Study of pollutant transport in depth-averaged flows using random walk method

Abstract

The random walk particle tracking (RWPT) method is compared with the Eulerian methods in investigating pollutant transport in depth-averaged flows. As a typical representative of the Eulerian model with high performance, the MacCormack scheme with Total Variation Diminishing modification (TVD-Mac) is selected for comparison. Solute concentration is simulated in four case studies. First, both numerical models have been tested in two idealized cases and compared against analytical solutions. Numerical dissipation is observed for TVD-Mac model where the concentration changes abruptly, especially under the circumstances of low resolution and misalignment between the flow direction and grid orientation. On the contrary, simulations by the random walk model achieve higher accuracy in both cases and are free of fictitious oscillations in the vicinity of sharp concentration gradients. Then, the solute oscillation along a one-dimensional hypothetical tidal estuary is simulated, with the RWPT accurately conserving mass and suffering less numerical diffusion compared with the Eulerian method. Finally, the process of pollutant transport in a Yangzte River reach is predicted by the RWPT. The longitudinal dispersion coefficient DL is calculated accordingly. It is compared favorably with the theoretical/empirical formulae, indicating the validity of the RWPT in solving complex natural problems.