An ALE formulation for explicit Runge–Kutta residual distribution

Luca Arpaia, Mario Ricchiuto, Rémi Abgrall
2015
In this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation of the Runge-Kutta Residual Distribution (RD) schemes of Ricchiuto and Abgrall (J Comput Phys 229(16):5653-5691, 2010). Up to the authors knowledge, the problem of recasting RD schemes into ALE framework has been solved with first order explicit schemes and with second order implicit schemes. Our resulting scheme is explicit and second order
more » ... ate when computing discontinuous solutions. Abstract: 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 J. Comput.Phys 229, 2010). The discretizations obtained are thoroughly tested on a large number of benchmarks Résumé : Dans ce travail on considère 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 J. Comput.Phys 229, 2010). Les schémas ainsi obtenus sont testés sur des nombreux benchmarks.
doi:10.5167/uzh-121483 fatcat:h4aoheme3fa2td3rhiibngnpw4