Partial differential equations/Numerical analysis
Asynchronous numerical scheme for modeling hyperbolic systems
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 843-847.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.06.010
Toumi, Asma 1; Dufour, Guillaume 1; Perrussel, Ronan 2; Unfer, Thomas 2

1 ONERA, 2, avenue Edouard-Belin, 31400 Toulouse, France
2 Université de Toulouse, LAPLACE, CNRS/UPS/INPT, Toulouse, France
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Toumi, Asma; Dufour, Guillaume; Perrussel, Ronan; Unfer, Thomas. Asynchronous numerical scheme for modeling hyperbolic systems. Comptes Rendus. Mathématique, Volume 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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