A path probability approach to the solute transport problem

An alternative solute transport algorithm, termed the path probability approach, is presented. The method may be more effective than typical finite methods in some numerical solution problems. The method differs from predominant numerical techniques in that the conventional conservation differential is replaced by a series of equations defining solute migration in terms of a finite number of representative particle position histories and corresponding probabilities. The governing physical assumptions applied in model development are conditionally consistent with those of conventional Lagrangian and Eulerian conceptualizations, but mathematical expression and development of the problem differ from traditional approaches. The method represents dispersion orthogonal to the primary axis of advective transport explicitly, according to arbitrary user-defined probability functions; longitudinal dispersion effects result from the existence of velocity shear effects along the primary axis of movement. It is possible to incorporate Fickian dispersive processes, and thereby reproduce results obtainable with traditional stream tube models; but non-Fickian alternatives can also be explored. Simulation results of the path probability model are compared to analogous results from a representative finite difference model for a hypothetical test flow channel. The comparison demonstrated the ability of the new model to effectively generate simulation results with a computational effeciency considerably higher than conventional techniques under the conditions tested.