Simulation of the Lock-Exchange Hydraulics using the Discontinuous Galerkin Method

Abstract

simulations of the lock-exchange hydraulics have been carried out using a discontinuous Galerkin finite element method. The basic water circulation in the lock-exchange hydraulics consists in an upper layer of cold, fresh surface water and an opposite deep current of warmer, salty outflowing water. The governing equations are the well- established two-layer shallow water system including bathymetric forces. The considered discontinuous Galerkin method is a stable, highly accurate and locally conservative finite element method whose approximate solutions are discontinuous across interelement boundaries; this property renders the method ideally suited for the hp-adaptivity. The proposed method can handle complex topography using unstructured grids and it satisfies the conservation property. Several numerical results are presented to demonstrate the high resolution of the proposed method and to confirm its capability to provide accurate and efficient simulations for the lock-exchange hydraulics. KeywordsGalerkin method; Two-layer shallow water equations; Finite element; Lock-exchange hydraulics.