# Central-Upwind Schemes for the Saint-Venant System

Alexander Kurganov; Doron Levy

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 3, page 397-425
- ISSN: 0764-583X

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topKurganov, Alexander, and Levy, Doron. "Central-Upwind Schemes for the Saint-Venant System." ESAIM: Mathematical Modelling and Numerical Analysis 36.3 (2010): 397-425. <http://eudml.org/doc/194110>.

@article{Kurganov2010,

abstract = {
We present one- and two-dimensional central-upwind schemes
for approximating solutions of the Saint-Venant system
with source terms due to bottom topography.
The Saint-Venant system has steady-state solutions
in which nonzero flux gradients are exactly balanced by
the source terms. It is a challenging problem to preserve
this delicate balance with numerical schemes.
Small perturbations of these states are also very difficult
to compute. Our approach is based on extending semi-discrete central schemes for
systems of hyperbolic conservation laws to balance laws.
Special attention is paid to the discretization of the source
term such as to preserve stationary steady-state
solutions. We also prove that the second-order version of our
schemes preserves the nonnegativity of the height of the water.
This important feature allows one to compute solutions for problems
that include dry areas.
},

author = {Kurganov, Alexander, Levy, Doron},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Saint-Venant system; shallow water equations;
high-order central-upwind schemes; balance laws
conservation laws; source terms.; high-order central-upwind schemes; balance laws; conservation laws; source terms},

language = {eng},

month = {3},

number = {3},

pages = {397-425},

publisher = {EDP Sciences},

title = {Central-Upwind Schemes for the Saint-Venant System},

url = {http://eudml.org/doc/194110},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Kurganov, Alexander

AU - Levy, Doron

TI - Central-Upwind Schemes for the Saint-Venant System

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 3

SP - 397

EP - 425

AB -
We present one- and two-dimensional central-upwind schemes
for approximating solutions of the Saint-Venant system
with source terms due to bottom topography.
The Saint-Venant system has steady-state solutions
in which nonzero flux gradients are exactly balanced by
the source terms. It is a challenging problem to preserve
this delicate balance with numerical schemes.
Small perturbations of these states are also very difficult
to compute. Our approach is based on extending semi-discrete central schemes for
systems of hyperbolic conservation laws to balance laws.
Special attention is paid to the discretization of the source
term such as to preserve stationary steady-state
solutions. We also prove that the second-order version of our
schemes preserves the nonnegativity of the height of the water.
This important feature allows one to compute solutions for problems
that include dry areas.

LA - eng

KW - Saint-Venant system; shallow water equations;
high-order central-upwind schemes; balance laws
conservation laws; source terms.; high-order central-upwind schemes; balance laws; conservation laws; source terms

UR - http://eudml.org/doc/194110

ER -

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## Citations in EuDML Documents

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- Smadar Karni, Eduard Kirr, Alexander Kurganov, Guergana Petrova, Compressible two-phase flows by central and upwind schemes
- Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto, An entropy-correction free solver for non-homogeneous shallow water equations
- Smadar Karni, Eduard Kirr, Alexander Kurganov, Guergana Petrova, Compressible two-phase flows by central and upwind schemes
- Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova, Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
- Alina Chertock, Alexander Kurganov, On a hybrid finite-volume-particle method
- Alina Chertock, Alexander Kurganov, On a hybrid finite-volume-particle method
- Jorge Balbás, Smadar Karni, A central scheme for shallow water flows along channels with irregular geometry
- Jorge Balbás, Gerardo Hernandez-Duenas, A positivity preserving central scheme for shallow water flows in channels with wet-dry states

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