Finite analytic method for modeling variably saturated flows.

This paper develops a finite analytic method (FAM) for solving the two-dimensional Richards' equation. The FAM incorporates the analytic solution in local elements to formulate the algebraic representation of the partial differential equation of unsaturated flow so as to effectively control both numerical oscillation and dispersion. The FAM model is then verified using four examples, in which the numerical solutions are compared with analytical solutions, solutions from VSAFT2, and observational data from a field experiment. These numerical experiments show that the method is not only accurate but also efficient, when compared with other numerical methods.