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Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation

David Coulette 1, 2 Emmanuel Franck 1, 2 Philippe Helluy 1, 2 Michel Mehrenberger 1, 2 Laurent Navoret 1, 2 
1 TONUS - TOkamaks and NUmerical Simulations
IRMA - Institut de Recherche Mathématique Avancée, Inria Nancy - Grand Est
Abstract : We present a high order scheme for approximating kinetic equations with stiff relaxation. The objective is to provide efficient methods for solving the underlying system of conservation laws. The construction is based on several ingredients: (i) a high order implicit upwind Discontinuous Galerkin approximation of the kinetic equations with easy-to-solve triangular linear systems; (ii) a second order asymptotic-preserving time integration based on symmetry arguments; (iii) a palindromic composition of the second order method for achieving higher orders in time. The method is then tested at orders 2, 4 and 6. It is asymptotic-preserving with respect to the stiff relaxation and accepts high CFL numbers.
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https://hal.archives-ouvertes.fr/hal-01422922
Contributor : Philippe Helluy Connect in order to contact the contributor
Submitted on : Tuesday, December 27, 2016 - 7:29:32 PM
Last modification on : Friday, January 21, 2022 - 3:08:43 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:17:04 PM

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  • HAL Id : hal-01422922, version 1
  • ARXIV : 1612.09422

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David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, Laurent Navoret. Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation. 2016. ⟨hal-01422922⟩

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