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Unconditionally stable splitting methods for the shallow water equations. (English) Zbl 0945.76059
Summary: The front-tracking method for hyperbolic conservation laws is combined with operator splitting to study the shallow water equations. Furthermore, the method includes adaptive grid refinement in multi-dimensions and shock tracking in one dimension. The front-tracking method is unconditionally stable, but for practical computations feasible CFL numbers are moderately above unity (typically between 1 and 5). The method resolves shocks sharply and is efficient.
The numerical technique is applied to four test cases: an expanding bore with rotational symmetry; the time development of two constant water levels separated by a dam that breaks instantaneously; comparison with an explicit analytic solution of water waves rotating over a parabolic bottom profile; the flow over an obstacle in one dimension.

76M20 Finite difference methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35L65 Hyperbolic conservation laws
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