A Semi-Analytical Particle-Tracking Method for Groundwater Flows Simulated on Unstructured Control-Volume Finite-Difference Grids

Particle tracking is a numerical method that involves computing the trajectories of hypothetical particles embedded in a simulated flow field. Applications in groundwater hydrology include simulation of contaminant transport, delineation of source areas, and simulation of groundwater age. The U.S. Geological Survey's (USGS's) MODPATH 7 code can track particles through flow fields generated by the USGS's MODFLOW 6 groundwater flow simulator, which is based on control-volume finite differences. However, the method used by MODPATH 7 to interpolate particle velocities within a cell or subcell requires that the cell or subcell be rectangular. As a result, MODPATH 7 can track particles on rectangular, quadtree, or quadpatch grids, but not on the full variety of unstructured grids supported by MODFLOW 6.

In this work, a new method is presented that enables particle tracking on three-dimensional, unstructured grids of cells that are convex polygonal prisms with horizontal tops and bottoms - the most general type of grid supported by MODFLOW 6. For rectangular cells, the new method is mathematically equivalent to the method currently used in MODPATH 7. The new method subdivides a polygonal cell into triangles and uses barycentric interpolation to define particle velocity within each triangle. The new method is semi-analytical in that particle trajectories within each triangle are determined analytically but exit times and locations are computed by numerical iteration. Features and limitations of the new method are discussed, and examples of particle tracks through flow fields generated by MODFLOW 6 on unstructured grids are presented.