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Explicit Runge-Kutta Residual Distribution schemes for Time Dependent Problems: second order case

Mario Ricchiuto 1, 2 Remi Abgrall 1, 2
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
CNRS - Centre National de la Recherche Scientifique : UMR5800, UB - Université de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : In this paper we construct spatially consistent second order explicit discretizations for time dependent hyperbolic problems, starting from a given Residual Distribution (RD) discrete approximation of the steady operator. We explore the properties of the RD mass matrices necessary to achieve consistency in space, and finally show how to make use of second order mass lumping to obtain second order explicit schemes. The discussion is particularly relevant for schemes of the residual distribution type which we will use for all our numerical experiments. However, similar ideas can be used in the context of residual based finite volume discretizations.
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https://hal.inria.fr/inria-00406958
Contributor : Mario Ricchiuto <>
Submitted on : Saturday, July 25, 2009 - 1:41:30 AM
Last modification on : Thursday, February 11, 2021 - 2:56:37 PM
Long-term archiving on: : Thursday, September 23, 2010 - 5:14:59 PM

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Mario Ricchiuto, Remi Abgrall. Explicit Runge-Kutta Residual Distribution schemes for Time Dependent Problems: second order case. [Research Report] RR-6998, INRIA. 2009. ⟨inria-00406958v3⟩

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