NONE 20260716100056721 wseas/wseas content-registration-form@crossref.org content-registration-form International Journal of Applied Mathematics Computational Science and Systems Engineering 2766-9823 Irla Mantilla Universidad Nacional de Ingeniería, Av. Túpac Amaru 210, Rímac, 27 PERÚ Mihael Arce Universidad Nacional de Ingeniería, Av. Túpac Amaru 210, Rímac, 27 PERÚ 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. 07 16 2026 07 16 2026 116 11 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232026.2026.8.11 https://wseas.com/journals/amcse/2026/a22amcse-011(2026).pdf Chow, V. T. Open-Channel Hydraulics. McGraw–Hill, 1959. Henderson, F. M. Open Channel Flow. Macmillan, 1966. Chaudhry, M. H. Open-Channel Flow. Springer, 2008. https://doi.org/10.1007/978-0- 387-68648-6 Sturm, T. W. Open Channel Hydraulics. McGraw–Hill, 2001. Graf, W. H. Hydraulics of Sediment Transport. McGraw–Hill, 1971. French, R. H. Open-Channel Hydraulics. McGraw–Hill, 1985. LeVeque, R. J. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, 2002. https://doi.org/10.1017/CBO9780511791253 Toro, E. F. Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd ed. Springer, 2009. https://doi.org/10.1007/b79761 Cunge, J. A., Holly, F. M., Verwey, A. Practical Aspects of Computational River Hydraulics. Pitman, 1980. https://doi.org/10.1007/978-3- 642-85567-2 Abbott, M. B., Ionescu, F. “On the numerical computation of nearly horizontal flows.” Journal of Hydraulic Research, 1967. https://doi.org/10.1080/00221686709500207 Whitham, G. B. Linear and Nonlinear Waves. Wiley, 2011. https://doi.org/10.1002/9781118032954 Evans, L. C. Partial Differential Equations, 2nd ed. AMS, 2010. https://doi.org/10.1090/gsm/019 Strikwerda, J. C. Finite Difference Schemes and Partial Differential Equations, 2nd ed. SIAM, 2004. https://doi.org/10.1137/1.9780898717938 Morton, K. W., Mayers, D. F. Numerical Solution of Partial Differential Equations. Cambridge University Press, 2005. https://doi.org/10.1017/CBO9780511811203 Hirsch, C. Numerical Computation of Internal and External Flows. Butterworth–Heinemann, 2007. https://doi.org/10.1016/B978-0-7506- 6594-0.X5000-1 Toro, E. F. “Shock-capturing methods for freesurface shallow flows.” Wiley, 2001. https://doi.org/10.1002/9780470020944