The current rapid development of hydroinformatic systems demands further improvements in numerical modelling, and thus in the computational hydraulics which underlies such modelling. This work is a study in the development of flow adaptive numerical schemes in computational hydraulics that are directed to enhancing modelling capabilities. The general domain of the work is unsteady nearly horizontal flow in one and two space dimensions. It follows different advances in computational hydraulics situated in different physical situations. Four particular examples have been studied.; additional flow resistance due to flexible vegetation, one dimensional supercritical flow, flow in networks of channels and nearly horizontal two dimensional flow.

All of the schemes thereby developed show similar features, employing intermideate results of computation in order to achieve a better performance. By adopting the point of view of cybernetics, these numerical schemes are examined as control systems. This provides a generalisation of features common to the notion of flow-adaptivity. For the purpose of characterising flow adaptive schemes, a process of deconstruction was followed, starting with the most simple example of an implicit numerical scheme.