An Easy Control of the Artificial Numerical Viscosity to Get Discrete Entropy Inequalities When Approximating Hyperbolic Systems of Conservation Laws

Autor: Arnaud Duran, Christophe Berthon, Khaled Saleh

Publikováno v: Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy ISBN: 9783030388690

When considering the numerical approximation of weak solutions of systems of conservation laws, the derivation of discrete entropy inequalities is, in general, very difficult to obtain. In the present work, we present a suitable control of the numeri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d07e0ad8ddf73a6cdcacb54d49f81b5f
https://doi.org/10.1007/978-3-030-38870-6_5

Semi-implicit staggered mesh scheme for the multi-layer shallow water system

Autor: Arnaud Duran, Rémy Baraille, Jean-Paul Vila

Publikováno v: Comptes Rendus. Mathématique
Comptes Rendus. Mathématique, Académie des sciences (Paris), 2017, 355 (12), pp.1298-1306. ⟨10.1016/j.crma.2017.09.011⟩

International audience; We present a semi-implicit scheme for a two-dimensional multilayer shallow water system with density stratification, formulated on general staggered meshes. The main result of the present note concerns the control of the mecha

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9633e80d8b05f436b20ff8099e3138ff
https://doi.org/10.1016/j.crma.2017.09.011

Modelling coastal wave trains and wave breaking

Autor: G.L. Richard, Arnaud Duran

Publikováno v: Ocean Modelling. 147:101581

The model of coastal waves based on the depth-averaging of the large eddy simulation equations (Kazakova and Richard, 2019) is extended to the case of regular and irregular wave trains. To take into account a stronger turbulence, the third moment of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bdc0ce3a7581a96c4310695821baa0b2
https://doi.org/10.1016/j.ocemod.2020.101581

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Autor: Arnaud Duran, Fabien Marche

Publikováno v: 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⟩

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81768fdf427243abe4faa6ad59eff58c
https://doi.org/10.4208/cicp.150414.101014a

On the well-balanced numerical discretization of shallow water equations on unstructured meshes

Autor: Fabien Marche, Qiuhua Liang, Arnaud Duran

Publikováno v: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2013, 235, pp.565--586. ⟨10.1016/j.jcp.2012.10.033⟩

International audience; We consider in this work a finite volume numerical approximation of weak solutions of the shallow water equations with varying topography, on unstructured meshes. Relying on an alternative formulation of the shallow water equa

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::487eee8e01f6a3f179e2dd744bae876a
https://doi.org/10.1016/j.jcp.2012.10.033