One-dimensional modelling of curvilinear free surface flow: generalized Matthew theory

The potential flow theory is a good mathematical approximation to various problems in the fields of free surface open channel and groundwater flows. In both fields, second-order equations are commonly derived using perturbation methods to account for the non-hydrostatic pressure distribution. However, an alternative technique is Picard's iteration approach, used by Matthew for steady open channel flows. Regretfully, this technique was not expanded to unsteady potential flow, limiting its full impact. The purpose of this work is to generalize the theory of Matthew to unsteady potential free surface flow, both for open channels and groundwater. The new development is an alternative to perturbation techniques, highlighting the relevance of Matthew's work. To illustrate the widespread problems to which the theory applies, simulations are made for a dambreak wave and for flow in sloping and curved aquifers. In both cases one-dimensional results are in good agreement with two-dimensional data.