This publication details a novel advection scheme for tracer transport in climate model components.
The Characteristic Discontinuous Galerkin (CDG) scheme is conservative, unconditionally stable with time step, may be implemented on unstructured grids, entends to high order accuracy and has a computational cost, which scales sub-linearly with the number of tracers being advected. These properties make it an appealing option for geophysical models, which involve the transport of large numbers of tracers and where the tracer transport time step may be decoupled from that on which the dynamics is solved.
The CDG scheme is based on a Lagrangian form of the tracer flux, which is swept back from the edge along velocity characteristics. If differs from other characteristic based flux form schemes in that the fluxes also serve to update the higher order components of the flux, which are solved via system of linear equations for each cell, as opposed to other schemes where these higher order components are reconstructed from the mean values in neighboring cells.