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A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations. (English) Zbl 0766.76067
A high-order Godunov-type scheme based on MUSCL variable extrapolation and slope limiters is presented for the resolution of 2D free-surface flow equations. In order to apply a finite volume technique of integration over body-fitted grids, the construction of an approximate Jacobian (Roe type) of the normal flux function is proposed. This procedure allows conservative upwind discretization of the equations for arbitrary cell shapes. The main advantage of the model stems from the adaptability of the grid to the geometry of the problem and the subsequent ability to produce correct results near the boundaries.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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