New class of solutions for water infiltration problems in unsaturated soils

Abstract

This paper presents the results of approximate analytical solutions to Richards' equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical situations. In the present study, two approximate analytical methods known as the differential transform method (DTM) and homotopy perturbation method (HPM) were employed to find analytical solutions to Richards' equation. The methods were found to be robust in finding solutions practically identical to those from the existing analytical and numerical methods. Two representative examples were considered in order to evaluate the accuracy of the solutions obtained by DTM and HPM, revealing high level of accuracy in both cases.

Keywords:

• unsaturated flow
• Richards equation
• analytical solution
• homotopy perturbation method
• differential transform method