IMPROVED 3-DIMENSIONAL FINITE-ELEMENT TECHNIQUES FOR FIELD SIMULATION OF VARIABLY SATURATED FLOW AND TRANSPORT

Accurate three-dimensional simulations of saturated-unsaturated groundwater flow and contaminant transport in highly heterogeneous subsurface media require extreme agility in the numerical techniques of solution. The primary limitations of simulating large-scale complex field problems are the available computing power, and the considerable data management effort required to calibrate, validate and perform sensitivity analyses to these systems. An efficient finite-element model is presented which overcomes many of the challenges encountered in solving complex problems. The Galerkin and upstream weighted residual procedures are employed for solving the flow and transport equations. Options for using chord-slope Newton-Raphson linearization and upstream weighting of the relative permeabilities are necessary for highly nonlinear flow problems. Computational savings are otherwise achieved using the less robust Picard scheme. Underrelaxation formulas further alleviate convergence difficulties in the solution of the nonlinear equations. Hexahedral orthogonal curvilinear elements are used to accurately and efficiently discretize domains with irregular formation geometry, and transition elements are employed to grade the finite-element mesh for finer discretization only in regions of high gradients. Element matrices are generated using influence coefficient formulas, thus avoiding costly numerical integration. The 7-, 11- and 27-point lattice connectivity structures are provided as options that increase the accuracy of solution, or enhance computational speed and storage requirements. Galerkin and upstream weighting schemes alleviate stability problems in solving the transport equations without excessive smearing of concentrations. Preconditioned conjugate gradient (PCG) and ORTHOMIN techniques are used to solve the large symmetric and asymmetric matrix equations arising from the assembly of the elemental flow and transport equations, respectively, and repeated matrix assembly and decomposition are eliminated from the calculations, if the situation permits. Assembly of the entire model is discussed, with reference to previously published works for details of schemes already tested and implemented. Only further developments of the schemes are detailed herein. Application of the model is demonstrated by selected simulation examples involving assessment of moisture movement and contaminant migration from a shallow waste disposal design above a multilayer unconfined aquifer system.