Transparent boundary conditions for the shallow water equations with a mixed finite element formulation Original Research Article

We study the application of characteristic-based transparent boundary conditions to the shallow water equations. A numerical method based on semi-Lagrangian time discretization and space discretization by the mixed finite element method, is presented in detail. The transparent boundary conditions are imposed weakly, which is natural for the space discretization we use. The numerical method is implemented in an experimental code, and several of the implementation aspects are addressed. Numerical experiments are presented showing that the boundary conditions allow both the outgoing waves to radiate out and the incoming waves to enter the domain in a transparent manner. The numerical results are also confirming previous theoretical results.