Finite element modelling of free surface flows on inclined and curved beds

The solution of gravity-driven free surface flows typically resorts to the Shallow Water Equations, SWE. In turn, the derivation of the SWE incorporates a number of assumptions and within them, it should be stressed that of quasi-horizontal fluid velocities. However, when the flow occurs onto a steep and curved topography, the velocities are parallel to the bed rather than horizontal and curvature effects may affect the fluid flow. This paper extends the SWE incorporating the inclined and curved bed effects thus, allowing the analysis of gravity flows on actual topographies. Due to the similarity between the generalized and the standard SWE, the numerical methods available for the solution of the SWE can be easily applied for the solution of the generalized equations. Within these methods, this paper uses the Taylor–Galerkin algorithm. The results obtained in the numerical test cases indicate that incorporating the slope and curvature effects in the model is relevant for granular flows and of reduced effect in the remaining cases.