10.4122/1.1000000379
Dresback, Kendra
Kendra
Dresback
dresback@ou.edu
Kolar, Randall
Randall
Kolar
kolar@ou.edu
Luettich, Rick
Rick
Luettich
rick_luettich@unc.edu
Dresback, Kendra
Kendra
Dresback
dresback@ou.edu
Weak Lateral Boundary Conditions in Coupled Shallow Water Flow and Transport Models
XVI International Conference on Computational Methods in Water Resources
2006
2006
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.