A Numerical and Analytical Framework for Estimating Water Pollution in A 3-D Aquatic Region Using Diffusion Model with Du Fort Frankel and Adomian Decomposition Methods

Water pollution is an important environmental issue that affects human health, aquatic habitats, and the sustainability of natural resources. Reliable mathematical models that can forecast the behaviour of pollutants in three-dimension (3-D) water systems are needed to address this issue. In this study, a 3-D diffusion model is used to determine the periodic and location-based fluctuation of the pollutant concentration in water. Investigating the slow increase in pollution levels in a 3-D area and evaluating the precision of analytical and numerical approaches to diffusion-based pollution problems are the objectives of this work. Two approaches are used to accomplish this: the Adomian Decomposition Method (ADM), which is an analytical approach, and the Du Fort Frankel (DF) scheme, which is a numerical approach.  Initial and boundary conditions required for the modelling are provided by experimented data (Exp. data) from a 3-D cuboid tank filled with water and introduced with an iodized salt water solution as the pollutant.  Direct monitoring of pollution dispersion across time and space is made possible by this configuration, producing useful data for confirming the mathematical models. The results of the experiment verify that the levels of pollutants rise with time at each location in the 3-D region.  When comparing the outcomes of the DF approach with Exp. data and ADM, an insignificant difference, measured in parts per million (PPM), is observed, demonstrating the reliability and strength of the suggested model.  This study is important because it combines mathematical models and realistic observations to examine pollution of water in 3-D. The results show that the model is accurate and applicable to both controlled experiments and larger-scale water systems.  Additionally, this work advances the mathematical solutions for diffusion equations and offers useful information for sustainable resource use, pollution control, and water quality evaluation.

Water pollution, 3-D Diffusion equation, Du Fort Frankel method, Adomian Decomposition method

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