Abstract
A meshless numerical model for nonlinear free surface water waves is presented in this paper, to demonstrate that the localized method of fundamental solutions (MFS) is a stable, accurate tool for simulating and modeling the nonlinear propagation of gravity waves in the approximation of irrotational, incompressible and the fluid is assumed to be inviscid. Using the fundamental solution of the Laplace equation as the radial basis function, the problem is solved by collocation of boundary points. The present model is a first applied to simulate the generation of monochromatic periodic gravity waves by applying a semi-analytical or semi-numerical method to resolve the nonlinear gravity waves propagation, have verified by different orders of linear problems. As an application we are interested in the mechanisms of the interaction of a rectangular obstacle fixed on the bottom of the numerical wave tank (NWT) in the presence of the waves in order to provide information on attenuation process, and validate the numerical tool that we have developed for the treatment of this problem.
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References
Craik, A.D.D.: The origins of water wave theory. Annu. Rev. Fluid Mech. 36, 1–28 (2004)
Xiao, L.F., Yang, J.M., Peng, T., Tao, T.: A free surface interpolation approach for rapid simulation of short waves in meshless numerical wave tank based on the radial basis function. J. Comput. Phys. 307, 203–224 (2016)
Loukili, M., Mordane, S., Chagdali, M.: Formulation semi analytique de la propagation non linéaire de la houle. XIVèmes Journées Nationales Génie Côtier – Génie Civil (2016)
Zhang, X., Song, K.Z., Lu, M.W., Liu, X.: Meshless methods based on collocation with radial basis functions. Comput. Mech. 26, 333–343 (2000)
Hongmei, Y., Liu, Y.: An efficient high-order boundary element method for nonlinear wave-wave and wave-body interactions. J. Comput. Phys. 230, 402–424 (2011)
Wu, N.J., Tsay, T.K., Young, D.L.: Meshless simulation for fully nonlinear water waves. Int. J. Numer. Methods Fluids 50, 219–234 (2006)
Wu, N.J., Tsay, T.K., Young, D.L.: Computation of nonlinear free-surface flows by a meshless numerical method. J. Waterways Port Coast Ocean Eng. 134, 97–103 (2008)
Loukili, M., Mordane, S.: Modélisation de l’interaction houle-marche rectangulaire par la méthode des solutions fondamentales. 13ème Congrès de Mécanique Meknès, MAROC (2017)
Xiao, L.F., Yang, J.M., Peng, T., Li, J.: A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water. Int. J. Numer. Methods Fluids 61, 165–184 (2009)
Mordane, S.: Contribution numérique à la résolution du problème d’interaction houle-obstacles. Thèse de Doctorat d’Etat, Université Hassan II- Mohammedia, Casablanca, Maroc (2001)
Orlansky, I.: A simple boundary condition for unbonded hyperbolic flows. J. Comput. Phys. 21(3), 251–269 (1976). https://doi.org/10.1016/0021-9991(76)90023-1
Chahine, C.: Contribution à l’étude expérimentale de la houle avec des obstacles immergés. Thèse de Doctorat d’état, Université Hassan II-Mohammedia, Casablanca-Maroc (2002)
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Loukili, M., El Aarabi, L., Mordane, S. (2019). Computation of Nonlinear Free-Surface Flows Using the Method of Fundamental Solutions. In: Silhavy, R. (eds) Software Engineering and Algorithms in Intelligent Systems. CSOC2018 2018. Advances in Intelligent Systems and Computing, vol 763. Springer, Cham. https://doi.org/10.1007/978-3-319-91186-1_44
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DOI: https://doi.org/10.1007/978-3-319-91186-1_44
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