A hybrid three‐dimensional computational model of groundwater solute transport in heterogeneous media

Abstract

This study examines a new hybrid three‐dimensional computational solution for groundwater solute transport in a layered aquifer. In this study, the horizontal length scale of the computational domain, referring to the nature geometry, is assumed much larger than the vertical length scale. Thus the computation of solute transportation in the horizontal direction is more complex than the computation in the vertical direction. Using the Dupuit‐Forchheimer approximation of groundwater flow as a reference, this study employs the vertical/horizontal splitting (VHS) concept to divide the three‐dimensional solute transport equations into depth averaged (two‐dimensional) and vertical variation (one‐dimensional) equations. The two‐dimensional equations are processed via the so‐called finite analytic method, while the one‐dimensional equations are solved analytically. The three‐dimensional solute transport is effectively reduced to a hybrid three‐dimensional model by combining the two‐dimensional computations and the one‐dimensional analytical solutions. The resultant hybrid three‐dimensional method is capable of large computational time steps and large spatial grids and is thus suitable for simulating solute transport in large‐scale sites of layered aquifers with negligible spatial variation of both thickness and hydraulic properties within each layer, where traditional numerical schemes fall short of satisfying the requirements of both accuracy and efficiency. Nevertheless, the use of this method is necessarily restricted when (1) the site is extremely heterogeneous and thus cannot be treated as layers or (2) the flows in the aquifer and in the aquitard are highly three‐dimensional. This method is verified by analytical solutions as well as by the numerical model MT3D.