Integrated 2D-3D free surface hydro-environmental modelling

An integrated horizontally two- and fully three-dimensional numerical model system has been developed based on a combined unstructured and σ-coordinate grid to simulate the flow and water quality process in large water bodies with a focus on the three dimensional behaviours at specific areas. The model is based on the time dependent Reynolds-Averaged Navier-Stokes equations with a non-hydrostatic pressure distribution and a baroclinic force being incorporated in the three dimensional (3D) model. The two sub models interact dynamically during the solution procedure with no time-step restriction due to integration. The main idea is to use a fractional step algorithm for each model and then integrate the two models fraction by fraction. Hybrid 2D-3D finite volume cells have been introduced for the link nodes which are partly in the 2D domain and partly in the 3D domain. Thus an interpolation/averaging procedure at the interface and domain overlapping is no longer needed. The 3D model uses the projection method for pressure calculation. The advection equation is solved by the semi-Lagrangian method. Other components are solved via the finite element - finite volume (FV) method. The water surface is determined implicitly through a global matrix equation created by assembling the domain's matrices. The cell integrals are calculated analytically to eliminate a common source of numerical diffusion due to the use of approximation techniques for the FV integrals. The horizontal gradients of the density and shear stresses are calculated on true horizontal planes, in order to avoid artificial velocity and diffusion in highly stratified flows. Neumann interpolation elements with virtual nodes have been introduced at Neumann type of boundaries for more accuracy. The integrated model has been verified using analytical solutions and benchmark test cases, including the Ekman velocity distribution, wind driven circulation, lock exchange and integrated 2D-3D flows in basin. The results show the model is capable of the model for accurate simulation and implicit 2D-3D integration. Keywords: integrated modelling, hydrodynamic numerical model, non-hydrostatic, unstructured mesh, hybrid finite element finite volume method