Building an Ocean Model Using Mimetic Operators
Abstract
This thesis explores the application of mimetic operators in solving the Navier-Stokes equations, focusing on the Boussinesq approximation and its implications for computational fluid dynamics. Mimetic operators, acclaimed for their unique ability to preserve crucial properties of the underlying physics, present a promising avenue for accurate and efficient numerical simulations.
The work begins by explaining mimetic operators, highlighting their mathematical foundations and significance in discretizing partial differential equations while maintaining fundamental properties such as conservation laws and divergence-free constraints. It then shows that solving the Navier-Stokes equations with mimetic operators provides a computationally simplified yet effective framework for modeling buoyancy-driven flows in stratified fluids, underlining the mimetic operator's adaptability to complex geometries.
Furthermore, the thesis addresses the parallelization of computational codes leveraging mimetic operators, aiming to exploit modern high-performance computing architectures for efficient simulations. Parallelization strategies and optimizations are discussed, focusing on scalability and computational efficiency.
A series of test cases are investigated to validate the proposed methodology, encompassing canonical flow problems and applications relevant to ocean modeling. The thesis presents detailed numerical experiments, comparing simulation results with analytical solutions, empirical data, and existing numerical benchmarks. In particular, emphasis is placed on the steps toward validating the ocean model, highlighting the capability of mimetic operators to capture complex oceanic phenomena while maintaining computational efficiency accurately.
Overall, this thesis not only contributes to the advancement of computational fluid dynamics but also offers practical insights. It integrates mimetic operators in solving the Navier-Stokes equations, providing a deeper understanding of their application, parallelization, and validation in the context of buoyancy-driven flows and ocean modeling.