TR(BR)-111 : Soil moisture simulation by improved numerical method

Abstract

The theory for transient isothermal flow of water into non swelling unsaturated soil is well understood and has been developed to a large extent in terms of solutions of the non-linear Richards equation. In the field, the description of infiltration is highly complicated since the initial and boundary conditions are usually not constant while the soil characteristics may vary with time and space. In view of this, most efforts in recent past, have been concentrated on seeking numerical solutions.

There exist quite a variety of finite difference solutions employing different forms of the non-linear Richards equation and different ways of discretization, the most common being explicit, implicit, and Crank-Nicolson approximation. The explicit approximation is derived by replacing the derivatives by their finite difference analogue at the j time level. The implicit scheme replaces the derivatives by their finite difference analogue at the (j+1) time level. The Crank-Nicolson approximation averages the derivatives at the j and (j+1) time levels to obtain an approximation at the (j+1/2) level implying that 50 % weightages are assigned to each of the derivatives at the j and (j+1) time levels.

The purpose of this study is to develop a numerical model to simulate the soil moisture profile in an initially unsaturated soil during infiltration. A model has been formulated for finite difference solution of the non-linear Richards equation applicable to transient, one-dimensional water flow through the unsaturated porous medium. The modification of explicit, implicit, and Crank-Nicolson schemes has been examined by varying the weightages assigned to the derivatives at the j and (j+1) time levels and comparing the simulated soil moisture profiles with the quasi-analytical solution of Philip.