A semi-implicit finite element model for natural water bodies

In this work, a semi-implicit model, applied to the shallow water equations, is developed for natural water bodies. In the proposed model, the shallow water equations are integrated in the vertical direction, finite elements are employed in the spatial discretization, and finite differences in the time discretization. The model is based on the uncoupling of the governing equations, in which the expressions of the velocity components, obtained explicitly from the discretized momentum equations, are substituted in the continuity equation. Therefore, there is an uncoupling of the solution; initially the continuity equation is solved, and, in the sequence, the momentum equations are solved. Yet, this uncoupling produces a significant reduction in the number of equations of the resulting systems, when compared to standard coupled systems. This reduction improves substantially the computer performance.