in a uniform flow. (English) Zbl 1023.76044 Math. Models Methods Appl. Sci. 12, No. 5, 625-647 (2002). Summary: We present a mathematical framework for the problem of acoustic diffraction by a plate located in a duct, in the presence of a uniform flow. The model is based on a velocity potential representation outside a vortex sheet which is induced by the trailing edge of the plate. Using limiting absorption techniques and singular functions decompositions, we show how to get a theoretical and numerical well-suited formulation. Cited in 4 Documents MSC: 76Q05 Hydro- and aero-acoustics 35Q35 PDEs in connection with fluid mechanics 35P99 Spectral theory and eigenvalue problems for partial differential equations Keywords:Kutta condition; convergence; dissipative model problem; Fredholm alternative; uniqueness; nodal finite element approximation; acoustic diffraction; plate; uniform flow; velocity potential representation; vortex sheet; limiting absorption techniques; singular functions decompositions PDFBibTeX XMLCite \textit{A. S. Bonnet-Bendhia} et al., Math. Models Methods Appl. Sci. 12, No. 5, 625--647 (2002; Zbl 1023.76044) Full Text: DOI References: [1] Bechert D., Acustica 33 pp 287– (1975) [2] DOI: 10.1002/mma.1670170502 · Zbl 0817.35109 · doi:10.1002/mma.1670170502 [3] DOI: 10.1017/S0022112075000584 · Zbl 0294.76029 · doi:10.1017/S0022112075000584 [4] DOI: 10.1017/S0022112058000148 · doi:10.1017/S0022112058000148 [5] DOI: 10.1146/annurev.fl.17.010185.002211 · doi:10.1146/annurev.fl.17.010185.002211 [6] DOI: 10.1017/S0022112081001602 · Zbl 0472.76002 · doi:10.1017/S0022112081001602 [7] DOI: 10.1017/S0022112076000864 · Zbl 0344.76051 · doi:10.1017/S0022112076000864 [8] Jaoua M., Math. Comput. 36 pp 404– (1981) [9] DOI: 10.1093/imamat/9.1.114 · Zbl 0242.76046 · doi:10.1093/imamat/9.1.114 [10] Lohrengel S., Université de Paris pp 6– (1998) [11] DOI: 10.1006/jsvi.1998.1711 · doi:10.1006/jsvi.1998.1711 [12] DOI: 10.1016/0022-460X(90)90659-N · doi:10.1016/0022-460X(90)90659-N [13] DOI: 10.1002/sapm1970492167 · Zbl 0218.76062 · doi:10.1002/sapm1970492167 [14] DOI: 10.1017/S0022112081002206 · Zbl 0473.76061 · doi:10.1017/S0022112081002206 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.