Adaptive Q-tree Godunov-type scheme for shallow water equations

B Rogers, M Fujihara, AGL Borthwick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

This paper presents details of a second-order accurate, Godunov-type numerical model of the two-dimensional shallow water equations (SWEs) written in matrix form and discretized using finite volumes. Roe's flux function is used for the convection terms and a non-linear limiter is applied to prevent unwanted spurious oscillations. A new mathematical formulation is presented, which inherently balances flux gradient and source terms. It is, therefore, suitable for cases where the bathymetry is non-uniform, unlike other formulations given in the literature based on Roe's approximate Riemann solver. The model is based on hierarchical quadtree (Q-tree) grids, which adapt to inherent flow parameters, such as magnitude of the free surface gradient and depth-averaged vorticity. Validation tests include wind-induced circulation in a dish-shaped basin, two-dimensional frictionless rectangular and circular dam-breaks, an oblique hydraulic jump, and jet-forced flow in a circular reservoir. Copyright (C) 2001 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)247-280
Number of pages34
JournalInternational Journal for Numerical Methods in Fluids
Volume35
Issue number3
Publication statusPublished - 15 Feb 2001

Keywords / Materials (for Non-textual outputs)

  • adaptive quadtree grids
  • Roe's Riemann solver
  • shallow water equations
  • APPROXIMATE RIEMANN SOLVERS
  • FINITE-VOLUME METHOD
  • FLOW
  • MESHES
  • RIVER

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