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.
