Water pollution control in stream network by finite element and linear programming method

A stream water pollution control model based on the concept of the finite element and linear programming method (FE and LP method) is presented. The model considers a network of interconnected streams and two water quality constituents, biochemical oxygen demand (BOD) and dissolved oxygen (DO). The finite element method is used to cast BOD and DO transport equations into a system of linear algebraic equations which are directly employed as equality constraints of a linear programming problem. To evaluate some of the coefficients of those constraints, dynamic and continuity equations for steady-state gradually varied flow are solved by the Newton–Raphson method. Operating the model, an optimal allocation of BOD loads from outfalls in the stream network can be obtained. An application is made to a hypothetical network to demonstrate that the model could be a useful tool for stream water pollution control.