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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2014

High order Semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues

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Georges-Henri Cottet
Franck Pérignon
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Christophe Picard

Abstract

This paper is devoted to the definition, analysis and implementation of semi-Lagrangian methods as they result from particle methods combined with remeshing. We give a complete consistency analysis of these methods, based on the regularity and momentum properties of the remeshing kernels, and a stability analysis of a large class of second and fourth order methods. This analysis is supplemented by numerical illustrations. We also describe a general approach to implement these methods in the context of hybrid computing and investigate their performance on GPU processors as a function of their order of accuracy.
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Dates and versions

hal-00991150 , version 1 (14-05-2014)

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Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Pérignon, Christophe Picard. High order Semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues. ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (4), pp.1029-1060. ⟨10.1051/m2an/2014009⟩. ⟨hal-00991150⟩
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