SOLUTIONS OF ONE-DIMENSIONAL WATER-FLOW AND MASS-TRANSPORT EQUATIONS IN VARIABLY SATURATED POROUS-MEDIA BY THE FINITE-ELEMENT METHOD

The Galerkin finite element method is used to solve problems of one-dimensional, vertical flow of water and mass transport of conservative solutes in variably saturated porous media. The method is applied to solve the original equation of mass transport, where Green's theorem is used to remove the second derivatives, either of the total mass flux (convection and dispersion) term or of the flux due only to dispersion. The method is also applied to solve a modified mass transport equation. In all cases, linear one-dimensional elements are used. The resulting computational schemes are applied to (a) a clay loam soil, where the flow conditions lead to small Peclet numbers ranging from 0.5 to 2.4, (b) a sandy soil, where the Peclet numbers ranged from 7.5 to 32.7, and (c) another sandy soil, where the Peclet numbers are large and ranged from 24 to 50. The modified mass transport equation gives better results than does the original equation. Comparison of the solutions obtained by the application of the original equation shows that the results obtained by removing the second derivatives of the dispersion term are close to those obtained by the modified equation. © 1990.