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Finite volume scheme with local high order discretization of Hydrostatic equilibrium for Euler equations with external forces

Abstract : In this note, we introduce a new finite volume scheme for Euler equations with source terms: the gravity and the friction. The classical finite volume schemes are not able to cap- ture correctly the dynamic induced by the balance between convective terms and external forces. Firstly, by plugging the source terms in the fluxes with the Jin-Levermore procedure, we modify the Lagrangian+remap scheme to obtain a method able to capture the asymp- totic limit induced by the friction (asymptotic preserving scheme) and discretize with good accuracy the steady state linked to the gravity (well-balanced scheme). Secondly we will give some properties about this scheme and introduce a modification which allows us to obtain an arbitrary high order discretization of the hydrostatic steady state.
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https://hal.inria.fr/hal-01114437
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Submitted on : Monday, February 9, 2015 - 2:14:07 PM
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Emmanuel Franck, Laura Mendoza. Finite volume scheme with local high order discretization of Hydrostatic equilibrium for Euler equations with external forces. Journal of Scientific Computing, Springer Verlag, 2016, ⟨10.1007/s10915-016-0199-4⟩. ⟨hal-01114437⟩

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