Abstract: This work presents a computational evaluation of water flow in an open agricultural irrigation channel with variable depth using the one- and two-dimensional Saint–Venant equations. The mathematical formulation is derived from mass and momentum conservation principles for shallow water flow. A linearized one-dimensional model is first analyzed to obtain an equivalent wave-type equation through perturbation and separation of variables. A nonlinear formulation with variable bottom topography and discontinuities is then considered, incorporating analytical integration with Dirac delta representation of step changes in the channel bed. The two-dimensional Saint–Venant system is subsequently introduced to model spatially distributed depth and velocity fields. Numerical implementation is carried out using a finite difference FTCS scheme, including stability constraints of CFL type. Simulations illustrate the temporal evolution of water depth under step-type bottom discontinuities in both 1D and 2D configurations. The results show the capacity of the model to capture wave propagation, depth transitions, and spatial flow redistribution. The framework provides a computational basis for hydraulic analysis and future high-resolution modeling of irrigation channels.

Keywords: Saint–Venant equations, shallow water flow, irrigation channels, FTCS scheme, variable depth, computational hydraulics

Pages: 116-125

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