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Article Dans Une Revue Journal of Scientific Computing Année : 2016

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

Résumé

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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Dates et versions

hal-01114437 , version 1 (09-02-2015)

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Emmanuel Franck, Laura S. Mendoza. Finite volume scheme with local high order discretization of Hydrostatic equilibrium for Euler equations with external forces. Journal of Scientific Computing, 2016, ⟨10.1007/s10915-016-0199-4⟩. ⟨hal-01114437⟩
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