Well-balanced scheme between flux and source terms for computation of shallow-water equations over irregular bathymetry

Dae Hong Kim, Yong Sik Cho, Hyung Jun Kim

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43 Scopus citations

Abstract

Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL-Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry.

Original languageEnglish
Pages (from-to)277-290
Number of pages14
JournalJournal of Engineering Mechanics - ASCE
Volume134
Issue number4
DOIs
StatePublished - Apr 2008

Keywords

  • Bathymetry
  • Computation
  • Numerical models
  • Shallow waters
  • Subcritical flow
  • Supercritical flow

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