Date of Award

Spring 1-1-2011

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Oleg V. Vasilyev

Second Advisor

David R. Kassoy

Third Advisor

Olivier Desjardins


Ocean modeling is a crucial component in understanding our climate system. The advancement of the numerical methods used for ocean modeling is the focus of this dissertation. In this work, an integrated approach for modeling common ocean test problems, western boundary currents, and tsunamis on adaptive grids using novel boundary techniques is considered. The use of the adaptive wavelet collocation method is explored for these ocean problems. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. In addition to developing wavelet-based computational models, this work also sets out to improve the representation of continental topology and bottom bathymetry through several extensions of the Brinkman volume penalization methods. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is a numerical technique used to enforce no slip boundary conditions through the addition of a term to the governing equations. When coupled with the adaptive wavelet collocation method, the flow near the boundary can be well resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This thesis can be viewed as a proof of concept. The general foundation is established for future, more specific, applications.