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Journal of Scientific Computing

Erschienen in:

05.04.2016

Finite Volume Scheme with Local High Order Discretization of the Hydrostatic Equilibrium for the Euler Equations with External Forces

verfasst von: Emmanuel Franck, Laura S. Mendoza

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

A new finite volume scheme for the Euler equations with gravity and friction source terms is presented. Classical finite volume schemes are not able to capture correctly the dynamics generated by the balance between convective terms and external forces. Our purpose is to develop a method better suited for dealing with this problem. To that end, firstly, we modify the Lagrangian+remap scheme by plugging the source terms into the fluxes using the Jin–Levermore procedure. The scheme obtained is able to capture the asymptotic limit induced by the friction (Asymptotic Preserving scheme) and to discretize with a good accuracy the steady-state linked to gravity (Well-Balanced scheme). Secondly, we present some properties about this scheme and introduce a modification for an arbitrary high order discretization of the hydrostatic steady-state.

Vorheriger Artikel On the Use of ANOVA Expansions in Reduced Basis Methods for Parametric Partial Differential Equations

Nächster Artikel A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection–Diffusion Equations

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Titel: Finite Volume Scheme with Local High Order Discretization of the Hydrostatic Equilibrium for the Euler Equations with External Forces
verfasst von: Emmanuel Franck
Laura S. Mendoza
Publikationsdatum: 05.04.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0199-4

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