The Role of Advection and Diffusion Terms on the Concentration of Dissolved Oxygen in River Pollution

Dissolved oxygen concentration (DOC) is a crucial metric for assessing and monitoring the overall quality of a water body. A mathematical model utilizes various water quality parameters as inputs to evaluate, monitor, and manage DOC, offering valuable insights into river water quality. Specifically, we propose modeling the transport of DOC using a time-dependent 1-D linear advection-diffusion equation (ADE), subject to defined initial and boundary conditions. To obtain numerical solutions, we applied two different methods: the finite element scheme (FES) and the Taylor-Galerkin scheme. Our results show that the FES is appropriate for problems where diffusion is the dominant effect. However, we observed that as advection becomes dominant, the FES becomes unstable and difficult to evaluate. Consequently, the Taylor-Galerkin schemewas designed and employed as an alternative approach. From the simulation results, we conclude that increasing parameters such as river velocity (w), the diffusion coefficient (d), and the combined advection-diffusion effect all contribute to significantly faster DO transport within the river over a shorter period.