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Volume 6, Issue 2
Robust a Simulation for Shallow Flows with Friction on Rough Topography

Jian Deng, Ruo Li, Tao Sun & Shuonan Wu

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 384-407.

Published online: 2013-06

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  • Abstract

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.

  • AMS Subject Headings

65M10, 65M15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-384, author = {}, title = {Robust a Simulation for Shallow Flows with Friction on Rough Topography}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {2}, pages = {384--407}, abstract = {

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1129nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5910.html} }
TY - JOUR T1 - Robust a Simulation for Shallow Flows with Friction on Rough Topography JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 384 EP - 407 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1129nm UR - https://global-sci.org/intro/article_detail/nmtma/5910.html KW - Shallow water, free interface, Manning force. AB -

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.

Jian Deng, Ruo Li, Tao Sun & Shuonan Wu. (2020). Robust a Simulation for Shallow Flows with Friction on Rough Topography. Numerical Mathematics: Theory, Methods and Applications. 6 (2). 384-407. doi:10.4208/nmtma.2013.1129nm
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