Mathematical model of flat-vertical profile moisture transfer under trickle irrigation in conditions of incomplete saturation

Abstract

Aim. To develop an effi cient method of building a numerical model for the process of moisture transfer under trickle irrigation, with the mathematical modeling of the method involving the system of differential equations in partial derivatives of Klute-Richards, and to perform computing experiments regarding fl at-vertical profi le moisture transfer with point sources. Methods. The mathematical apparatus of the theory of differential schemes of solving differential equations in partial derivatives, and Newton’s method of iterative approximate solving of non-linear equations. Results. A stable differential two-step symmetrized algorithm (TS-algorithm) along with the corresponding scheme of the method of numerical solution for initially-boundary task for Richards’ equation was created. The method was realized in the form of a computer program in C++ language, the computing experiments were performed with three deeper points, the humidity zones for volume moisture and potential were obtained. Conclusions. The numerical method was suggested, ensuring the effi cient solution to Richards’ non-linear equation in conditions of several deep point sources. The algorithm structure allows reducing the system of non-linear algebraic equations with many unknowns to solving independent non-linear equations with one unknown. The presented method may easily be expanded for three-dimensional cases. The results of computing experiments are in agreement with natural observations.