An adaptive Eulerian-Lagrangian approach for the numerical simulation of unsaturated flow.

The classical Eulerian equation is reformulated through an Eulerian-Lagrangian approach, so that the phenomenon is formally decomposed into advection, typical to the Lagrangian concept and propagation of the residual handled by the Eulerian approach. The moisture potential is decoupled into an advection term and a residual term. Advection is solved by the method of characteristics along pathlines while the residual, discretized within a fixed grid, is solved by a finite element method. Similar to the dispersion/advection phenomena where the method proved its superiority in the treatment of steep concentration gradients, for the unsaturated flow equation, the method presents advantages in solving flow problems with sharp saturation profiles, e.g. as occurring in infiltration into dry soils. (from authors' abstract)