On the Connection between Residual Distribution Schemes and Flux Reconstruction

Abstract: In this short paper, we are considering the connection between the \emph{Residual Distribution Schemes} (RD) and the \emph{Flux Reconstruction} (FR) approach. We demonstrate that flux reconstruction can be recast into the RD framework and vice versa. Because of this close connection we are able to apply known results from RD schemes to FR methods. In this context we propose a first demonstration of entropy stability for the FR schemes under consideration and show how to construct entropy stable numerical schemes based on our FR methods. Simultaneously, we do not restrict the mesh to tensor structures or triangle elements, but rather allow polygons. The key of our analysis is a proper choice of the correction functions for which we present an approach here.