Computation of shallow water waves with hybrid finite elements

The numerical computation of two-dimensional incompressible long-period shallow water waves using the method of finite elements is presented. It is shown that the set of equations having been solved in each time step is reduced to a third of the usual size by satisfying the equations of motion on the element level only (hybrid finite elements). The water levels in all nodes are the sole parameters computed from the set of equations. The velocities are subsequently calculated on the element level in each time step. Special emphasis is placed on reproducing eddies behind corners using an anisotropic turbulent exchange tensor.