Explicit Runge-Kutta Residual Distribution

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. Key-words: numerical analysis, second order schemes, hyperbolic problems, residual distribution, explicit schemes ∗ INRIA Bordeaux Sud-Ouest † INRIA Bordeaux Sud-Ouest in ria -0 04 06 95 8, v er si on 3 25 J ul 2 00 9 Explicit Runge-Kutta Residual Distribution schemes for Time Dependent Problems : second order case Résumé : 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. Mots-clés : numerical analysis, second order schemes, hyperbolic problems, residual distribution, explicit schemes in ria -0 04 06 95 8, v er si on 3 25 J ul 2 00 9 Explicit RK-RD schemes 3