Two-dimensional mixing of pollutants in streams with transvere line source

Abstract

A numerical scheme based on the split-operator approach was developed for the solution of two-dimensional mixing equation with a transverse line-slug source in open channels. An exact solution of the advection equation was developed by adopting the Courant number equal to unity for the computational nodes lying on the flow surface. For the other computational nodes, the cubic spline interpolation scheme was utilized. The computation of the diffusion rate involved the alternate-direction implicit method. The scheme was illustrated by hypothesizing the transverse line injection of tracer at the flow surface, at mid-depth and at the channel bed; it was found that the numerical model is mass conservative. The scheme was validated by comparing its results with Fischer's analytical solution for one-dimensional mixing, the analytical solution by Lipsett and Beltaos for a continuous injection of pollutant as a steady transverse line source, and the laboratory data for slug injection. © 2009 International Association of Hydraulic Engineering and Research.