A stabilized finite element method to compute transient shallow water flows

The shallow water equations fall into the category of symmetric advective-diffusive systems with source terms. This type of equations can be very effectively solved using stabilized methods, such as SUPG and GLS. A semi-discrete finite element method based on these ingredients is presented for the computation of transient shallow water hows. Special care has been taken in the design of the operators in order to improve the performance for unsteady calculations. The solution is advanced in time via a predictor multi-corrector algorithm which includes as special cases the second order trapezoidal rule, a first order "explicit" method and a first order implicit method, equivalent to the constant-in-time element of the space-time formulation.