SEMIANALYTICAL SOLUTION TO RICHARDS EQUATION FOR LAYERED POROUS-MEDIA

Traditional finite-difference and finite-element solutions to Richards ' equation can exhibit stability problems and mass balance errors when sharp saturation fronts migrate across material interfaces. Several s emianalytical solutions to Richards' equation have been developed for layered media, but none allow for arbitrary constitutive relationships between capillary pressure, water saturation, and relative water perm eability. This paper develops a more general semianalytical solution t o Richards' equation that can simulate unsaturated flow in layered med ia and utilize arbitrary constitutive relationships. Based on a combin ation of the Runge-Kutta and shooting methods, initial-boundary-value problems are solved for layered systems without experiencing the types of stability problems commonly associated with numerical models. The proposed numerical scheme is computationally efficient and numerically stable, and it compares favorably with other analytical solutions. Re sults of two example simulations demonstrate the versatility of the me thod for solving both horizontal and vertical unsaturated flow problem s. The primary disadvantages of the numerical approach are that it is limited to one-dimensional flow and that it requires the development o f specific iteration schemes for different categories of boundary-valu e problems.