Godunov-type solution of the shallow water equations on adaptive unstructured triangular grids

Z. D. Skoula*, A. G. L. Borthwick, C. I. Moutzouris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A Godunov-type upwind finite volume solver of the non-linear shallow water equations is described. The shallow water equations are expressed in a hyperbolic conservation law formulation for application to cases where the bed topography is spatially variable. Inviscid fluxes at cell interfaces are computed using Roe's approximate Riemann solver. Second-order accurate spatial calculations of the fluxes are achieved by enhancing the polynomial approximation of the gradients of conserved variables within each cell. Numerical oscillations are curbed by means of a non-linear slope limiter. Time integration is second-order accurate and implicit. The numerical model is based on dynamically adaptive unstructured triangular grids. Test cases include an oblique hydraulic jump, jet-forced flow in a flat-bottomed circular reservoir, wind-induced circulation in a circular basin of non-uniform bed topography and the collapse of a circular dam. The model is found to give accurate results in comparison with published analytical and alternative numerical solutions. Dynamic grid adaptation and the use of a second-order implicit time integration scheme are found to enhance the computational efficiency of the model.

Original languageEnglish
Pages (from-to)621-636
Number of pages16
JournalInternational journal of computational fluid dynamics
Volume20
Issue number9
DOIs
Publication statusPublished - 2006

Keywords / Materials (for Non-textual outputs)

  • shallow water equations
  • Godunov
  • adaptive finite volume
  • variable bed topography
  • unstructured grids
  • implicit time integration
  • FINITE-VOLUME METHOD
  • NAVIER-STOKES EQUATIONS
  • SOURCE TERMS
  • DAM-BREAK
  • MODEL
  • FLOW
  • SCHEME
  • MESHES

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