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Volume 16, Issue 5
Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

Manuel Jesús Castro Díaz, Yuanzhen Cheng, Alina Chertock & Alexander Kurganov

DOI: 10.4208/cicp.180513.230514a

Commun. Comput. Phys., 16 (2014), pp. 1323-1354.

Published online: 2014-11

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  • Abstract

In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches – two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme – and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

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@Article{CiCP-16-1323, author = {Manuel Jesús Castro Díaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov}, title = {Solving Two-Mode Shallow Water Equations Using Finite Volume Methods}, journal = {Communications in Computational Physics}, year = {2014}, volume = {16}, number = {5}, pages = {1323--1354}, abstract = {

In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches – two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme – and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180513.230514a}, url = {http://global-sci.org/intro/article_detail/cicp/7082.html} }
TY - JOUR T1 - Solving Two-Mode Shallow Water Equations Using Finite Volume Methods AU - Manuel Jesús Castro Díaz, Yuanzhen Cheng, Alina Chertock & Alexander Kurganov JO - Communications in Computational Physics VL - 5 SP - 1323 EP - 1354 PY - 2014 DA - 2014/11 SN - 16 DO - http://doi.org/10.4208/cicp.180513.230514a UR - https://global-sci.org/intro/article_detail/cicp/7082.html KW - AB -

In this paper, we develop and study numerical methods for the two-mode shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms. We present several numerical approaches – two operator splitting methods (based on either Roe-type upwind or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme – and test their performance in a number of numerical experiments. The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.

Manuel Jesús Castro Díaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov. (2014). Solving Two-Mode Shallow Water Equations Using Finite Volume Methods. Communications in Computational Physics. 16 (5). 1323-1354. doi:10.4208/cicp.180513.230514a
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