Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations
| Autor: | Arnaud Duran, Fabien Marche |
|---|---|
| Přispěvatelé: | Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-13-BS01-0009,BoND,Frontières, numérique, dispersion.(2013), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2015 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Basis (linear algebra) Discretization Mathematical analysis shallow water dispersive Discontinuous Galerkin method Simple (abstract algebra) Free surface discontinuous-Galerkin Degree of a polynomial Shallow water equations [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics Variable (mathematics) |
| Zdroj: | Communications in Computational Physics Communications in Computational Physics, Global Science Press, 2015, 17 (3), pp.721-760. ⟨10.4208/cicp.150414.101014a⟩ Communications in Computational Physics, 2015, 17 (3), pp.721-760. ⟨10.4208/cicp.150414.101014a⟩ |
| ISSN: | 1991-7120 1815-2406 |
| DOI: | 10.4208/cicp.150414.101014a |
| Popis: | 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 apre-balancedformulation 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. |
| Databáze: | OpenAIRE |
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