Tracer Transport within an Unstructured Grid Ocean Model using Characteristic Discontinuous Galerkin Advection
New tracer transport methods for unstructured grids for use in an ocean model.
This article describes the implementation of a new scheme for computing the movement of tracers (e.g., salt, biological species) with the fluid flow as part of ocean models built on variable-resolution, unstructured meshes. The new scheme is stable, conserves tracer mass, and is computationally efficient when transporting many tracer quantities.
The implementation of a new numerical scheme in MPAS-Ocean allows for the transport of tracers at much reduced computational expense while also conserving the tracer mass and avoiding the introduction of any new extreme values of tracer concentration (monotonicity). Additional care is taken to ensure that this transport is consistent with the transport of mass computed as part of underlying fluid dynamics. The new method is formulated for general meshes that are being introduced in new ocean and atmosphere models. The scheme as currently implemented provides a foundation from which future optimizations may be built off in order to provide a transport scheme which is more computationally efficient than older schemes for the large numbers of tracers currently used in MPAS-Ocean.
A new computationally efficient scheme has been developed for tracer transport in ocean models. This new method, called characteristic discontinuous Galerkin (CDG), uses the fluid velocity and geometry of the mesh to compute trajectories (characteristics) for the volume of fluid moving into a mesh cell in a given time interval. This geometric volume can then be re-used and combined with very accurate (discontinuous Galerkin) representations of the tracer concentration to compute how the amount of a tracer changes in time in an ocean simulation. Because the scheme is based on geometric factors that can be re-used for all tracers, the scheme is computationally efficient (lower cost when transporting many different tracers) and automatically conserves the total tracer mass. The scheme is also stable at longer time steps, further reducing computational expense. Great care has been taken to make sure the movement of tracers is consistent with the movement of water mass, an important requirement for an accurate solution. Solutions are presented for a suite of test cases and comparisons are made to existing transport schemes in the MPAS-Ocean model.
Los Alamos National Laboratory
Funding was provided by the Earth System Modeling program within the DOE Office of Science Office of Biological and Environmental Research.
Lee, D., M. Peterson, R. Lowrie, and T. Ringler. “Tracer Transport within an Unstructured Grid Ocean Model using Characteristic Discontinuous Galerkin Advection.” submitted to Computers and Mathematics with Applications. 2017.