Alternative Advection Schemes for the Baroclinic ADCIRC Model: Application to the Lock-Exchange Problem

It is well know that standard Galerkin finite element methods are prone to numerical instabilities for advection-dominated flows and a variety of methods have been proposed to stabilize the advection terms. One large class is upstream weighting; herein, three variants of that method are examined. The first, which is unique to the ADvanced CIRCulation (ADCIRC) model, looks at the possibility of introducing an upstream weighting coefficient to the elemental fluid velocities in the non-conservative form of the advection terms in the generalized wave continuity, momentum and transport equations. Results from truncation error analysis show consistent convergence, as well as the presence of a numerical diffusion term. However, this term is not sufficient to increase the stability of the model. The second method is flux corrected transport (FCT). Herein, we examine this method qualitatively by comparing results of the FCT implementation within the Quoddy model to spatially and temporally refined ADCIRC model runs using the same parameter values. Results indicate that with enough resolution ADCIRC can match these FCT results; however this is not practical for real world applications. Finally, we examine the Streamline upwind Petrov Galerkin (SuPG) method applied to the transport equation.