Robust a simulation for shallow flows with friction on rough topography

Jian Deng, Ruo Li, Tao Sun, Shuonan Wu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 O (δx 3). The method is applied to solve problems with complex rough topography, coupled with h-adaptive mesh techniques to demonstrate its robustness and efficiency.

Original languageEnglish (US)
Pages (from-to)384-407
Number of pages24
JournalNumerical Mathematics
Volume6
Issue number2
DOIs
StatePublished - May 2013

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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