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Finite volume schemes for dispersive wave propagation and runup. (English) Zbl 1218.65092
Summary: Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.
Reviewer: Reviewer (Berlin)

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M12 Finite volume methods applied to problems in fluid mechanics
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