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. I 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.
@article{M2AN_2013__47_1_57_0,
author = {Weynans, Lisl and Magni, Adrien},
title = {Consistency, accuracy and entropy behaviour of remeshed particle methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {57-81},
doi = {10.1051/m2an/2012019},
mrnumber = {2968695},
zbl = {1278.65136},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_1_57_0}
}
Weynans, Lisl; Magni, Adrien. Consistency, accuracy and entropy behaviour of remeshed particle methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 57-81. doi : 10.1051/m2an/2012019. http://gdmltest.u-ga.fr/item/M2AN_2013__47_1_57_0/
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