2020/03/20 by Caterina Bassi, Luca Bonaventura, Bassi, Caterina +5 · 1 citation
Physics and Astronomy · Earth and Planetary Sciences · #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Coastal and Marine Dynamics
paper · pdf · doi:10.48550/arxiv.2003.14309
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN)\nmodel for the description of dispersive water waves. Contrarily to the\nclassical Boussinesq-type models, it contains only first order derivatives,\nthus allowing to overcome the numerical difficulties and the severe time step\nrestrictions arising from higher order terms. The proposed model reduces to the\noriginal SGN model when an artificial sound speed tends to infinity. Moreover,\nit is endowed with an energy conservation law from which the energy\nconservation law associated with the original SGN model is retrieved when the\nartificial sound speed goes to infinity. The governing partial differential\nequations are then solved at the aid of high order ADER discontinuous Galerkin\nfinite element schemes. The new model has been successfully validated against\nnumerical and experimental results, for both flat and non-flat bottom. For\nbottom topographies with large variations, the new model proposed in this paper\nprovides more accurate results with respect to the hyperbolic reformulation of\nthe SGN model with the mild bottom approximation recently proposed in "C.\nEscalante, M. Dumbser and M.J. Castro. An efficient hyperbolic relaxation\nsystem for dispersive non-hydrostatic water waves and its solution with high\norder discontinuous Galerkin schemes, Journal of Computational Physics 2018".\n