Error measures for finite element ocean modelling
File(s)
Author(s)
Power, Philip William
Type
Thesis
Abstract
This thesis presents goal-based error measures and applies them, via appropriate metric tensors, to the adaptation of three dimensional anisotropic tetrahedral finite element meshes for a range of oceanographic modelling problems. The overall aim of this work is to produce error measures which are able to resolve the flow features of an ocean over a wide range of spatial and temporal scales simultaneously. For example, western boundary currents, the Antarctic Circumpolar Current (ACC), equatorial jets, meddies (mid-latitude eddies) and Open Ocean Deep Convection. 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.
Mesh quality is gauged with respect to the metric tensor which embodies the error measure, such that an ideal element has sides of unit length when measured with respect to this metric tensor. The result is meshes in which each finite element node has approximately equal (subject to certain boundary confonning constraints and the performance of the mesh optimisation procedure) error contribution. Error measures are formulated which measure the error contribution of each solution variable to an overall goal, which encompasses important features of the flow structure and is embodied in an integral form, e.g. the integral of the solution in a small region of the domain of interest. The sensitivity of the functional, taken with respect to the solution variables, is used as the basis from which error measures are derived. The error measures then act to predict those areas of the domain where resolution should be changed and lead to the solution of so-called forward and adjoint (backward) problems. Focus is given to developing relatively simple methods that refer to information readily accessible from the discretized equation sets and do not explicitly use equation residuals.
Mesh quality is gauged with respect to the metric tensor which embodies the error measure, such that an ideal element has sides of unit length when measured with respect to this metric tensor. The result is meshes in which each finite element node has approximately equal (subject to certain boundary confonning constraints and the performance of the mesh optimisation procedure) error contribution. Error measures are formulated which measure the error contribution of each solution variable to an overall goal, which encompasses important features of the flow structure and is embodied in an integral form, e.g. the integral of the solution in a small region of the domain of interest. The sensitivity of the functional, taken with respect to the solution variables, is used as the basis from which error measures are derived. The error measures then act to predict those areas of the domain where resolution should be changed and lead to the solution of so-called forward and adjoint (backward) problems. Focus is given to developing relatively simple methods that refer to information readily accessible from the discretized equation sets and do not explicitly use equation residuals.
Version
Open Access
Date Issued
2008
Date Awarded
2008
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Pain, Christopher
Goddard, Antony
Publisher Department
Earth Science and Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)