Numerical analysis of Richards' problem for water penetration in unsaturated soils

Abstract. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining appropriate solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of Richards' equation mostly fall in the category of numerical methods, often having restrictions for practical cases. In this research, two analytical methods known as Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been successfully utilized for solving Richards' equation. Results obtained from the two methods mentioned show a remarkably high precision in the obtained solution, compared with the existing exact solutions available.