A numerical model is described that calculates lateral and downstream mixing of contaminant species in two-dimensional confined flows. It consists of partially parabolized, vertically averaged time-dependent equations of motion, continuity, and concentration of non-conservative species. Pertinent equations are solved using finite differences for both laminar and turbulent flow. Results of calculations using the present model are compared with results of other investigators. The model is used to study species mixing for two different discharge concepts.