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Robust a Simulation for Shallow Flows with Friction on Rough Topography
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- Journal:
- Numerical Mathematics: Theory, Methods and Applications / Volume 6 / Issue 2 / May 2013
- Published online by Cambridge University Press:
- 28 May 2015, pp. 384-407
- Print publication:
- May 2013
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- Article
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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
. The method is applied to solve problems with complex rough topography, coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.
. The method is applied to solve problems with complex rough topography, coupled with 