A combination of Residual Distribution and the Active Flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations

Rémi Abgrall

Published 2020-11-25Version 1

We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the Residual Distribution one, and the Active Flux formulations. This new class of scheme is proved to satisfy a Lax-Wendroff like theorem. We also develop a method to perform non linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.