• ocean modelling;
  • multi-scale;
  • finite element;
  • unstructured mesh;
  • adaptivity;
  • anisotropic


A new modelling framework is presented for application to a range of three-dimensional (3D) multi-scale oceanographic problems. The approach is based upon a finite element discretization on an unstructured tetrahedral mesh which is optimized to represent highly complex geometries. Throughout a simulation the mesh is dynamically adapted in 3D to optimize the representation of evolving solution structures. The adaptive algorithm makes use of anisotropic measures of solution complexity and a load-balanced parallel mesh optimization algorithm to vary resolution and allow long, thin elements to align with features such as boundary layers. The modelling framework presented is quite different from the majority of ocean models in use today, which are typically based on static-structured grids. Finite element (and volume) methods on unstructured meshes are, however, gaining popularity in the oceanographic community. The model presented here is novel in its use of unstructured meshes and anisotropic adaptivity in 3D, its ability to represent a range of coupled multi-scale solution structures and to simulate non-hydrostatic dynamics. Copyright © 2007 John Wiley & Sons, Ltd.