[Schéma numérique asynchrone du second ordre pour la modélisation des systèmes hyperboliques]
Nous présentons une méthode asynchrone pour l'intégration explicite des équations aux dérivées partielles multi-échelles. Cette méthode est limitée par une condition CFL locale plutôt que par la condition CFL globale classique. Tout d'abord, nous avons développé un schéma d'Euler asynchrone pour la discrétisation de l'équation de transport et nous avons prouvé que le schéma asynchrone est convergent au premier ordre. Pour la montée en ordre, nous avons proposé un schéma Runge–Kutta 2 asynchrone, dérivé d'un schéma RK2 classique, pour obtenir un schéma numériquement d'ordre 2.
We present an asynchronous method for the explicit integration of multi-scale partial differential equations. This method is restricted by a local CFL condition rather than the traditional global CFL condition. First, we developed an upwind asynchronous forward Euler scheme for the transport equation and we proved that the asynchronous scheme is first order convergent. To improve the convergence rate of the asynchronous scheme, we derived an asynchronous Runge–Kutta 2 scheme from a standard explicit Runge–Kutta method.
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@article{CRMATH_2015__353_9_843_0,
author = {Toumi, Asma and Dufour, Guillaume and Perrussel, Ronan and Unfer, Thomas},
title = {Asynchronous numerical scheme for modeling hyperbolic systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {843--847},
publisher = {Elsevier},
volume = {353},
number = {9},
year = {2015},
doi = {10.1016/j.crma.2015.06.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.010/}
}
TY - JOUR AU - Toumi, Asma AU - Dufour, Guillaume AU - Perrussel, Ronan AU - Unfer, Thomas TI - Asynchronous numerical scheme for modeling hyperbolic systems JO - Comptes Rendus. Mathématique PY - 2015 SP - 843 EP - 847 VL - 353 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.06.010/ DO - 10.1016/j.crma.2015.06.010 LA - en ID - CRMATH_2015__353_9_843_0 ER -
%0 Journal Article %A Toumi, Asma %A Dufour, Guillaume %A Perrussel, Ronan %A Unfer, Thomas %T Asynchronous numerical scheme for modeling hyperbolic systems %J Comptes Rendus. Mathématique %D 2015 %P 843-847 %V 353 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.06.010/ %R 10.1016/j.crma.2015.06.010 %G en %F CRMATH_2015__353_9_843_0
Toumi, Asma; Dufour, Guillaume; Perrussel, Ronan; Unfer, Thomas. Asynchronous numerical scheme for modeling hyperbolic systems. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 843-847. doi : 10.1016/j.crma.2015.06.010. http://www.numdam.org/articles/10.1016/j.crma.2015.06.010/
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