Abstract
The Lagrange-Flux schemes are Eulerian finite volume schemes that make use of an approximate Riemann solver in Lagrangian description with particular upwind convective fluxes. They have been recently designed as variant formulations of Lagrange-remap schemes that provide better HPC performance on modern multicore processors, see [De Vuyst et al., OGST 71(6), 2016]. Actually Lagrange-Flux schemes show several advantages compared to Lagrange-remap schemes, especially for multidimensional problems: they do not require the computation of deformed Lagrangian cells or mesh intersections as usually done in the remapping process. The paper focuses on the entropy property of Lagrange-Flux schemes in their semi-discrete in space form, for one-dimensional problems and for the compressible Euler equations as example. We provide pseudo-viscosity pressure terms that ensure entropy production of order \(O(|\varDelta u|^3)\), where \(|\varDelta u|\) represents a velocity jump at a cell interface. Pseudo-viscosity terms are also designed to vanish into expansion regions as it is the case for rarefaction waves.
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Acknowledgements
The work is part of the LRC MESO joint lab between CEA DAM DIF and CMLA. The author would like to thank Dr. Jean-Philippe Braeunig for valuable discussions on this subject. The author also thanks the anonymous reviewers for their constructive comments.
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De Vuyst, F. (2017). Lagrange-Flux Schemes and the Entropy Property. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_16
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DOI: https://doi.org/10.1007/978-3-319-57397-7_16
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