Graduate Defense: Yao Gahounzo

Dissertation Information

Title: Multi-Scale Ocean Modeling Using The Discontinuous Galerkin Method

Program: Doctor of Philosophy in Computing

Advisor: Dr. Michal Kopera, Mathematics

Committee Members: Dr. Donna Calhoun, Mathematics and Dr. Ellyn Enderlin, Geosciences

Abstract

Ocean models often employ the hydrostatic assumption for large-scale applications when the horizontal scale is larger than the depth. Nonetheless, the non-hydrostatic effects are of great importance in submesoscale studies, such as modeling the physical processes of ice-ocean interactions. Most non-hydrostatic ocean models used in ice-ocean interaction studies are low-order finite-difference and finite-volume methods, often with significant dispersive errors. Therefore, there is a need for a high-order ocean model for ice-ocean interaction applications.

The first part of this thesis focuses on deriving the boundary conditions at the ice-ocean interface and incorporating them into the high-order discontinuous Galerkin (DG) method based ocean model, the Non-hydrostatic Unified Model of the Ocean (NUMO). This integration empowers NUMO to conduct accurate simulations of ice-ocean interactions. We provide evidence of NUMO’s precision in capturing small-scale processes at the ice-ocean interface and validate our findings with published results.

In the second part of the thesis, we develop a high-order unstructured DG-based hydrostatic model using multilayer shallow water equations for large-scale applications. We derived and developed high-order numerical schemes based on the nodal DG method. We demonstrate the correctness and accuracy of the model on well-balance and perturbation of baroclinic wave propagation problems and validate our model with the HYbrid Coordinate Ocean Model (HYCOM), where we consider wind-driven double-gyre circulations in different configurations. Our hydrostatic model produces accurate results and resolves more dynamic features at the same resolution as in HYCOM as we increase the polynomial order approximation.