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Stability, accuracy and efficiency of a semi-implicit method for three- dimensional shallow water flow. (English) Zbl 0796.76052
The stability analysis, the accuracy and the efficiency of a semi- implicit finite difference scheme for the numerical solution of a three- dimensional shallow water model are presented and discussed. The governing equations are the three-dimensional Reynolds equations in which pressure is assumed to be hydrostatic. The pressure gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the \(\theta\)-method, with \(\theta\) being an implicitness parameter. The resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D99 Incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
86A05 Hydrology, hydrography, oceanography
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