Adjoint or goal-based error norms for adaptive mesh ocean modelling
P.W. Power, C.C. Pain, M.D. Piggott, G.J. Groman, F. Fang, D.P. Marshall, A.J.H. Goddard, I.M. Navon
Flow in the world's oceans occurs at a wide range of spatial scales from micro-meters to mega-meters. In particular, regions of intense flow are often highly localized, for example western boundary currents, equatorial jets and the Antarctic Circumpolar Current. Conventional numerical ocean models generally use static meshes. The use of dynamically - adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics.
A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method is described here.
The method is based upon a functional encompassing important features of the flow structure.The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method.The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required.