The discontinuous Galerkin coastal and estuarine modelling system (DGCEMS v1.0.0): a three-dimensional, nonsplit-mode, implicit–explicit Runge–Kutta hydrostatic model

Numerical methods of discontinuous Galerkin (DG) discretisation for coastal ocean modelling have advanced significantly, but there are still challenges in accurately simulating phenomena such as wetting and drying processes and baroclinic flows in coastal and estuarine regions. This study develops a novel three-dimensional (3D) coastal and estuarine modelling system named DGCEMS, using a quadrature-free nodal DG method. The model adopts σ coordinates, employs a nonsplit-mode framework, and integrates a semi-implicit Runge–Kutta scheme. A series of numerical experiments demonstrate the model's second-order convergence, low spurious mixing, and capability to simulate salt–freshwater interactions in the presence of wetting and drying boundaries.