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Journal of Scientific Computing

Erschienen in:

01.02.2020

High Order Still-Water and Moving-Water Equilibria Preserving Discontinuous Galerkin Methods for the Ripa Model

verfasst von: Jolene Britton, Yulong Xing

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2020

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Abstract

Shallow water equations with horizontal temperature gradients, also known as the Ripa system, are used to model flows when the temperature fluctuations play an important role. These equations admit steady state solutions where the fluxes and source terms balance each other. We present well-balanced discontinuous Galerkin methods for the Ripa model which can preserve the still-water or the general moving-water equilibria. The key ideas are the recovery of well-balanced states, separation of the solution into the equilibrium and fluctuation components, and appropriate approximations of the numerical fluxes and source terms. The same framework is also extended to design well-balanced methods for the constant height and isobaric steady state solutions of the Ripa model. Numerical examples are presented to verify the well-balanced property, high order accuracy, and good resolution for both smooth and discontinuous solutions.

Vorheriger Artikel Sweeping Preconditioners for the Iterative Solution of Quasiperiodic Helmholtz Transmission Problems in Layered Media

Nächster Artikel An Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model

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Titel: High Order Still-Water and Moving-Water Equilibria Preserving Discontinuous Galerkin Methods for the Ripa Model
verfasst von: Jolene Britton
Yulong Xing
Publikationsdatum: 01.02.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01134-y

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