A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying

A. Ern; Serge Piperno; K. Djadel

doi:10.1002/fld.1674

A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying

A. Ern
, Serge Piperno
, K. Djadel

École des ponts

Research output: Contribution to journal › Article › peer-review

Abstract

We build and analyze a Runge-Kutta discontinuous Galerkin method to approximate the one- and two-dimensional shallow-water equations. We introduce a flux modification technique to derive a well-balanced scheme preserving steady states at rest with variable ground elevation and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	International Journal for Numerical Methods in Fluids
Volume	58
Issue number	1
DOIs	https://doi.org/10.1002/fld.1674
Publication status	Published - 10 Sept 2008

Keywords

Flooding and drying
Runge-Kutta discontinuous Galerkin
Shallow-water equations
Source terms
Well- balanced schemes

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10.1002/fld.1674

Cite this

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abstract = "We build and analyze a Runge-Kutta discontinuous Galerkin method to approximate the one- and two-dimensional shallow-water equations. We introduce a flux modification technique to derive a well-balanced scheme preserving steady states at rest with variable ground elevation and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.",

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AU - Ern, A.

AU - Piperno, Serge

AU - Djadel, K.

PY - 2008/9/10

Y1 - 2008/9/10

N2 - We build and analyze a Runge-Kutta discontinuous Galerkin method to approximate the one- and two-dimensional shallow-water equations. We introduce a flux modification technique to derive a well-balanced scheme preserving steady states at rest with variable ground elevation and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

AB - We build and analyze a Runge-Kutta discontinuous Galerkin method to approximate the one- and two-dimensional shallow-water equations. We introduce a flux modification technique to derive a well-balanced scheme preserving steady states at rest with variable ground elevation and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

KW - Flooding and drying

KW - Runge-Kutta discontinuous Galerkin

KW - Shallow-water equations

KW - Source terms

KW - Well- balanced schemes

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DO - 10.1002/fld.1674

M3 - Article

AN - SCOPUS:50249144099

SN - 0271-2091

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JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

IS - 1

ER -

A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying

Abstract

Keywords

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