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[1] Fahy, F., Sound and Structural Vibration: Radiation, Transmission and Response, Else-vier Press: Amsterdam, Heidelberg, 2007.
[2] Junger, M. & Feit, D., Sound, Structures, and Their Interaction: Basic Concepts, 2nd ed., The MIT Press, 1986.
[3] Zienkiewicz, O. & Taylor, R., The Finite Element Method, Volume 1: The Basis, Butterworth Heinemann: Oxford, 2000.
[4] Wu, T., Boundary Element Acoustics. Fundamentals and Computer Codes, WIT Press: Southampton, 2000.
[5] Rokhlin, V., Diagonal forms of translation operators for the Helmholtz equation. Applied and Computational Harmonic Analysis, 1(1), pp. 82–93, 1993. [Crossref]
[6] Gyure, M. & Stalzer, M., A prescription for the multilevel Helmholtz FMM. Computing in Science & Engineering, 5, pp. 39–47, 1998. [Crossref]
[7] Rjasanow, S. & Steinbach, O., The Fast Solution of Boundary Integral Equations, Springer: New York, 2007.
[8] Fischer, M., The Fast Multipole Boundary Element Method and its Application to Structure-Acoustic Field Interaction. PhD thesis, University of Stuttgart, 2004.
[9] Gumerov, N. & Duraiswami, R., Fast Multipole Methods for the Helmholtz Equation in Three Dimensions, Elsevier: Oxford, 2004.
[10] Stephan, E., Boundary integral equations for mixed boundary value problems in R3. Mathematische Nachrichten, 184, pp. 21–53, 1987. [Crossref]
[11] Seybert, A. & Wu, T., Modified Helmholtz integral equation for bodies sitting on an infinite plane. The Journal of the Acoustical Society of America, 85, pp. 19–23, 1989. [Crossref]
[12] Hughes, M. & Chen, K., An efficient preconditioned iterative solver for solving a cou-pled fluid structure interaction problem. International Journal for Computer Mathemat-ics, 81, pp. 583–594, 2004. [Crossref]
[13] Amini, S., Harris, P. & Wilton, D., Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem, Springer: Berlin, 1992.
[14] Brunner, D., Junge, M. & Gaul, L., A comparison of FE-BE coupling schemes for large scale problems with fluid-structure interaction. International Journal for Numerical Methods in Engineering, 77(5), pp. 664–688.
[15] Gaul, L., Kögl, M. & Wagner, M., Boundary Element Methods for Engineers and Scien-tists. An Introductory Course with Advanced Topics, Springer: Berlin, 2003.
[16] Brunner, D., Of, G., Junge, M., Steinbach, O. & Gaul, L., A fast BE-FE coupling for partly immersed bodies. International Journal for Numerical Methods in Engineering, 81(1), pp. 28–47, 2010.
[17] Coifman, R., Rokhlin, V. & Wandzura, S., The fast multipole method for the wave equation: A pedestrian description. Antennas and Propagation Magazine, IEEE 35(3), pp. 7–12, 1993. [Crossref]
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Acadlore takes over the publication of IJCMEM from 2025 Vol. 13, No. 3. The preceding volumes were published under a CC BY 4.0 license by the previous owner, and displayed here as agreed between Acadlore and the previous owner. ✯ : This issue/volume is not published by Acadlore.

Open Access
Research article

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

gaul, l,
brunner, d.,
junge, m.
Institute for Nonlinear Mechanics, Research Group Prof. Gaul, University of Stuttgart, Germany
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 293-305
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: 03-31-2017
View Full Article|Download PDF

Abstract:

The vibration behaviour of ships is noticeably influenced by the surrounding water, which represents a fluid of high density. In this case, the feedback of the fluid pressure onto the structure cannot be neglected and a strong coupling scheme between the fluid domain and the structural domain is necessary. In this work, fast boundary element methods (BEMs) are used to model the semi-infinite fluid domain with the free water surface. Two approaches are compared: A symmetric mixed formulation is applied where a part of the water surface is discretized. The second approach is a formulation with a special half-space fundamental solution, which allows the exact representation of the Dirichlet boundary condition on the free water surface without its discretization. Furthermore, the influence of the compressibility of the water is investigated by comparing the solutions of the Helmholtz and the Laplace equation. The ship itself is modeled with the finite element method (FEM). A binary interface to the commercial finite element package ANSYS is used to import the mass matrix and the stiffness matrix. The coupled problems are formulated using Schur complements. To solve the resulting sys- tem of equations, a combination of a direct solver for the finite element matrix and a preconditioned GMRES for the overall Schur complement is chosen. The applicability of the approach is demonstrated using a realistic model problem.

Keywords: Burton–Miller method, fast multipole method, fluid-structure interaction, half-space BEM, mixed BEM for acoustic domain
References
[1] Fahy, F., Sound and Structural Vibration: Radiation, Transmission and Response, Else-vier Press: Amsterdam, Heidelberg, 2007.
[2] Junger, M. & Feit, D., Sound, Structures, and Their Interaction: Basic Concepts, 2nd ed., The MIT Press, 1986.
[3] Zienkiewicz, O. & Taylor, R., The Finite Element Method, Volume 1: The Basis, Butterworth Heinemann: Oxford, 2000.
[4] Wu, T., Boundary Element Acoustics. Fundamentals and Computer Codes, WIT Press: Southampton, 2000.
[5] Rokhlin, V., Diagonal forms of translation operators for the Helmholtz equation. Applied and Computational Harmonic Analysis, 1(1), pp. 82–93, 1993. [Crossref]
[6] Gyure, M. & Stalzer, M., A prescription for the multilevel Helmholtz FMM. Computing in Science & Engineering, 5, pp. 39–47, 1998. [Crossref]
[7] Rjasanow, S. & Steinbach, O., The Fast Solution of Boundary Integral Equations, Springer: New York, 2007.
[8] Fischer, M., The Fast Multipole Boundary Element Method and its Application to Structure-Acoustic Field Interaction. PhD thesis, University of Stuttgart, 2004.
[9] Gumerov, N. & Duraiswami, R., Fast Multipole Methods for the Helmholtz Equation in Three Dimensions, Elsevier: Oxford, 2004.
[10] Stephan, E., Boundary integral equations for mixed boundary value problems in R3. Mathematische Nachrichten, 184, pp. 21–53, 1987. [Crossref]
[11] Seybert, A. & Wu, T., Modified Helmholtz integral equation for bodies sitting on an infinite plane. The Journal of the Acoustical Society of America, 85, pp. 19–23, 1989. [Crossref]
[12] Hughes, M. & Chen, K., An efficient preconditioned iterative solver for solving a cou-pled fluid structure interaction problem. International Journal for Computer Mathemat-ics, 81, pp. 583–594, 2004. [Crossref]
[13] Amini, S., Harris, P. & Wilton, D., Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem, Springer: Berlin, 1992.
[14] Brunner, D., Junge, M. & Gaul, L., A comparison of FE-BE coupling schemes for large scale problems with fluid-structure interaction. International Journal for Numerical Methods in Engineering, 77(5), pp. 664–688.
[15] Gaul, L., Kögl, M. & Wagner, M., Boundary Element Methods for Engineers and Scien-tists. An Introductory Course with Advanced Topics, Springer: Berlin, 2003.
[16] Brunner, D., Of, G., Junge, M., Steinbach, O. & Gaul, L., A fast BE-FE coupling for partly immersed bodies. International Journal for Numerical Methods in Engineering, 81(1), pp. 28–47, 2010.
[17] Coifman, R., Rokhlin, V. & Wandzura, S., The fast multipole method for the wave equation: A pedestrian description. Antennas and Propagation Magazine, IEEE 35(3), pp. 7–12, 1993. [Crossref]
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L, G., D., B., & M., J. (2017). Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches. Int. J. Comput. Methods Exp. Meas., 5(3), 293-305. https://doi.org/10.2495/CMEM-V5-N3-293-305
G. L, B. D., and J. M., "Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 293-305, 2017. https://doi.org/10.2495/CMEM-V5-N3-293-305
@research-article{L2017AcousticFI,
title={Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches},
author={Gaul, L and Brunner, D. and Junge, M.},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={293-305},
doi={https://doi.org/10.2495/CMEM-V5-N3-293-305}
}
Gaul, L, et al. "Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches." International Journal of Computational Methods and Experimental Measurements, v 5, pp 293-305. doi: https://doi.org/10.2495/CMEM-V5-N3-293-305
Gaul, L, Brunner, D., Junge and M.. "Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 293-305. doi: https://doi.org/10.2495/CMEM-V5-N3-293-305
GAUL L， BRUNNER D， JUNGE M. Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 293-305. https://doi.org/10.2495/CMEM-V5-N3-293-305