Study of the relative efficiency of finite difference and Galerkin techniques for modeling soil‐water transfer

Horizontal infiltration of water into a dry soil is used to study the efficiency of finite difference and Galerkin procedures in accurately locating the steep wetting front. The location of the wetting front is determined by a quasi‐analytic solution to Richards' equation. The Galerkin technique is evaluated by using linear, Hermite cubic, and Lagrange quintic elements. These schemes are compared with the performances of the Crank‐Nicolson central difference method where a standard and a modified averaging procedure for soil‐water diffusivity on grid subintervals is utilized. The comparisons are made on the basis of error as a function of spatial grid refinement and the relative efficiency in achieving a practical level of accuracy. The results lead to the conclusion that the Galerkin scheme wih linear elements or the finite differencing scheme with the modified averaging procedure is preferable to the other techniques.