Abstract
This paper describes a second-order accurate Godunov-type scheme for solving the 2D 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.
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