02 January 2018

Tracer Transport within an Unstructured Grid Ocean Model using Characteristic Discontinuous Galerkin Advection

Science

This article describes the implementation of a new scheme for tracer transport in the MPAS-Ocean model. The scheme is conservative, monotone, unconditionally stable and scales sub-linearly with the number of tracers, and has been implemented on a spherical unstructured grid in the horiztonal and an arbitrary Lagrangian Eulerian grid in the vertical.

Impact

The implementation of the CDG scheme in MPAS-Ocean allows for the conservative, monotone transport of tracers with larger time steps that the existing FCT scheme. Additional care is taken to ensure that fluxes are consistent with respect to volume fluxes derived from the continuity equation, and that the scheme preserves its properties on a spherical unstructured grid in the horizontal and on an arbitrary Lagrangian Eulerian grid in the vertical. 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 FCT for the large numbers of tracers currently used in MPAS-Ocean.

Summary

A characteristic discontinuous Galerkin (CDG) advection is used for tracer transport in the MPAS-Ocean model. The scheme is conservative, unconditionally stable with respect to time step and scales sub-linearly with the number of tracers. The scheme is implemented within both the vertical and horizontal dimensions, and special care is taken to ensure that the scheme remains conservative in the context of moving layers. Consistency is ensured with respect to the dynamics by a renormalization of the fluxes with respect to the volume fluxes derived from the continuity equation. For spherical implementations, the intersection of the flux swept regions and the Eulerian grid are determined for great circle arcs, and the fluxes and element assembly are performed on the plane via a length preserving projection. Solutions are presented for a suit of test cases and comparisons are made to the existing flux corrected transport (FCT) scheme in MPAS-Ocean.

Contact
David Lee
Los Alamos National Laboratory