Weak Lateral Boundary Conditions in Coupled Shallow Water Flow and Transport Models

Proper specification of boundary conditions in shallow water models have been the subject of much research over the years and still remains an active area of research. When coupled to transport models, as in baroclinic or water quality simulations, the number of conditions on the boundary increases. Yet, few studies have looked at boundary conditions for coupled models. In many instances, the following "traditional" conditions have been used: a strong boundary condition for ocean boundaries in the continuity equation; for the land boundaries, a strong boundary condition is employed in the momentum equation, while a weak formulation of the boundary condition for the velocities is used in the continuity equation; finally for the transport equation, a strong boundary condition is utilized on the ocean boundary with a weak boundary conditions applied for the land boundary. However, our experience is that such implementations of the boundary conditions can lead to instabilities in both the flow and transport models, or they can degrade the accuracy of the solution for the continuity, momentum and transport equations. In this study, we examine an alternative treatment to the strong formulation at the ocean boundary for both the continuity and transport equation, utilizing a weak form of these boundary conditions for both the surface elevation field and the baroclinic fields. This implementation allows for both inflow and outflow boundaries to exist on the ocean boundary for the transport equation. We will assess the impact of the weak implementation by evaluating the stability and accuracy changes within the shallow water model, ADCIRC (ADvanced CIRCulation). ADCIRC, which is based on over 20 years of research and applications, is a hydrodynamic model capable of simulating water surface elevation and velocity fields in lakes, bays, estuaries, and oceans. Model applications range from determining the effects of dredging on circulation to determining the storm surge that accompanies the landfall of a hurricane. The model is based on the full non-linear St. Venant (shallow water) equations, using the traditional hydrostatic pressure and Boussinesq approximations; the equations are discretized in space using linear finite elements, while time is discretized using an efficient split-step Crank-Nicolson algorithm. The transport equation utilized in the study also uses linear finite elements and utilizes a split-step Crank- Nicolson algorithm in the temporal discretization.Presenters: name: Dresback, Kendra affiliation: University of Oklahom