An ALE formulation for explicit Runge-Kutta Residual Distribution

Luca Arpaia (1) , Mario Ricchiuto (1, 2) , Remi Abgrall (1)

1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
2 IMB - Institut de Mathématiques de Bordeaux

In this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation. In particular we propose an ALE framework for the genuinely explicit residual distribution schemes of (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). The discretizations obtained are thoroughly tested on a large number of benchmarks.

Dans ce travail on considére la resolution de lois de conservation sur maillages mobiles par une formulation Arbitrary Lagrangian Eulerian (ALE). On propose en particulier un formalisme ALE pour les schémas RD explicites de (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). Les schémas ainsi obtenus sont testés sur des nombreux benchmarks.

Domains: Numerical Analysis [math.NA]; Fluid Dynamics [physics.flu-dyn]

Luca Arpaia, Mario Ricchiuto, Remi Abgrall. An ALE formulation for explicit Runge-Kutta Residual Distribution. [Research Report] RR-8367, INRIA. 2013. ⟨hal-00863154v2⟩