An entropy-correction free solver for non-homogeneous shallow water equations

Tomás Chacón Rebollo; Antonio Domínguez Delgado; Enrique D. Fernández Nieto

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 5, page 755-772
  • ISSN: 0764-583X

Abstract

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In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.

How to cite

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Rebollo, Tomás Chacón, Delgado, Antonio Domínguez, and Enrique D. Fernández Nieto. "An entropy-correction free solver for non-homogeneous shallow water equations." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 755-772. <http://eudml.org/doc/194190>.

@article{Rebollo2010,
abstract = { In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme. },
author = {Rebollo, Tomás Chacón, Delgado, Antonio Domínguez, Enrique D. Fernández Nieto},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite Volume Method; upwinding; shallow water; Harten Regularization; source terms; entropy-correction ; generalized conservation form; finite volume solvers},
language = {eng},
month = {3},
number = {5},
pages = {755-772},
publisher = {EDP Sciences},
title = {An entropy-correction free solver for non-homogeneous shallow water equations},
url = {http://eudml.org/doc/194190},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Rebollo, Tomás Chacón
AU - Delgado, Antonio Domínguez
AU - Enrique D. Fernández Nieto
TI - An entropy-correction free solver for non-homogeneous shallow water equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 5
SP - 755
EP - 772
AB - In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
LA - eng
KW - Finite Volume Method; upwinding; shallow water; Harten Regularization; source terms; entropy-correction ; generalized conservation form; finite volume solvers
UR - http://eudml.org/doc/194190
ER -

References

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