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Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers

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  • Yongou Zhang

    (Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430070, China
    School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China)

  • Zhongjian Ling

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China)

  • Hao Du

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China)

  • Qifan Zhang

    (Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430070, China
    School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China)

Abstract

Understanding the effect of vortexes on sound propagation is of great significance in the field of target detection and acoustic imaging. A prediction algorithm of the two-dimensional vortex scattering is realized based on a finite-difference frequency-domain (FDFD) numerical scheme with perfectly matched layers (PML). Firstly, the governing equation for flow–sound interaction is given based on the perturbation theory, and the FDFD program is built. Subsequently, the mesh independence is verified, and the result has a good convergence when the mesh corresponds to over 15 nodes per wavelength. Then, computational parameters of the PML are discussed to achieve better absorbing boundary conditions. Finally, the results of this algorithm are compared with previous literature data. Results show that for different cortex scattering cases, the absorption coefficient should vary linearly with the density of the medium and the incident wave frequency. When the thickness of the PML boundary is greater than 2.5 times the wavelength, the PML boundary can absorb the scattering sound effectively. This provides a reliable algorithm for the numerical study of the effect of vortexes on sound propagation.

Suggested Citation

  • Yongou Zhang & Zhongjian Ling & Hao Du & Qifan Zhang, 2023. "Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers," Mathematics, MDPI, vol. 11(18), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3959-:d:1242227
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    References listed on IDEAS

    as
    1. G. Brillant & F. Chillá & J.-F. Pinton, 2004. "Transmission of sound through a single vortex," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 37(2), pages 229-239, January.
    2. Jesús Flores & Ángel García & Mihaela Negreanu & Eduardo Salete & Francisco Ureña & Antonio M. Vargas, 2022. "Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method," Mathematics, MDPI, vol. 10(3), pages 1-9, January.
    3. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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