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Godunov solution of shallow water equations on curvilinear and quadtree grids. (English) Zbl 1056.76052

Toro, E. F. (ed.), Godunov methods. Theory and applications. International conference, Oxford, GB, October 1999. New York, NY: Kluwer Academic/ Plenum Publishers (ISBN 0-306-46601-5). 141-148 (2001).
Summary: We describe a second-order accurate Godunov-type scheme for solving two-dimensional shallow water equations on non-orthogonal curvilinear boundary-fitted and Cartesian quadtree grids. The shallow water equations are written in a new matrix-hyperbolic form suitable for spatially non-uniform bed profiles. The equations are discretised spatially using finite volumes and temporally using the fourth-order Runge-Kutta method. Convection terms are modelled using Roe’s flux function with a nonlinear minmod limiter. Validation tests include wind-induced circulation in a dish-shaped basin, an inviscid dam break simulation, and jet-forced flow in a flat-bottomed circular reservoir.
For the entire collection see [Zbl 0978.00036].

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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