Reduced order modelling of an adaptive mesh ocean model

F. Fang, C.C. Pain, I.M. Navon, M.D. Piggott , G.J. Gorman , A.J.H. Goddard

A novel Proper Orthogonal Decomposition (POD) model has been developed for use with an advanced unstructured mesh finite element ocean model, the Imperial College Ocean Model (hereafter, ICOM, described in detail below) which includes many recent developments in ocean modelling and numerical analysis. The advantages of the POD model developed here over existing POD approaches are the ability: To increase accuracy when representing geostrophic balance (the balance between the Coriolis terms and the pressure gradient). This is achieved through the use of two sets of geostrophic basis functions where each one is calculated by basis functions for velocities u and v; To speed up the POD simulation. To achieve this a new numerical technique is introduced, whereby a time-dependent matrix in the discretised equation is rapidly constructed independent of time. This development imparts considerable efficiency gains over the oft used alternative of calculating each finite element and node over the computational domain at each time level; To use dynamically adaptive meshes in the above POD model. keywords : POD; reduced-order modelling; ocean model; finite element; unstructured adaptive mesh.