FlexSemFlexSemAarhus University department of Ecoscience
FlexSem Hydrodynamics

The hydrodynamic (HD) module of FlexSem is documented in A versatile marine modelling tool applied to arctic, temperate and tropical waters. It implements a 3D semi-implicit, finite difference-finite volume, hydrostatic and nonhydrostatic solution to the Navier-Stokes equations on an unstructured computational mesh as outlined by Casulli and Zanolli 2002

Horizontal and vertical advection and diffusion of momentum is discretized using an eulerian second order Adam-Bashford approach following Finger et al. 2006

The model includes a Smagorinsky formulation (Smagorinsky 1963) of the turbulent viscosity, a semi-implicit advection diffusion scheme (Casulli and Zanolli 2002). Options to include clamped open boundary forcings, surface heat budget, Coriolis forces, sources as well as bottom, vertical wall and surface drag are also included.

An orthogonal unstructured computational mesh is required for the implementation to be accurate. Mixed meshes e.g. triangles and squares as in the Roskilde Fjord setup are supported. The velocities in the model are defined on the interfaces between the cells and the scalars in the cell centers, hence it is a finite difference-finite volume formulation. The model uses horizontal layers (z-level).

A theta formulation is used to define the degree of implicitness. When theta equals zero the model is explicit and when theta equals one it is fully implicit. It can be show that the highest accuracy and efficiency is achieved when theta equals 0.5 (Casulli and Cattani 1992).

A predictor-corrector algorithm is used, where first, a provisional solution is calculated where the nonhydrostatic pressure component is neglected, thereby obtaining the hydrostatic (barotropic) solution. Subsequently the provisional solution can optionally be corrected by solving the implicit equation system for the nonhydrostatic pressure component, thereby obtaining the nonhydrostatic solution. Both the nonhydrostatic and hydrostatic solutions are mass conservative.