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Journal of Scientific Computing

Erschienen in:

03.09.2015

Well-Balanced Discontinuous Galerkin Methods for the Euler Equations Under Gravitational Fields

verfasst von: Gang Li, Yulong Xing

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2016

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Abstract

Euler equations under gravitational field admit hydrostatic equilibrium state where the flux produced by the pressure is exactly balanced by the gravitational source term. In this paper, we present well-balanced Runge–Kutta discontinuous Galerkin methods which can preserve the isothermal hydrostatic balance state exactly and maintain genuine high order accuracy for general solutions. To obtain the well-balanced property, we first reformulate the source term, and then approximate it in a way which mimics the discontinuous Galerkin approximation of the flux term. Extensive one- and two-dimensional simulations are performed to verify the properties of these schemes such as the exact preservation of the hydrostatic balance state, the ability to capture small perturbation of such state, and the genuine high order accuracy in smooth regions.

Vorheriger Artikel Analysis of a Reduced-Order HDG Method for the Stokes Equations

Nächster Artikel An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics

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Titel: Well-Balanced Discontinuous Galerkin Methods for the Euler Equations Under Gravitational Fields
verfasst von: Gang Li
Yulong Xing
Publikationsdatum: 03.09.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0093-5

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