Simulation of nonlinear wave run-up with a high-order Boussinesq model |
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| Authors: | David R Fuhrman Per A Madsen |
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| Institution: | Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark |
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| Abstract: | This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach. |
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| Keywords: | Boussinesq equations Run-up Tsunami Finite difference method Extrapolating boundary technique |
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