NORMAL FLOW BOUNDARY CONDITIONS IN SHALLOW WATER MODELS- INFLUENCE ON MASS CONSERVATION AND ACCURACY

Finite element solution of the shallow water wave equations has found increasing use by researchers and practitioners in the modeling of oceans and coastal areas. Wave equation models, most of which use equal-order, C0 interpolants for both the velocity and the surface elevation, successfully elimi-nate spurious oscillation modes without resorting to artificial or numerical damping. An important question for both primitive equation and wave equation models is the interpretation of boundary conditions. Analysis of the characteristics of the governing equations shows that a single condition at each boundary is sufficient. Yet there is not a consensus in the literature as to what that boundary condition must be or how it should be implemented in a finite element code. Traditionally (partly because of limited data) surface elevation is specified at open ocean boundaries while the normal flux is specified as zero at land boundaries. In most finite element wave equation models, both of these boundary conditions are implemented as essential conditions. Our recent work focuses on alternate ways to numerically implement normal flow boundary conditions with an eye toward improving the mass-conserving properties of wave equation models. In particular, we have found that treating normal fluxes as natural conditions with the flux interpreted as external to the compu