Authors:
(1) Simone Silvestri, Massachusetts Institute of Technology, Cambridge, MA, USA;
(2) Gregory Wagner, Massachusetts Institute of Technology, Cambridge, MA, USA;
(3) Christopher Hill, Massachusetts Institute of Technology, Cambridge, MA, USA;
(4) Matin Raayai Ardakani, Northeastern University, Boston, MA, USA;
(5) Johannes Blaschke, Lawrence Berkeley National Laboratory, Berkeley, CA, USA;
(6) Valentin Churavy, Massachusetts Institute of Technology, Cambridge, MA, USA;
(7) Jean-Michel Campin, Massachusetts Institute of Technology, Cambridge, MA, USA;
(8) Navid Constantinou, Australian National University, Canberra, ACT, Australia;
(9) Alan Edelman, Massachusetts Institute of Technology, Cambridge, MA, USA;
(10) John Marshall, Massachusetts Institute of Technology, Cambridge, MA, USA;
(11) Ali Ramadhan, Massachusetts Institute of Technology, Cambridge, MA, USA;
(12) Andre Souza, Massachusetts Institute of Technology, Cambridge, MA, USA;
(13) Raffaele Ferrari, Massachusetts Institute of Technology, Cambridge, MA, USA.
Table of Links
5.1 Starting from scratch with Julia
5.2 New numerical methods for finite volume fluid dynamics on the sphere
5.3 Optimization of ocean free surface dynamics for unprecedented GPU scalability
6 How performance was measured
7 Performance Results and 7.1 Scaling Results
9 Acknowledgments and References
5.2 New numerical methods for finite volume fluid dynamics on the sphere
Our results use Oceananigans.HydrostaticFreeSurfaceModel, which solves the hydrostatic Boussinesq equations in a finite volume framework on staggered C-grids [3]. Oceananigans’ hydrostatic model employs an implicit-explicit second-order Adams-Bashforth time stepping scheme. Vertically implicit diffusion is implemented with a backward Euler time-discretization and tridiagonal solver.
A major innovation is a new adaptive-order scheme based on weighted essentially non-oscillatory (WENO) reconstructions [42] for advecting momentum and tracers on curvilinear finite-volume grids [43]. This new scheme automatically adapts to changing spatial resolution and permits stable, high-fidelity simulations of ocean turbulence without explicit dissipation or hyper-dissipation. This innovation reduces setup time when changing or increasing resolution while guaranteeing high-fidelity solutions that exhibit the minimum necessary dissipation of sharp, near-grid scale features.
This paper is available on arxiv under CC BY 4.0 DEED license.
