A High Order Langrangian Scheme for Flow Through Unsaturated Porous Media

Abstract

A new high order Lagrangian method uses moving basis functions to represent the moisture content in an unsaturated porous material. The basis functions are localized elliptical Gaussians that can move, spread, elongate and rotate under the action of the local velocity, velocity deviations, and diffusivity with corrections for local material properties. The velocity and its deviations are calculated from the local moisture potential and its derivatives which can be obtained from published experiments. This numerical technique is natu- rally adaptive in the sense that computational effort is expended only where there is moisture and nowhere else, and this method is capable of capturing infiltration instabilities in the wetting front observed by experimentalists and predicted by linear stability analysis. This method borrows many ideas from high Reynolds number vortex methods and other applications of Lagrangian schemes to nonlinear partial differential equations.