Shooting Method for Saint Venant Equations of Furrow Irrigation

Abstract

Flow in surface irrigation is subcritical and downstream conditions can propagate upstream. The shooting or initial‐value method started from the downstream end and proceeded upstream against the flow. Saint Venant hydrodynamic equations were solved cell by cell for flow area and flow rate in the upstream direction, given the advance increment of the wave front and an estimate of the time required to achieve that advance. This was in contrast to the two‐point boundary‐value solution of the full hydrodynamic model where the process started at the upstream end and swept downstream and then upstream during each iteration. Flow area and discharge were solved simultaneously for all nodes and advance distance was calculated for the given time step.