A mathematical formulation for the hydraulic analysis of flow conditions in furrow and border irrigation systems is presented in this research study. The methodology is based on applying the one-dimensional Galerkin formulation of the finite element method to the numerical solution of the hydrodynamic or the so-called Saint-Venant equations. Numerical developments of the complete and simplified forms of the hydrodynamic equations were prepared using both linear and quadratic one-dimensional finite element forms of these equations. The studied models include the hydrodynamic, zero-inertia, and kinematic wave models. A general one-dimensional surface irrigation computer model (FE-SURFDSGN) was developed based on this formulation. This computer model simulates the various phases of flow in border and furrow irrigation systems using the hydrodynamic, zero-inertia, and kinematic wave models. Currently, only the kinematic wave finite element analysis is fully operational for a complete irrigation cycle in the present version of the computer model. The Kostiakov-Lewis equation was used as the infiltration function in this development even though both the mathematical development and the developed finite element model allow for utilization of any other infiltration function. Actual field measurements were utilized to validate FE-SURFDSGN. These data were taken from previous studies that were conducted in Colorado and Idaho. Although the computer model is still in the developmental stage, its application to the simulation of the various phases of flow in surface irrigation systems is very reasonable as demonstrated through the various runs that were conducted. The results of this research work indicate that the finite element method provides accurate simulation of the flow conditions in both border and furrow irrigation systems. These results also suggest that the method developed through this research can be used as an effective tool for the hydraulic analysis of flow conditions in surface irrigation systems.
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