Internal wave generation in an improved two-dimensional Boussinesq model |
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| Institution: | 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;3. Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing 210044, China;1. Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt;2. Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia;3. Mathematics Department, Faculty of Science, Beni-Suef University, Egypt |
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| Abstract: | A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model. |
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