Steady-state particle tracking in the object-oriented regional groundwater model ZOOMQ3D

Abstract

This report describes the development of a steady-state particle tracking code for use in conjunction with the object-oriented regional groundwater flow model, ZOOMQ3D (Jackson, 2001). Like the flow model, the particle tracking software, ZOOPT, is written using an object-oriented approach to promote its extensibility and flexibility. ZOOPT enables the definition of steady-state pathlines in three dimensions. Particles can be tracked in both the forward and reverse directions enabling the rapid definition of borehole catchments, recharge and discharge areas and the visualisation of groundwater flow fields, for example. Pathlines are defined using the semi-analytical method (Pollock, 1988), however, around particular model features the Runge-Kutta technique is implemented in order to solve some specific problems associated with particle tracking. The problem of particle termination at ‘weak’ sink nodes is solved by the application of the special velocity interpolation scheme presented by Zheng (1994). This approach enables the definition of borehole catchments around wells that induce weak sinks which is not possible with many other widely used particle tracking codes. ZOOMQ3D incorporates the representation of the vertical variation of hydraulic conductivity with depth (VKD) within finite difference nodes. This has been implemented in the flow model to enable the more accurate description of the variation of hydraulic conductivity in limestone, and particularly Chalk aquifers, in which higher hydraulic conductivities are often associated with the zone of fluctuation of the water table. ZOOPT is fully compatible with VKD models and the application of particle tracking in such inhomogeneous aquifers is a development that is expected to be of significant benefit. ZOOMQ3D also enables the local refinement of the finite difference grid, for example, around pumping wells. Again, ZOOPT is fully compatible with this model feature and can be used to track particles through such refined meshes. ZOOPT has been rigorously tested through its comparison with an analytical solution and another particle tracking code and through the visual inspection of pathlines generated using numerous test models. A subset of these tests is presented to illustrate the correct operation of ZOOPT. Whilst the particle tracking routine currently facilitates the definition of steady-state pathlines only, it enables the rapid visualisation of flow fields, which are based on the node-by-node flows at a specific instant of a time-variant simulation. For example, this capability allows the examination of the changing shape of an approximate borehole catchment over an annual recharge or abstraction cycle. The next stage in the development of the code will be to implement time-variant particle tracking, which given its structure should be relatively straightforward