A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property
This work provides a numerical method for simulating shallow water waves with improved dispersion, relevant for coastal engineering and geophysical fluid dynamics.
The authors developed a central discontinuous Galerkin-finite element (CDG-FE) method for the two-dimensional Green-Naghdi model with enhanced dispersive properties. Numerical tests demonstrated the accuracy and efficiency of the scheme, including well-balanced and positivity-preserving features.
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.