An implicit wetting and drying approach for non-hydrostatic baroclinic flows in high aspect ratio domains

Abstract

A new approach to modelling free surface flows is developed that enables, for the first time, 3D consistent non-hydrostatic baroclinic physics that wets and dries in the large aspect ratio spatial domains that characterise geophysical systems. This is key in the integration of physical models to permit seamless simulation in a single consistent arbitrarily unstructured multiscale and multi-physics dynamical model. A high order continuum representation is achieved through a general Galerkin finite element formulation that guarantees local and global mass conservation, and consistent tracer advection. A flexible spatial discretisation permits conforming domain bounds and a variable spatial resolution, whilst atypical use of fully implicit time integration ensures computational efficiency. Notably this brings the natural inclusion of nonhydrostatic baroclinic physics and a consideration of vertical inertia to flood modelling in the full 3D domain. This has application in improving modelling of inundation processes in geophysical domains, where dynamics proceeds over a large range of horizontal extents relative to vertical resolution, such as in the evolution of a tsunami, or in urban environments containing complex geometric structures at a range of scales.

Numerical Modelling of Oil Spill Transport in Tide-Dominated Estuaries: A Case Study of Humber Estuary, UK

“…This study employs the hydrostatic pressure approximation due to the intense computational power demanded by non-hydrostatic pressure models. Furthermore, the impact of using hydrostatic pressure approximation on the reliability of the model is expected to be relatively insignificant, as there is no indication that the processes (i.e., small scale ocean processes) [57,58] emphasised using non-hydrostatic pressure models influence estuarine oil slick transportation. TELEMAC3D uses a sigma transformation to resolve the vertical direction and unstructured triangular grid in the horizontal direction [50,59].…”

An implicit wetting–drying algorithm for the discontinuous Galerkin method: application to the Tonle Sap, Mekong River Basin

“…For solving the shallow-water equations, explicit time marching schemes must meet the CFL condition to ensure numerical stability, leading to small values of the time step. Implicit time marching allows for much longer time steps, which is appropriate for meshes with variable resolution and long simulations [18,19], and corresponds to the choice made for the present simulations. To maintain this implicit time stepping efficient even at wet/dry fronts, appropriate algorithms have to be developed.…”

“…The first of three idealized 1D test cases developed by Balzano [29] is widely used to evaluate the accuracy of various wetting -drying methods [30] because they exhibit problematic conditions in a simple setup [19]. Originally, the computational domains of these three Balzano test cases are 1D basins with a length of 13800 m. However, as the purpose of this paper is to test the implementation of the new wetting -drying algorithm in the 2D version of SLIM, these domains are modified by adding a width of 7200 m. It is then verified that the solutions of the 2D simulations performed by means of SLIM on unstructured meshes correspond to the 1D solutions of the original Balzano test cases.…”

“…In addition, a lack of mass conservation is observed [11] because of artificial mass transfers from dry to wet areas [17]. Even though semi-implicit schemes exist [10], most of the current methods resort to explicit time-marching schemes, which are constrained by the Courant-Friedrichs-Lewy (CFL) condition [18][19][20]. Explicit time integration requires high temporal resolutions making such schemes rather expensive in terms of computational cost.…”

Numerical simulation of wetland hydrodynamics and water quality

“…Several numerical approaches for shallow water flows describe wetting and drying processes, see e.g., [6,8,10,11]. The most popular models are the Princeton Ocean Model (POM) [12], the Regional Ocean Modeling System (ROMS) [13], the Unstructured Grid Finite Volume Community Ocean Model (FVCOM) [14], the Advanced Circulation (ADCIRC) [15], the RMA2 [16,17], the Delft3D-FLOW [18], and the TELEMAC-2D [19].…”