Finite volume model for steady-state transverse mixing in streams

Transverse mixing is arguably more important in water quality management than either vertical or longitudinal mixing, especially when dealing with the discharge of pollutants from point sources or the mixing of tributary inflows. A finite volume model with upwind scheme is developed to solve the equation for transverse mixing in steady flow in prismatic channel. The model takes care of variation of transverse mixing coefficient across the channel width. The model has been verified with analytical solutions for constant mixing coefficient and for pollutant injection in the middle and near the bank of streams. The model is inherently mass conservative and captures successfully the discontinuity existing at the upstream boundary. Effect of variable transverse mixing coefficient on the pollutant concentration profiles has been shown for a typical cross-section of the Lesser Slave River. It is found that the computed concentration profiles for variable transverse mixing coefficient are significantly different from those for constant coefficient.