A tree-based solver for adaptive ocean modelling

The development of an adaptive (in space and time) ocean model from an existing adaptive finite-volume Navier–Stokes model is described. A flexible and efficient quadtree spatial discretisation is used which requires collocation of all variables (i.e. an A-grid discretisation). We demonstrate that the use of an approximate projection method allows for implicit damping of instabilities generally associated with the A-grid, at the expense of a relatively small amount of numerical energy dissipation, while accurately preserving dispersive properties and geostrophic balance. The finite-volume formulation also maintains second-order spatial accuracy at all solid boundaries. Test cases demonstrate the efficacy of the adaptive ocean model, and the advantages it has in terms of efficient representation of multi-scale behaviour within a single model. The model is freely available as open-source code.