Keynote lecture: The CBS (Characteristic Based Split) algorithm in hydraulic and shallow water flow

An efficient finite element model for the computation of a wide range of shallow water problems is introduced. The algorithm presented can be used in an explicit, semi-explicit and in a nearly and fully implicit forms. The semi-explicit version shows robustness and economy in problems characterised by low Froude numbers, even for large timesteps. Also, the optimal diffusion properties of the method makes it suitable for very demanding high speed flows such as supercritical flows in hydraulic structures. Ln this case, an explicit version is recommended. The so-called ‘nearly’ implicit form considers implicitly the diffusion term. Here this possibility is illustrated for a scalar transport equation coupled with the Shallow Water Equations.