Semianalytical Computation of Path Lines for Finite‐Difference Models

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Abstract
A semianalytical particle tracking method was developed for use with velocities generated from block centered finite‐difference ground‐water flow models. The method is based on the assumption that each directional velocity component varies linearly within a grid cell in its own coordinate directions. This assumption allows an analytical expression to be obtained describing the flow path within an individual grid cell. Given the initial position of a particle anywhere in a cell, the coordinates of any other point along its path line within the cell, and the time of travel between them, can be computed directly. For steady‐state systems, the exit point for a particle entering a cell at any arbitrary location can be computed in a single step. By following the particle as it moves from cell to cell, this method can be used to trace the path of a particle through any multidimensional flow field generated from a block‐centered finite‐difference flow model.

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