Hydrodynamics of Border Irrigation — Complete Model

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Abstract
The equations of border irrigation are solved by the method of characteristics using a prescribed time increment. At each time step the flow conditions are computed at irregularly spaced nodes on a grid moving with time. Characteristic curves are drawn backwards from each node until they intersect the previous time line. The resulting system of four nonlinear algebraic equations is solved iteratively by the Newton-Raphson method leading to second-order accuracy with respect to the time step. The complete irrigation phenomenon is modeled, i.e., advance, depletion, recession and runoff or ponding, by using the pertinent characteristic equations for the associated boundary conditions. The second-order accuracy of the processes permits use of larger time steps and fewer computational nodes than in first-order models. The moving grid precisely encompasses the solution domain and permits concentration of nodes in highly nonlinear regions. The result is an efficient algorithm that permits programming and application to practical situations at reasonable cost.

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