  In this work, we investigate numerical solutions of the two-dimensional
shallow water wave using a fully nonlinear Green-Naghdi model with an improved
dispersive effect. For the purpose of numerics, the Green-Naghdi model is
rewritten into a formulation coupling a pseudo-conservative system and a set of
pseudo-elliptic equations. Since the pseudo-conservative system is no longer
hyperbolic and its Riemann problem can only be approximately solved, we
consider the utilization of the central discontinuous Galerkin method which
possesses an important feature of needlessness of Riemann solvers. Meanwhile,
the stationary elliptic part will be solved using the finite element method.
Both the well-balanced and the positivity-preserving features which are highly
desirable in the simulation of the shallow water wave will be embedded into the
proposed numerical scheme. The accuracy and efficiency of the numerical model
and method will be illustrated through numerical tests.
