Analytical and numerical results of dissolved oxygen and biochemical oxygen demand in non-uniform open channel

A mathematical model for DO (dissolved oxygen) and BOD (biochemical oxygen demand) in a non-uniform open channel is presented in this work. This model can be used to study transport processes in one-dimensional flow. An accurate numerical scheme based on the finite element method with linear polynomial basis is developed for studying flows both upstream and downstream with respect to a point source. The accuracy of numerical solutions have been studied and compared with certain analytical solutions at steady state. Various test cases including only dispersion effect, DO sag curve, and the linear variation of cross-sectional area are investigated. We have also derived an analytical solution for the last case when the model is simplified under certain conditions. This model has been applied to real flow parameters of Tha Chin river in Thailand. Furthermore, the impacts of flow velocity, kinetic reaction order, and dispersion coefficients have been simulated to observe the dissolved oxygen and biochemical oxygen demand dynamics along the channel.