Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.1129nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 2 : pp. 384–407
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Shallow water free interface Manning force.