Practical finite analytic methods for simulation of solute transport with scale-dependent dispersion under advection-dominated conditions

The practical finite analytic (PFA) method was applied to the solution of the one-dimensional advection equation with scale-dependent dispersion equation (ASDE) for solute transport in porous media under advection-dominated (high Peclet number) conditions. A triangular explicit PFA (EPFA) with three different approaches (EPFA 1, 2 and 3) and the Crank–Nicolson (CN) centered and upwind techniques were developed to solve the ASDE with a dispersivity with linear dependence on transport distance. In EPFA 1, to get more accurate results for the ASDE, the existing PFA method was developed and combined with the FD method. In EPFA 2 the original PFA method was employed to check its accuracy for modeling the ASDE without any modifications. Finally, in EPFA 3, based on the current PFA solution, new formulations are proposed to evaluate the accuracy of this approach. For all conditions, EPFA 3 has the best behavior in comparison with other numerical techniques for different linear functions for distance dependence of dispersivity.