Application of Advection Diffusion Equation for Determination of Contaminants in Aqueous Solution: A Mathematical Analysis

Muhammad Masudur Rahaman¹, Humaira Takia^2, , Md. Kamrul Hasan³, Md. Bellal Hossain¹, Shamim Mia⁴ and Khokon Hossen²

¹Department of Mathematics, Patuakhali Science and Technology University, Dumki, Patuakhali-8602, Bangladesh

²Department of Physics and Mechanical Engineering, Patuakhali Science and Technology University, Dumki, Patuakhali-8602, Bangladesh

³Department of Civil Engineering, Uttara University, House No. 4 & 6, Road No. 15, Uttara, Dhaka-1230, Bangladesh

⁴Department of Agronomy, Patuakhali Science and Technology University, Dumki, Patuakhali-8602, Bangladesh

Cite this paper:
Muhammad Masudur Rahaman, Humaira Takia, Md. Kamrul Hasan, Md. Bellal Hossain, Shamim Mia and Khokon Hossen. Application of Advection Diffusion Equation for Determination of Contaminants in Aqueous Solution: A Mathematical Analysis. Applied Mathematics and Physics. 2022; 10(1):24-31. doi: 10.12691/amp-10-1-2

Abstract

Water pollution is one of the leading environmental issues faced especially at developing countries all over the World. However, the study of pollution movement is a necessary basis for solving water quality problems. The mathematical model for soluble and insoluble water pollutants has been formulated in light of partial differential equations. This research proposes the motion of flowing pollution by using a mathematical model in one-dimensional advection diffusion equation. Therefore, the study explored finite difference method for the numerical solutions of advection diffusion equation (ADE). Moreover, the study considered the ADE as an initial boundary value problem (IBVP) for the estimation of water pollution. By implementing a finite difference scheme for the IBVP, we examined as well as analyzed the extent of water pollution at different times and different points in an 1-dimensional spatial domain. We estimated relative error of the schemes in comparison with an exact solution of ADE and the numerical features of the rate of convergence are presented graphically. Finally, we compared our numerical solution of the ADE with solution obtained by finite element method. Numerical analysis indicates that water treatment is an essential tool for obtaining quality water for human consumption.

Keywords:
advection diffusion equation finite difference schemes water pollutants mathematical modeling feasibility of solution stability analysis

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