Helmholtz Equation Applied to the Vertical Fixed Cylinder in Wave Using Boundary Element Method
Abstract
Helmholtz equation is employed to the wide variety of engineering problems. This paper presents using Helmholtz equation to the vertical fixed cylinder against regular wave by the boundary element method (BEM). The results are included the pressure and forces on the cylinder. The present results are compared with available data, and show in good agreement. The results show that up to a certain dimensionless wave length, the wave force has a direct relation with the dimensionless wavelength, while after the force decreases with the increase of the dimensionless wave length.
##Keywords:##
Wave-cylinder interaction, Boundary element method, Helmholtz equation.
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Published
Oct 30, 2016
How to Cite
GHASSEMI, Hassan et al.
Helmholtz Equation Applied to the Vertical Fixed Cylinder in Wave Using Boundary Element Method.
Journal of Ocean, Mechanical and Aerospace -science and engineering-, [S.l.], v. 36, n. 1, p. 7 - 11, oct. 2016.
ISSN 2527-6085.
Available at: <https://isomase.org/Journals/index.php/jomase/article/view/401>. Date accessed: 22 june 2026.
doi: http://dx.doi.org/10.36842/jomase.v36i1.401.
References
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16. Chuang, S.H., Yueh, C.Y. and Huang, L.H. (2015). Dual boundary element model coupled with the dual reciprocity method to determine wave scattering by a concentric cylindrical system mounted on a conical shoal, Engineering Analysis with Boundary Elements, Vol. 56, pp. 30-38.
2. Chen, J.T., Lin, T.W., Chen, I.L, and Lee, Y.J. (2005). Fictitious frequency for the exterior Helmholtz equation subject to the mixed-type boundary condition using BEMs, Mechanics Research Communications, Vol. 32, pp. 75-92.
3. Tamioka, S. and Nishiyama, S. (2010). Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method, Engineering Analysis with Boundary Elements, Vol.34, pp. 393-404.
4. Bin-Mohsin, B. and Lesnic, D. (2011). The method of fundamental solutions for Helmholtz-type equations in composite materials, Computers & Mathematics with Applications, Vol.62, pp. 4377-4390.
5. Dogan, H., Popov, V. and Ooi, E.H. (2012). The radial basis integral equation method for solving the Helmholtz equation, Engineering Analysis with Boundary Elements, Vol. 36, pp. 934-943.
6. Darbas, M., Darrigrand, E. and Lafranche, Y. (2013). Combining analytic preconditioner and Fast Multiple Method for the 3-D Helmholtz equation, Journal of Computational Physics, Vol. 236, pp. 289-316. 7. Casenave, F., Ern, A. and Sylvand, G. (2014). Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain, Journal of Computational Physics, Vol. 257, pp. 627-644. 8. Hosseinzadeh, H. and Dehghan, M. (2014). A new scheme based on boundary elements method to solve linear Helmholtz and semi-linear Poisson’s equations, Engineering Analysis with Boundary Elements, Vol. 43, pp. 124-135.
9. Loeffler, C.F., Mansur, W.J., Barcelos, H.D.M. and Bulcao, A. (2015). Solving Helmholtz problems with the boundary element method using direct radial basis function interpolation, Engineering Analysis with Boundary Elements, Vol. 61, pp. 218-225, 2015.
10. Ghassemi, H., Kohansal, A.R. and Iranmanseh, M. (2016). Solutions of the Acoustic Problem in the 3D Form of the Helmholtz Equation Using DRBEM, International Journal of Multidisciplinary Science and Engineering, Vol.7, pp. 8-13.
11. Au, M.C. and Brebbia, C.A. (1983). Diffraction of water waves for vertical cylinders using boundary elements, Applied Mathematical Modeling, Vol. 7, pp. 106-114, 1983.
12. Kim, N.H., Park, M.S. and Yang, S.B. (2007). Wave force analysis of the vertical circular cylinder by Boundary Element Method, KSCE Journal of Civil Engineering, Vol. 11, pp. 31-35.
13. Zhu, S. (1993). A new DRBEM model for wave refraction and diffraction, Engineering Analysis with Boundary Elements, Vol. 12, pp. 261-274.
14. Kim, N.H. and Cao, T.N.T. (2008). Wave Force Analysis of the Two Vertical Cylinders by Boundary Element Method, KSCE Journal of Civil Engineering, Vol. 12, pp.359-366.
15. Ketabdari, M.J., Abaiee, M.M. and Ahmadi, A. (2013). 3D numerical modeling of wave forces on tandem fixed cylinders using the BEM, Journal of Marine Science and application, Vol. 12, pp. 279-285.
16. Chuang, S.H., Yueh, C.Y. and Huang, L.H. (2015). Dual boundary element model coupled with the dual reciprocity method to determine wave scattering by a concentric cylindrical system mounted on a conical shoal, Engineering Analysis with Boundary Elements, Vol. 56, pp. 30-38.
