Lois de Conservations Eulériennes, Lagrangiennes et Méthodes Numériques

Després, Bruno

doi:10.1007/978-3-642-11657-5

Cited by 11 publications

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“…We refer to [4,7] for a detailed review of the Lagrange-remap method and [5,10] for an interpretation of the Lagrange-remap approach as a splitting of operators in the Eulerian frame.…”

Section: Lagrange-remap Algorithmmentioning

confidence: 99%

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A second order anti-diffusive Lagrange-remap scheme for two-component flows

et al. 2011

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Abstract. We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves.Résumé. Nous construisons un algorithme d'ordre deux et non dissipatif pour la résolution approchée deséquations d'Euler de la dynamique des gaz compressiblesà deux constituants en dimension un. Le modèle que nous considérons est celuià cinqéquations proposé et analysé dans [1]. L'algorithme est basé sur [8] qui proposait une résolution approchéeà l'ordre un et non dissipative au moyen d'un splitting de type Lagrange-projection. Dans le présent article, nous décrivons, dans le même formalisme, un algorithme d'ordre deux en temps et en espace, qui préserve des interfaces "parfaites" entre les constituants. Les résultats numériques rapportésà la fin de l'article sont très encourageants ; ils montrent clairement les avantages d'un schéma d'ordre deux pour les ondes vraiment non linéaires.

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“…We refer to [4,7] for a detailed review of the Lagrange-remap method and [5,10] for an interpretation of the Lagrange-remap approach as a splitting of operators in the Eulerian frame.…”

Section: Lagrange-remap Algorithmmentioning

confidence: 99%

“…It consists in writing System (9) under the (vector) form W = W + λG(W) and to replace (4,5,9) here withW…”

Section: Second Order In Timementioning

confidence: 99%

A second order anti-diffusive Lagrange-remap scheme for two-component flows

et al. 2011

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“…JID: AMC [m3Gsc; May 11, 2015;15:46] To show the stability in L 1 it is sufficient to consider that non negative solutions of (69)-(70) satisfy one conservation law. In view of Proposition 9, one readily proves that (69)-(70) imply…”

Section: Article In Pressmentioning

confidence: 99%

“…Let us define a new variable β = Q(x)α = P(x)AU (13) so that (10) recasts as t α + x β = 0. The standard explicit finite volume discretization on a grid with varying mesh size…”

Section: Finite Volumes and Riemann Solvers In One Dimensionmentioning

confidence: 99%

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The structure of well-balanced schemes for Friedrichs systems with linear relaxation

Després

Buet²

2016

Applied Mathematics and Computation

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a b s t r a c tWe study the conservative structure of linear Friedrichs systems with linear relaxation in view of the definition of well-balanced schemes. We introduce a particular global change of basis and show that the change-of-basis matrix can be used to develop a systematic treatment of well-balanced schemes in one dimension. This algebra sheds new light on a family of schemes proposed recently by Gosse (2011). The application to the S n model (a paradigm for the approximation of kinetic equations) for radiation is detailed. The discussion of the singular case is performed, and the 2D extension is shown to be equal to a specific multidimensional scheme proposed in Buet et al. (2012). This work is dedicated to the 2014 celebration of C.D. Munz' scientific accomplishments in the development of numerical methods for various problems in fluid mechanics.

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Lois de Conservations Eulériennes, Lagrangiennes et Méthodes Numériques

Cited by 11 publications

References 0 publications

A second order anti-diffusive Lagrange-remap scheme for two-component flows

A second order anti-diffusive Lagrange-remap scheme for two-component flows

The structure of well-balanced schemes for Friedrichs systems with linear relaxation

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