Development of a Three-Dimensional Hydrodynamic Model Based on the Discontinuous Galerkin Method

Abstract

Though the discontinuous Galerkin method is attracting more and more applications in many fields due to its local conservation, high-order accuracy, and flexibility for resolving complex geometries, only a few three-dimensional hydrodynamic models based on the discontinuous Galerkin method are present. In this study, a three-dimensional hydrodynamic model with a σ-coordinate system in the vertical direction is developed. This model is discretized in space using the discontinuous Galerkin method and advanced in time with the implicit-explicit Runge–Kutta method. Numerical tests indicate that the developed model is convergent and can obtain better results with a smaller computational time when a higher approximation order is adopted. Other tests with exact solutions also indicate that the developed model can well simulate the vertical circulation under the effect of surface wind stress and the flow under the combined effect of wind stress and Coriolis acceleration terms. The simulation results of tidal flow in part of Bohai Bay, China, indicate that the model can be used for the simulation of tidal wave motion in realistic situations.