Towards next generation ocean models : novel discontinuous Galerkin schemes for 2D unsteady biogeochemical models

A new generation of efficient parallel, multi-scale, and interdisciplinary ocean models is required for better understanding and accurate predictions. The purpose of this thesis is to quantitatively identify promising numerical methods that are suitable to such predictions. In order to fulfill this purpose, current efforts towards creating new ocean models are reviewed, an understanding of the most promising methods used by other researchers is developed, the most promising existing methods are studied and applied to idealized cases, new methods are incubated and evaluated by solving test problems, and important numerical issues related to efficiency are examined. The results of other research groups towards developing the second generation of ocean models are first reviewed. Next, the Discontinuous Galerkin (DG) method for solving advection-diffusion problems is described, including a discussion on schemes for solving higher order derivatives. The discrete formulation for advection-diffusion problems is detailed and implementation issues are discussed. The Hybrid Discontinuous Galerkin (HDG) Finite Element Method (FEM) is identified as a promising new numerical scheme for ocean simulations. For the first time, a DG FEM scheme is used to solve ocean biogeochemical advection-diffusion-reaction equations on a two-dimensional idealized domain, and p-adaptivity across constituents is examined. Each aspect of the numerical solution is examined separately, and p-adaptive strategies are explored.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Ueckermann, Mattheus Percy

Advisor dc:contributor.advisor

• Pierre F. J. Lermusiaux.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/55281

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/55281