Idealised flow past an island in a dynamically adaptive finite element model

Abstract

The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive, unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow boundary layers that form on the island itself.

Submesoscale tidal eddies in the wake of coral islands and reefs: satellite data and numerical modelling

“…To model accurately the complex tidal currents in such regions, high-resolution models are necessary (Wolanski et al, 2003). Falconer et al (1986) studied the model sensitivity to the bathymetry representation, for which a high resolution is then crucial; Coutis and Middleton (2002) highlighted the importance of the island geometry on controlling the wake formation downstream this island; Munday et al (2010) went even further showing the potential of adaptive models. The simulation of such complex flows is now frequently done using finite element models, such as FINEL 2D (Dam et al, 2007), TELEMAC (Jones and Davies, 2008) or SLIM (Lambrechts et al, 2008).…”

Geostrophic balance preserving interpolation in mesh adaptive linearised shallow-water ocean modelling

“…Recently, dynamic mesh adaptive ocean modelling has been proposed by Pain et al (2005); Piggott et al (2008a). This approach utilises unstructured meshes in all three dimensions with dynamic mesh adaptivity applied using element-wise topological operations and nodal perturbations to optimise the mesh according to a metric derived from the interpolation error of simulation fields (Pain et al, 2001;Piggott et al, 2006;Munday et al, 2010). A feature of this approach is that, in each mesh adapt, the new optimised target mesh has, in general, no relationship to the original donor mesh, other than that each is some covering simplex partitioning of the same original domain.…”

Optimal Constrained Interpolation in Mesh-Adaptive Finite Element Modeling

“…Mesh-to-mesh interpolation may lead to a loss of more subtle numerical properties. In particular, dynamic mesh adaptivity has previously been applied for the solution of the time-dependent incompressible Navier-Stokes equations for applications in numerical ocean modeling (see, e.g., [75,74,68,54,55]). Numerical issues can be expected if the incompressible Navier-Stokes equations are supplied with a divergent initial condition for the velocity, as this implies a loss of regularity in time (see [47, sections 3.9 and 3.16] for detailed discussions relating to initializing a Navier-Stokes solver).…”