Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes

Remi Abgrall (1, 2) , Adam Larat (1, 2) , Mario Ricchiuto (1, 2)

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 very high order approximation of solutions of the Euler equations. We present a systematic generalization of the Residual Distribution method of \cite{ENORD} to very high order of accuracy, by extending the preliminary work discussed in \cite{abgrallLarat} to systems and hybrid meshes. We present extensive numerical validation for the third and fourth order cases with Lagrange finite elements. In particular, we demonstrate that we an both have a non oscillatory behavior, even for very strong shocks and complex flow patterns, and the expected accuracy on smooth problems.

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Remi Abgrall, Adam Larat, Mario Ricchiuto. Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes. [Research Report] RR-7236, INRIA. 2010, pp.60. ⟨inria-00464799⟩