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Staggered grids and kinetic fluxes for Euler equations

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FKTW05 - Frontiers in numerical analysis of kinetic equations

Of course, there are many performing methods for solving Euler equations, and the analysis of such schemes is quite well-developed. However, for certain applications, or certain regimes, it might be relevant to work, in contrast with the common practice, with staggered grids and numerical unknowns stored on different locations.For instance, in low Mach regimes, standard colocalized methods might present spurious oscillations. We present a scheme, developped with F. Berthelin, S. Minjeaud, J. Llobell, and S. Krellon staggered grids and with a specific definition of numerical fluxes inspired from kinetic theory.The staggered approach requires a new analysis, especially for the full Euler system where the total energy mixes up quantities stored on dual grids, and the conservation of total energy is a delicate issue.

This talk is part of the Isaac Newton Institute Seminar Series series.

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