Enriched Finite Element for Modelling Variable Boundary Conditions in Unsaturated Seepage Problems

Partial differential equations such as models for flow in unsaturated porous media are difficult to be solved when space-time variable boundary conditions are included. A general solution to this problem is discussed in this contribution and is devised in such a way that the face with variable boundary condition can be subjected to Dirichlet, Neumann or the so-called Signorini/ambiguous boundary conditions, considering the transition from one type to another. A method based on the enrichment of finite elements that is able to accurately model seepage with these complex boundary conditions is discussed. Simulations are presented illustrating the capabilities of the new method in 2D and 3D, including cases where the free surface varies due to rain.