  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.
