Mathematical model for river pollution

Abstract

River pollution is already a common natural disaster in today’s world due to human’s daily activities. Yet, researchers always come out with tonnes of ideas and alternatives to overcome the situation by hoping that we can save one of the main resources of our daily life. In this dissertation, there are three main purposes in order to finish up this thesis. The most important objective is to formulate a simple mathematical model that involved Advection-Diffusion equation. It consists of coupled equation; pollutant and dissolved oxygen. Both equations are consists of Menten-Michaelis Equation and Heaviside-step function. The main purpose of adding these two terms are just empirical relationship with in the literature review. The derivation of the model will be also attached together with this thesis. Finite difference method (FDM) will be used to solve the problem and used in our simulation. We will transform it into a simpler case. Then, we will investigate the effects of aeration on the degradation of pollutant. Finally, we considered that the problem can be solved in steady-state. By assuming that some terms are constant, we might get the solution for this problem. By the end of this thesis, we expect to obtain the results based on our objectives using MATLAB simulation. From here, we shall see that either this model is suitable or not to be one of the alternative to overcome the pollution.