期刊
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
卷 17, 期 3, 页码 721-760出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.150414.101014a
关键词
Green-Naghdi equations; discontinuous Galerkin; shallow water equations; wave breaking; nonlinear and dispersive water waves
资金
- French INSU-CNRS (Institut National des Sciences de l'Univers-Centre National de la Recherche Scientifique) program LEFE-MANU (Methodes Mathematiques et Numeriques), project SOLi
- ANR project BoND [ANR-13-BS01-0009-01]
We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, the models are recasted under a pre-balanced formulation and discretized using a nodal expansion basis. Independently from the polynomial degree in the approximation space, the preservation of the motionless steady-states is automatically ensured, and the water height positivity is enforced. A simple numerical procedure devoted to stabilize the computations in the vicinity of broken waves is also described. The validity of the resulting model is assessed through extensive numerical validations.
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