Search

Your search keyword '"Nicolas Seguin"' showing total 4 results
Start Over Author "Nicolas Seguin" Journal mathematical models and methods in applied sciences
4 results on '"Nicolas Seguin"'

1. A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles

Author

Nicolas Seguin, Frédéric Coquel, Khaled Saleh, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Mécanique des Fluides, Energies et Environnement (EDF R&D MFEE), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Numerical Analysis, Geophysics and Ecology (ANGE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Finite volume method, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Discretization, Applied Mathematics, Numerical analysis, Mathematical analysis, relaxation techniques, Dissipation, Solver, Riemann problem, Riemann solver, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], symbols.namesake, AMS subject classification: 76S05, 35L60, 35F55, Modeling and Simulation, symbols, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Relaxation (approximation), Discontinuous nozzle flows, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the cross-section and on an approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous sections with arbitrary large jumps. To do so, we introduce, in the first step of the relaxation solver, a singular dissipation measure superposed on the standing wave, which enables us to control the approximate speeds of sound and thus the time step, even for extreme initial data.

Published
2014
Full Text
View/download PDF

2. GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION

Author

Pierre-Arnaud Raviart, Frédéric Coquel, Christophe Chalons, Edwige Godlewski, and Nicolas Seguin

Subjects
Applied Mathematics, Mathematical analysis, Type (model theory), Euler system, Solver, Hyperbolic systems, Riemann solver, symbols.namesake, Consistency (statistics), Simple (abstract algebra), Modeling and Simulation, symbols, Parameter dependent, Mathematics
Abstract

Well-balanced or asymptotic preserving schemes are receiving an increasing amount of interest. This paper gives a precise setting for studying both properties in the case of Euler system with friction. We derive a simple solver which, by construction, preserves discrete equilibria and reproduces at the discrete level the same asymptotic behavior as that of the solutions of the continuous system. Numerical illustrations are convincing and show that not all methods share these properties.

Published
2010
Full Text
View/download PDF

3. ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS

Author

Julien Vovelle, Nicolas Seguin, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Conservation law, Finite volume method, Applied Mathematics, Numerical analysis, discontinuous coefficient, Mathematical analysis, Godunov's scheme, 010103 numerical & computational mathematics, 01 natural sciences, Nonlinear conservation law, 010101 applied mathematics, resonance, Modeling and Simulation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, finite volume, Entropy (arrow of time), Stationary state, Mathematics
Abstract

We study here a model of conservative nonlinear conservation law with a flux function with discontinuous coefficients, namely the equation ut + (k(x)u(1 - u))x = 0. It is a particular entropy condition on the line of discontinuity of the coefficient k which ensures the uniqueness of the entropy solution. This condition is discussed and justified. On the other hand, we perform a numerical analysis of the problem. Two finite volume schemes, the Godunov scheme and the VFRoe-ncv scheme, are proposed to simulate the conservation law. They are compared with two finite volume methods classically used in an industrial context. Several tests confirm the good behavior of both new schemes, especially through the discontinuity of permeability k (whereas a loss of accuracy may be detected when industrial methods are performed). Moreover, a modified MUSCL method which accounts for stationary states is introduced.

Published
2003
Full Text
View/download PDF

4. RELAXATION OF FLUID SYSTEMS

Author

Nicolas Seguin, Edwige Godlewski, Frédéric Coquel, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and LRC Manon (Laboratoire de recherche conventionné -- CEA/DM2S-LJLL -- Modélisation et approximation numérique orientées pour l'énergie nucléaire)

Subjects
010103 numerical & computational mathematics, 01 natural sciences, Godunov-type scheme, symbols.namesake, finite volume scheme, Hyperbolic system, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, fluid model, 0101 mathematics, Mathematics, Applied Mathematics, Numerical analysis, Degenerate energy levels, Mathematical analysis, Godunov's scheme, relaxation approximation, Solver, 16. Peace & justice, 010101 applied mathematics, Riemann problem, Lagrangian relaxation, Modeling and Simulation, symbols, Euler's formula, Relaxation (approximation), AMSC: 35L60, 65M08, 76M12, 35B25, 35Q35, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We propose a relaxation framework for general fluid models which can be understood as a natural ex- tension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibirum model. Discrete entropy inequalities are established under a natural Gibbs principle.

Published
2012
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results