On the control of noise in finite element tidal computations: A semi-implicit approach

Numerical solution of the two-dimensional shallow water equations is achieved by coupling the finite element method in space with finite difference time stepping schemes. Solutions obtained with an efficient leapfrog model are found to contain severe short-wavelength oscillations in space when compared to analytic solutions. An alternative semi-implicit formulation in the time domain, which retains most of the economical advantages of the leapfrog scheme is developed and tested. A significant reduction in the mode-to-node oscillations and improved agreement with analytical solutions are obtained. Both linear triangles and quadratic isoparametric quadrilaterals are examined. Emphasis is on the numerical behavior of the schemes tested and a comparison with a field case is not attempted.