An unstructured grid morphodynamic model with a discontinuous Galerkin method for bed evolution

A new unstructured grid two-dimensional, depth-integrated (2DDI), morphodynamic model is presented for the prediction of morphological evolutions in shallow water. This modelling system consists of two coupled model components: (i) a well-verified and validated continuous Galerkin (CG) finite element hydrodynamic model; and (ii) a new sediment transport/bed evolution model that uses a discontinuous Galerkin (DG) method for the solution of the sediment continuity equation. The DG method is a robust finite element method that is particularly well suited for this type of advection dominated transport equation. It incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form in the solution, and it possesses a local conservation property that conserves sediment mass on an elemental level. In this paper, we focus specifically on the implementation and verification of the DG model. Details are given on the implementation of the method, and numerical results are presented for three idealized test cases which demonstrate the accuracy and robustness of the method and its applicability in predicting medium-term morphological changes in channels and coastal inlets.