High-order element-base Galerkin methods offer interesting properties for ocean models. They can represent complex geometries by tiling the domain into non-overlapping, potentially curvilinear elements. They have a built-in arbitrary high-order accuracy controlled by a choice of the polynomial order approximating the solution within each element. Finally, they yield themselves to efficient implementation on parallel computers, as they have a large computation to communication ratio. In this talk, I will present efforts to utilize Galerkin methods for building ocean models, including Non-hydrostatic Unified Model of the Ocean (NUMO) and it’s hydrostatic version tailored to global simulations. The NUMO model was initially developed to simulate ice/ocean interactions in Greenland fjords. As such, it requires an unstructured mesh capability to represent the fjord geometry and the range of scales varying from near glacier small-scale processes to open-ocean large-scale processes. Recent work in this project focuses on development of an ice/ocean boundary condition which accounts for the thermodynamic and salinity exchanges at the glacier interface. In the hydrostatic NUMO, we focus on unstructured mesh in the horizontal, and layers of constant density in the vertical directions. I will present early validation results using continuous Galerkin method on limited-area test cases. The goal of the project is to create a prototype of a global ocean model capable of using unstructured, dynamically adaptive meshes.
BIO: Michal Kopera has earned a B.Sc. and M.Sc. in Mechanical Engineering from the Warsaw University of Technology in Poland in 2006. He then moved to the University of Warwick, UK, to pursue a Ph.D. in Scientific Computing. In 2011, Michal joined the Naval Postgraduate School in Monterey, CA as a National Research Council Postdoctoral Fellow in the Department of Applied Mathematics. He also held a Visiting Fellow position at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, in 2012. In 2016 Michal moved to the University of California, Santa Cruz, where he was an Assistant Researcher at the Department of Earth and Planetary Sciences. Since 2018 he is an Assistant Professor at Boise State University in the Department of Mathematics.