Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Steve Bryson; Yekaterina Epshteyn; Alexander Kurganov; Guergana Petrova

doi:10.1051/m2an/2010060

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova

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

91 Scopus citations

Abstract

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Original language	English (US)
Pages (from-to)	423-446
Number of pages	24
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	45
Issue number	3
DOIs	https://doi.org/10.1051/m2an/2010060
State	Published - Oct 11 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of Y. Epshteyn is based upon work supported by the Center for Nonlinear Analysis (CNA) under the NSF Grant # DMS-0635983. The research of A. Kurganov was supported in part by the NSF Grant # DMS-0610430. The research of G. Petrova was supported in part by the NSF Grant # DMS-0810869 and Award # KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system",

abstract = "We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves {"}lake at rest{"} steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. {\textcopyright} EDP Sciences, SMAI, 2010.",

author = "Steve Bryson and Yekaterina Epshteyn and Alexander Kurganov and Guergana Petrova",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The research of Y. Epshteyn is based upon work supported by the Center for Nonlinear Analysis (CNA) under the NSF Grant # DMS-0635983. The research of A. Kurganov was supported in part by the NSF Grant # DMS-0610430. The research of G. Petrova was supported in part by the NSF Grant # DMS-0810869 and Award # KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2010",

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doi = "10.1051/m2an/2010060",

language = "English (US)",

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journal = "ESAIM: Mathematical Modelling and Numerical Analysis",

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AU - Bryson, Steve

AU - Epshteyn, Yekaterina

AU - Kurganov, Alexander

AU - Petrova, Guergana

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The research of Y. Epshteyn is based upon work supported by the Center for Nonlinear Analysis (CNA) under the NSF Grant # DMS-0635983. The research of A. Kurganov was supported in part by the NSF Grant # DMS-0610430. The research of G. Petrova was supported in part by the NSF Grant # DMS-0810869 and Award # KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/10/11

Y1 - 2010/10/11

N2 - We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

AB - We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

UR - http://hdl.handle.net/10754/600189

UR - http://www.esaim-m2an.org/10.1051/m2an/2010060

UR - http://www.scopus.com/inward/record.url?scp=79952553523&partnerID=8YFLogxK

U2 - 10.1051/m2an/2010060

DO - 10.1051/m2an/2010060

M3 - Article

SN - 0764-583X

VL - 45

SP - 423

EP - 446

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

IS - 3

ER -

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

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