There are now a variety of groundwater modelling packages around from both commercial and public domain sources. MODFLOW 2005 can be freely downloaded from the United States Geological Survey (USGS) site.1 It has also been packaged by several companies to give a more user friendly graphic interface to help in setting up models and visualising the results of model runs. MODFLOW is widely used (see, e.g. Todd and Mays, 2004). It is based on a finite difference solution to the groundwater flow equations, can handle two- and three-dimensional (3D) problems, includes model calibration routines to fit aquifer parameters by matching observations, and can be linked to pollutant transport models (see next section). The International Groundwater Modelling Centre at the Colorado School of Mines2 also maintains a list of freeware groundwater modelling software, including MODFLOW and the United States Department of Agriculture (USDA)'s Hydrus 2D/3D,3 which is based on finite element solutions of the flow equations, which give more flexibility in the representation of irregular aquifers. An alternative freeware program for Windows is the Aquifer Simulation Model (ASMWin),4 which can be downloaded from the Institute of Environmental Engineering (IfU) at ETH Zurich, Switzerland. This is also based on finite difference approximations to the flow equations. ASMWin is limited to two-dimensional problems and relatively small grids, but includes both finite difference and random particle tracking transport components, a model parameter calibration routine and visualisation routines. Fig. 15.10 shows a typical finite difference grid for an application of MODFLOW. Where more detail is required in some parts of the simulation, e.g. around an abstraction well, 'nested' grids can be used, where a finer grid is embedded locally in the main grid, as in the ZOOM 3D modelling package developed by the British Geological Survey (BGS5).

Many sophisticated commercial packages for groundwater flow (and pollutant transport) modelling are also available, such as the finite element based FEFLOW (see a review by Trefry and Muffels, 2007). Fig. 15.11 shows the finite element mesh that might be used to simulate the flow field in an aquifer with element refinement close to a number of wells.

These groundwater modelling packages often involve large numbers of options in discretising the flow domain, setting up initial and boundary conditions, setting up the time stepping, specifying and optimising the model parameters, and so on. There is a danger that, with poor choices of time step, for example, that the solution will be affected by numerical artefacts such as numerical dispersion or, in some cases,

I nu

I nu

SPECIFIED FLOW FROM UPLAND AREAS TO AQUIFER-Flow is specified in layer 1

BOUNDARY OF ACTIVE AREA OF MODEL-No ground-water flow across this boundary

DRAIN CELL

SPECIFIED STREAM-INFLOW SITE

Fig. 15.10 Finite difference grid representation used in the application of MODFLOW to the Big River aquifer, Rhode Island, USA. (Reproduced from Granato and Barlow, 2004, courtesy of United States Geological Survey.)

C0W4«1

EXPLANATION

MODEL GRID SIMULATED STREAM CONSTANT-HEAD CELL INACTIVE CELL

SPECIFIED FLOW FROM UPLAND AREAS TO AQUIFER-Flow is specified in layer 1

BOUNDARY OF ACTIVE AREA OF MODEL-No ground-water flow across this boundary

DRAIN CELL

SPECIFIED STREAM-INFLOW SITE

Fig. 15.10 Finite difference grid representation used in the application of MODFLOW to the Big River aquifer, Rhode Island, USA. (Reproduced from Granato and Barlow, 2004, courtesy of United States Geological Survey.)

mass balance errors or stability problems (see also Section 15.7). Thus it is important to consider any outputs from such models with care. Techniques for the visualisation of model outputs have improved dramatically in recent years and can be very useful in checking and comparing results, but might also make incorrect solutions which look convincing if the programs are not used carefully.

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