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In this paper, we propose a novel development in the context of entropystable finite-volume/finite-difference schemes. In the first part, we focus onthe construction of high-order entropy conservative fluxes. Already in[LMR2002], the authors have generalized the second order accurate entropyconservative numerical fluxes proposed by Tadmor to high-order ($2p$) by asimple centered linear combination. We generalize this result additionally tonon-centered flux combinations which is in particular favorable if non-periodicboundary conditions are needed. In the second part, a Lax-Wendroff theorem forthe combination of these fluxes and the entropy dissipation steering from[Klein2022] is proven. In numerical simulations, we verify all of ourtheoretical findings.

Entropy conservative high-order fluxes in the presence of boundaries