# Consistency, accuracy and entropy behaviour of remeshed particle methods

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 47, Issue: 1, page 57-81
- ISSN: 0764-583X

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topWeynans, Lisl, and Magni, Adrien. "Consistency, accuracy and entropy behaviour of remeshed particle methods." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 57-81. <http://eudml.org/doc/222105>.

@article{Weynans2012,

abstract = {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.},

author = {Weynans, Lisl, Magni, Adrien},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Particle methods with remeshing; interpolation kernels; consistency; truncation error; entropy inequalities; total variation; limiters; convergence; particle methods with remeshing; Burgers equation; nonlinear scalar transport equation; infinite domain; finite difference scheme; total-variation diminishing-remeshing scheme; nonlinear conservation law; Euler equation},

language = {eng},

month = {7},

number = {1},

pages = {57-81},

publisher = {EDP Sciences},

title = {Consistency, accuracy and entropy behaviour of remeshed particle methods},

url = {http://eudml.org/doc/222105},

volume = {47},

year = {2012},

}

TY - JOUR

AU - Weynans, Lisl

AU - Magni, Adrien

TI - Consistency, accuracy and entropy behaviour of remeshed particle methods

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/7//

PB - EDP Sciences

VL - 47

IS - 1

SP - 57

EP - 81

AB - 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.

LA - eng

KW - Particle methods with remeshing; interpolation kernels; consistency; truncation error; entropy inequalities; total variation; limiters; convergence; particle methods with remeshing; Burgers equation; nonlinear scalar transport equation; infinite domain; finite difference scheme; total-variation diminishing-remeshing scheme; nonlinear conservation law; Euler equation

UR - http://eudml.org/doc/222105

ER -

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