A Wetting and Drying Approach for a Mode-Nonsplit Discontinuous Galerkin Hydrodynamic Model with Application to Laizhou Bay

Abstract

A wetting and drying treatment for a three-dimensional discontinuous Galerkin hydrodynamic model without mode splitting (external and internal modes) was developed. In this approach, computing elements are classified into wet, dry, and semidry elements, which are treated differently. In a Runge–Kutta time step, the reconstruction of the semidry elements and the combined utilization of two- and three-dimensional limiters help the model maintain stability. Numerical results show that the wetting and drying method can achieve a well-balanced property under the condition of still-water equilibrium and can reasonably describe the variation process of wetting and drying regions during a long wave run-up on a uniform slope and a tidal cycle in a basin with a variable slope. Analysis of the role of the limiters in the model indicated that the robustness of the three-dimensional hydrodynamic model can be effectively maintained when the two- and three-dimensional limiters are jointly applied for wetting and drying process simulation. A three-dimensional discontinuous Galerkin hydrodynamic model was applied with the presented wetting and drying method to simulate the tidal current evolution of a spring tidal cycle in southwestern Laizhou Bay in the Bohai Sea, in November 2003, and the simulated results of the water surface elevation and vertical layered current velocities agreed well with the measured data.

Keywords

• wetting and drying
• discontinuous Galerkin methods
• well-balanced property
• nonsplit scheme
• 3D shallow water equations
• 2D and 3D limiters