An advanced mixed Lagrangian-Eulerian and finite element method to simulate 3-D subsurface variably saturated flows

Abstract

This study proposes an advanced, efficient numerical solution involving the use of the mixed Lagrangian-Eulerian (LE) method and the finite element method (FEM) for producing 3D simulations of variably saturated subsurface flow as described by Richards’ equation. The LE approach with its particle tracking algorithm was selected for the resolution of numerical problems resulting from the penetration of a sharp front through flux boundaries during the infiltration process. In this new approach, the LE method is applied to interior nodes, and the FEM is applied to incoming-flux-boundary nodes. The proposed numerical scheme is implemented by first obtaining proper matrix equations for the boundary nodes in order to analyze flow behaviors in saturated/unsaturated porous media. In order to demonstrate the performance of the proposed algorithm, four examples are provided; the one-dimensional single- and multi-layered soil column problem, a three-dimensional drainage problem and a three-dimensional pumping well problem. In the four examples, the mixed LE and FEM method (MLE) using relatively large time steps obtained superior results in terms of the accuracy and computational efficiency in comparison with the conventional FEM. The outcome of the proposed study will contribute to efficient numerical solution for subsurface flow problems involving critical boundary conditions in real watershed.