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

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.Adaptive Schemes for Deterministic and Stochastic Flow Problem