• CONSISTENCY, ACCURACY AND ENTR...

Result: CONSISTENCY, ACCURACY AND ENTROPY BEHAVIOUR OF REMESHED PARTICLE METHODS

Title:
CONSISTENCY, ACCURACY AND ENTROPY BEHAVIOUR OF REMESHED PARTICLE METHODS
Authors:
WEYNANS, Lisl, MAGNI, Adrien
Source:
Modélisation mathématique et analyse numérique (Imprimé). 47(1):57-81
Publisher Information:
Les Ulis: EDP Sciences, 2013.
Publication Year:
2013
Physical Description:
print, 29 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Approximations et développements, Approximations and expansions, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse numérique, Numerical analysis, Análisis numérico, Approximation numérique, Numerical approximation, Aproximación numérica, Calcul 1 dimension, One-dimensional calculations, Entropie, Entropy, Entropía, Interpolation, Interpolación, Loi conservation, Conservation law, Ley conservación, Modèle mathématique, Mathematical model, Modelo matemático, Méthode particulaire, Particle method, Método partícula, Méthode stochastique, Stochastic method, Método estocástico, Schéma Euler, Euler scheme, Esquema Euler, Solution entropie, Entropy solution, Solución entropía, 35L65, 35L67, 40G05, 41A05, 65C35, 65D05, Méthode Euler
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Univ. Bordeaux, IMB, UMR 5251, 33400 Talence, France
CNRS, IMB, UMR 5251, 33400 Talence, France
INRIA, 33400 Talence, France
Laboratoire Jean Kuntzmann, Université Joseph Fourier, 51 rue des Mathématiques, 38041 Grenoble, France
ISSN:
0764-583X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26900875
Rights:
Copyright 2014 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.26900875
Database:
PASCAL Archive

Further Information

In this paper we analyze the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. As in [G.-H. Cottet and L. Weynans, C. R. Acad. Sci. Paris, Ser. I 343 (2006) 51-56] we re-write particle methods with remeshing in the finite-difference formalism. This allows us to prove the consistency of these methods, and accuracy properties related to the accuracy of interpolation kernels. Cottet and Magni devised recently in [G.-H. Cottet and A. Magni, C. R. Acad. Sci. Paris, Ser. 1 347 (2009) 1367―1372] and [A. Magni and G.-H. Cottet, J. Comput. Phys. 231 (2012) 152-172] TVD remeshing schemes for particle methods. We extend these results to the nonlinear case with arbitrary velocity sign. We present numerical results obtained with these new TVD particle methods for the Euler equations in the case of the Sod shock tube. Then we prove that with these new TVD remeshing schemes the particle methods converge toward the entropy solution of the scalar conservation law.