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Robust a Simulation for Shallow Flows with Friction on Rough Topography

Published online by Cambridge University Press:  28 May 2015

Jian Deng ,
Ruo Li ,
Tao Sun  and
Shuonan Wu
Jian Deng*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
Ruo Li*
Affiliation:
HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Tao Sun*
Affiliation:
Reservoir Characterization Division ExxonMobil Upstream Research Company, P O. Box 2189 Houston, Texas 77252, USA
Shuonan Wu*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
*
Corresponding author.Email address:lyricidyll3@gmail.com
Corresponding author.Email address:rli@math.pku.edu.cn
Corresponding author.Email address:tao.sun@exxonmobil.com
Corresponding author.Email address:wsnl987@gmail.com
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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 . The method is applied to solve problems with complex rough topography, coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.

Keywords

65M1065M1565N30Shallow waterfree interfaceManning force
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 384 - 407
Copyright
Copyright © Global Science Press Limited 2013

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