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Consistency, accuracy and entropic behaviour of remeshed particle methods

Lisl Weynans 1, 2 Adrien Magni 3 
2 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
3 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : In this paper we analyse the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. We re-write particle methods with remeshing in the finite-difference formalism. This allow us to prove the consistency of these methods, and accuracy properties related to the accuracy of interpolation kernels. Cottet and Magni devised recently TVD remeshing schemes for particle methods. We extend these results to the non linear 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.
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Submitted on : Tuesday, October 11, 2011 - 2:10:32 PM
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Lisl Weynans, Adrien Magni. Consistency, accuracy and entropic behaviour of remeshed particle methods. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2011, 47 (1), pp.57-81. ⟨10.1051/m2an/2012019⟩. ⟨inria-00631076⟩

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