Discontinuous boundary implementation for the shallow water equations

Quasi-bubble nite element approximations to the shallow water equations are investigated focusing on implementations of the surface elevation boundary condition. We rst demonstrate by numerical results that the conventional implementation of the boundary condition degrades the accuracy of the velocity solution. It is also shown that the degraded velocity leads to a critical instability if the advection term is present in the momentum equation. Then we propose an alternative implementation for the boundary condition. We refer to this alternative implementation as a discontinuous boundary (DB) implementation because it introduces at each boundary node two independent mass– ux values that result in a discontinuity at the boundary. Numerical results show that the proposed DB implementation is consistent, stabilizes the quasi-bubble scheme, and leads to second-order accuracy at the surface elevation speci ed boundary. Copyright ? 2004 John Wiley & Sons, Ltd.