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Semi-implicit finite difference methods for three-dimensional shallow water flow. (English) Zbl 0762.76068
A semi-implicit finite-difference method for solving the two- and three- dimensional shallow water equations has been presented. The combination of judicious selection of terms that are finite differenced implicitly and use of a Eulerian-Lagrangian method for treating the convective terms makes this formulation fast, accurate and stable. A conservative form of the continuity equation is used; the resulting finite difference method is locally and globally mass-conserving. This solution scheme solves a set of tridiagonal systems along the vertical layers and one five- diagonal linear system defined throughout the horizontal flow field. All these systems are symmetric and positive definite. These matrix properties assure the existence and uniqueness of the numerical solution.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
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