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In this talk, I will first derive a fully nonlinear weakly dispersive Green-Naghdi equations for shallow water waves over variable bottom topographies from the fully Euler equations, and then propose a family of accurate and robust numerical methods to solve it.Lastly, a set of numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the Green-Naghdi equations to describe a wide range of shallow water wave phenomena.