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 language | English |
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Pages (from-to) | 621-636 |
Number of pages | 16 |
Journal | International journal of computational fluid dynamics |
Volume | 20 |
Issue number | 9 |
DOIs | |
Publication status | Published - 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