Development of a 3-D Variable-Direction Anisotropy program, VDA-3D, to represent normal and tangential fluxes, in 3-D groundwater flow modeling

A computer program, VDA-3D, for groundwater flow simulation with a 3-dimensional anisotropic hydraulic conductivity tensor [K] has been developed, which represents normal fluxes with the Kxx, Kyy, Kzz components of [K], and tangential fluxes with the Kxy, Kxz, Kyz components. The need to simulate tangential fluxes occurs when the principal directions of the hydraulic conductivity tensor are not aligned with the model coordinates. Off-diagonal components of the conductivity tensor relate Darcy flux components to head gradient components that do not point in the same direction as the flux components. The program for 3-Dimensional Variable-Direction Anisotropy (VDA-3D) is based on a method developed by Edwards and Rogers (1998) and is an extension to 3 dimensions of the 2-dimensional Layer Variable-Direction Anisotropy (LVDA) package developed by Anderman and others (2002) for the USGS MODFLOW groundwater modeling program. The Edwards method is based on the traditional mass balance of water for a finite-difference-discretization cell of aquifer material, and enforces continuity of water flux across each of the 6 cell faces. VDA-3D is used to apply the Edwards method to a set of 1-D, 2-D, and 3-D test problems, some homogeneous, one with heterogeneity between two zones of the grid, and one with heterogeneity from cell to cell; each problem has boundary conditions of either constant head or constant flux. One test problem with constant head boundaries uses distributions of sources and sinks that are calculated to represent a problem with a given analytic solution. A second program has been written to implement an alternate method to simulate tangential fluxes, developed by Li and others (2010) and referred to as the Lzgh method. Like VDA-3D, the Lzgh method formulates the finite difference discretization of the flow equation for a medium with heterogeneous anisotropic hydraulic conductivity. In the Lzgh method, the conductivity is not required to be uniform over each finite difference cell as it is in VDA-3D, and the head function is required to be continuous across the cell faces, which it is not in VDA-3D. The only data requirement difference between the two methods is that the hydraulic conductivities are provided at cell centroids for VDA-3D and at cell interfaces for Lzgh. Early test results for a 2-D heterogeneous problem with a synthetic conductivity distribution and a dominantly 1-D flow pattern indicate that Lzgh can reproduce the results of VDA-3D, provided the harmonic means of all the components of the cell-centered VDA-3D hydraulic conductivity tensor are used to create the tensor at cell interfaces for Lzgh. Further work is planned to compare the accuracy of the resultant head distributions and the computational costs of the two methods, and to compare additional problems with different flow patterns.