The development of a simulation model of the surface water response of a catchment
Based on the physics of flow through porous media, on the dynamic equations of De Saint-Venant and on the kinematic wave approach a numerical model which links groundwater motion through an unconfined aquifer to stream and overland flows has been developed. Galerkin's method has been used to discretize the partial differential equations over the space domain, whereas finite difference schemes have been utilized to approximate the set of nonlinear ordinary differential equations into a set of difference equations which have been solved iteratively by Newton-Raphson's method by means of Gauss substitution of each time step.
It has been suggested that the use of two-dimensional models to simulate nonlinear aquifer motions by means of Dupuit's assumption has been the main cause of senseless numerical transient fluctuations on the water table levels. The fact that the accuracy of the solutions near the sinks is constrained to the magnitude of the pumping rates has been shown to be another consequence of having assumed the hydraulic gradient to be equal to the slope of the free surface.
A new approach to solve complex channel networks by means of penalty functions over the depths of flow in order to simulate abrupt cross-section width augmentation at the junctions has been presented. Stage-discharge rating functions which take the slope of free surface into account have been used as open downstream boundary conditions to allow the simulation of hysteresis even in these boundaries of the channel networks. It has been shown that approximation of natural cross-sections to asymmetric trapezia can minimize the errors of the main geometric elements of these natural channel cross-sections.
Several unsuccessful attempts to model surface runoff as shallow two-dimensional flow have led to the conclusion that it cannot be modelled using fixed boundaries.