Numerical Solution of the Advection-Dispersion Equation: Application to the Agricultural Drainage

Abstract

Subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. Water flow in these systems is described by the Boussinesq Equation, and the Advection-Dispersion Equation coupled with the Boussinesq Equation is used to study the solute transport. The objective of this study was to propose a finite difference solution of the Advection-Dispersion Equation using a lineal radiation condition in the drains. The equations’ parameters were estimated from a methodology based on the granulometric curve and inverse problems. The algorithm needs the water flow values, which were calculated with the Boussinesq Equation, where a fractal radiation condition and variable drainable porosity were applied. To evaluate the solution descriptive capacity, a laboratory drainage experiment was used. In the experiment, the pH, temperature, and electric conductivity of drainage water were measured to find the salt’s concentration. The salts concentration evolution was reproduced using the finite difference solution of the Advection-Dispersion Equation, and the dispersivity parameter was found by inverse modelling. The numerical solution was used to simulate the leaching of saline soil. The result showed that this solution could be used as a new tool for the design of agricultural drainage systems, enabling the optimal development of crops according to their water needs and the degree of tolerance to salinity. Keywords: Boussinesq Equation, Dispersivity parameter, Finite difference, Fractal radiation condition, Inverse modeling.