A finite-element ocean model: principles and evaluation

Abstract

We describe a three-dimensional (3D) finite-element ocean model designed for investigating the largescale ocean circulation on time scales from years to decades. The model solves the primitive equations in the dynamical part and the advection-diffusion equations for temperature and salinity in the thermodynamical part. The time-stepping is implicit. The 3D mesh is composed of tetrahedra and has a variable resolution. It is based on an unstructured 2D surface mesh and is stratified in the vertical direction. The model uses linear functions for horizontal velocity and tracers on tetrahedra, and for surface elevation on surface triangles. The vertical velocity field is elementwise constant. An important ingredient of the model is the Galerkin least-squares stabilization used to minimize effects of unresolved boundary layers and make the matrices to be inverted in time-stepping better conditioned. The model performance was tested in a 16-year simulation of the North Atlantic using a mesh covering the area between 7°and 80°N and providing variable horizontal resolution from 0.3°to 1.5°.

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

“…It has been shown, since the early work of Fix (1975) that the Finite-Element (FE) method in conjunction with an unstructured mesh can be a suitable approach to fulfil this requirement. The FE method provides an easy conservation of energy and a natural treatment of geometric boundaries (Danilov et al, 2004;Wang et al, 2008a;Timmermann et al, 2009). There have been only a few FE ocean general circulation models developed so far that employ the capability of unstructured meshes (Danilov et al, 2004;Ford et al, 2004;White et al, 2008a).…”

“…The FE method provides an easy conservation of energy and a natural treatment of geometric boundaries (Danilov et al, 2004;Wang et al, 2008a;Timmermann et al, 2009). There have been only a few FE ocean general circulation models developed so far that employ the capability of unstructured meshes (Danilov et al, 2004;Ford et al, 2004;White et al, 2008a). In this paper we use the Finite-Element Sea-Ice Ocean Model (FESOM) (Danilov et al, 2004(Danilov et al, , 2005Wang et al, 2008b;Timmermann et al, 2009), which is an ocean general circulation model coupled to a dynamic thermodynamic sea-ice model.…”

Impact of combining GRACE and GOCE gravity data on ocean circulation estimates

“…The ocean model used in this study is the Finite-Element Ocean circulation Model (FEOM) (Danilov et al, 2004;Wang et al, 2008). The model is configured on a global, almost regular triangular mesh with spatial resolution of 1.5 • , and with 24 unevenly spaced levels in the vertical.…”

Using sea-level data to constrain a finite-element primitive-equation ocean model with a local SEIK filter

“…The early version of FEOM used backward Euler time stepping for both momentum and vertically integrated continuity equation and solved for two component of horizontal velocity and η simultaneously by inverting a matrix at every time step that corresponds to combining (1) and (4) into a single matrix problem, see Danilov et al (2004). Although this approach does not introduce any additional approximations and should be preferred from a mathematical viewpoint it becomes impractical (numerically inefficient) as the size of the problem increases.…”

“…Similarly, FEOM has been described in much detail by Danilov et al (2004Danilov et al ( , 2005. For the sake of completeness and also to illustrate main differences and similarities between the finite-element and standard finite-difference approaches we present a brief description of FEOM below.…”