Modeling and Numerical Simulation of Incompressible Flows using a Pollutant Dispersion Approach

Aboubacar Sidiki Cisse; Roy Kiogora; Kennedy Awuor

doi:https://doi.org/10.14445/22315373/IJMTT-V68I11P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 11 | Year 2022 | Article Id. IJMTT-V68I11P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I11P505

Modeling and Numerical Simulation of Incompressible Flows using a Pollutant Dispersion Approach

Aboubacar Sidiki Cisse, Roy Kiogora, Kennedy Awuor

Citation :

Aboubacar Sidiki Cisse, Roy Kiogora, Kennedy Awuor, "Modeling and Numerical Simulation of Incompressible Flows using a Pollutant Dispersion Approach," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 11, pp. 46-62, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I11P505

Abstract

Pollution dispersion in water is of tremendous importance since it has a direct impact on water quality, particularly in the open ocean. Using experimental and computer tools, the behavior of contaminants spread in water has been anticipated. A mathematical model has been developed based on incompressible flow using a pollutants dispersion approach. These flows make up a substantial part of fluid mechanics and have applications in a variety of sectors, including aeronautics, machine propulsion, free flow hydraulics, and so on. We first established the general convection equation that control the flow of this type fluid, and then we performed several simulations of basic compressible flows of fluid mechanics, such as pollutant dispersion on the surface of a moving liquid. For the discretization of the terms occurring in the different equations of this model, the numerical resolution is based on the method of finite differences utilizing the Cranck Nicholson diagram and the analysis of the diffusion of pollutants, changeable position of the polluting source. We were able to establish data from the literature using the numerical method used in this investigation, displaying acceptable conformity.

Keywords

Convection equation; finite difference method; dispersion of pollutants; fluid mechanics ; Cranck Nicholson.

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