Date of Completion
8-3-2020
Embargo Period
8-3-2020
Keywords
air-sea, atmosphere-ocean, fluid-fluid, partitioned time stepping, conservative coupling
Major Advisor
Jeffrey Connors
Associate Advisor
Vasileios Chousionis
Associate Advisor
Dmitriy Leykekhman
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
This thesis investigates methods of coupling fluids across an interface, motivated by air-sea interaction in application codes. The algorithms investigated here have two primary classifications: sequential and concurrent, in reference to different code configurations for the air and sea modules on parallel computing systems. In the sequential mode, the modules run on the same set of processors. The air module is run first since atmospheric dynamics are thought of as driving ocean surface conditions. In the concurrent mode, the modules run simultaneously, in parallel, on different sets of processors. Different step sizes are allowed for the two fluid codes.
The focus is the temporal representation of flux-form boundary conditions. A least-squares polynomial flux reconstruction is proposed to couple the air and sea modules over a time interval called a coupling window. The high formal accuracy of these flux calculations is not shared by methods in application. The least-squares approach may reduce aliasing errors and numerical fluctuations that can occur with pointwise interpolants, although this comparison is not explicitly studied here.
An a posteriori stability indicator is defined, which can be computed efficiently on-the-fly over each coupling window. For a model of two coupled fluids with natural heat convection, using finite elements in space, sufficiency of the stability indicator is proved. Under certain conditions, it is also proved that stability can be enforced by iteration when the coupling window is small enough.
Computational tests illustrate the stability and accuracy properties as they relate to the choices of coupling mode, length of the coupling window, number of time steps on a coupling window, iterations performed, and order of least-squares data reconstruction. These tests motivate exploration of adaptive methods to control the coupling window size. Computational tests using two adaptive algorithms are performed that illustrate how significant computational cost savings might be achieved for applications by adjusting the size of the coupling window according to a local error indicator. That is, where errors are small, a larger-sized window is used to reduce coupling-related overheard costs. Large errors are mitigated by reducing the size of the window to maintain a target error tolerance.
Recommended Citation
Dolan, Robert D., "Flux Partitioning and Reconstruction Methods for Atmosphere-Ocean Interaction" (2020). Doctoral Dissertations. 2614.
https://digitalcommons.lib.uconn.edu/dissertations/2614