IGW Flow Solver

An Accurate, Efficient, and Robust Finite-Difference Scheme for Flows in General Anisotropic Media

In this paper, we present an improved methodology for solving groundwater flow problems in general anisotropic media. In particular, we address one of the major difficulties in solving the tensorial form of the groundwater flow equation. Traditional finite-difference techniques, when applied to the flow equation containing the complete conductivity tensor, often lead to unphysical results. Traditional methodologies are particularly problematic when the anisotropy is strong and its major orientation deviates significantly from the rectilinear coordinate system. 

Our new approach eliminates the problem by approximating the tensorial “diffusion" terms in a rotated coordinate system locally aligned with the major direction of anisotropy. It then expresses and interpolates the non-nodal heads in the resulting numerical expression in terms of global nodal heads. The result is a significantly improved scheme that is more accurate and robust than the traditional finite difference scheme. In addition, the new scheme is monotonic and always leads to physically meaningful solution. The improved methodology is implemented in a comprehensive software system called IGW. We demonstrate the advantage of the improved scheme with a a realistic groundwater flow example and systematic comparison with solutions obtained from traditional methodologies. 

Demonstrative Example

We consider in this example a realistic situation that involves 3D flow in a three-layer aquifer system characterized by highly variable elevations and complex sources and sinks (pumping, recharge, surface seepage). The aquifers are assumed to be anisotropic with the bedding oriented along the layers.

Improved IGW Solution

The solution is accurate, efficient, and robust. The matrix system is diagonally dominant for all anisotropies of any orientation.

Solution Obtained from the Traditional FD Methodology

The solution failed to converge due to ill-conditioned matrix system when cross-conductivities terms are significant.

Solution Obtained from MODFLOW Methodology

The solution is incorrect because it ignores the cross conductivities in the conductivity tensor