Despite the development of pressurized irrigation systems in the second half of the twentieth century, surface irrigation continues to be the most used system in the world. Computer tools are required to support performance improvements leading to its sustainability. A simulation model of basin/border irrigation is presented in this paper combining two-dimensional overland hydraulics based on Saint–Venant equations with three-dimensional infiltration based on the mixed form of Richards’ equation. The coupling of these equations is attained by enforcing continuity of pressure at the soil surface. The model applies a finite-volume approach using the diffusion-wave approximation form of the shallow water equations. Water flow on undulated topographies is simulated using a non-orthogonal curvilinear coordinate system. An underrelaxed-modified Picard iteration algorithm is used for Richards’ equation, and an underrelaxed Picard iteration algorithm is used for Saint–Venant equations. The model was validated using experiments from the literature. Model performance was robust and accurate, even in complex theoretical cases with strong soil-surface undulations. Mass conservation was judged satisfactory in all cases, with the long-term ratio of mass balance error in the order of 10−2 in the most complex simulations. Soil type, mesh nonorthogonality, and the interaction of these variables had a strong effect on CPU time. Additional research will be required to transform this simulation model into an operational tool for surface irrigation. Attention will need to be paid to additional surface irrigation systems, soil types, and the optimization of computational speed.

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