Modeling the distribution of a liquid contaminant using the diffusion equation in two dimensions

Abstract

In this work, the 2D-diffusion equation is used to model the diffusion process of a pollutant in calm and shallow waters. The diffusion coefficient was considered spatially constant and only dependent on the nature of the substance. The idea and the numerical schemes (forward difference, backward difference and center difference) were applied to a domain in the XY plane of sideways 1, where the distribution of the contaminant can be seen. Neumann boundary conditions equal to zero or zero flow at the boundary have been used, in order to make a cut at said boundary for the modeling. The computational program carried out allows moving the contaminant source to any point of the domain and seeing its distribution in real time, it is also possible to add other contaminant sources and observe their diffusion. As the value of the contaminant concentration decreases over time, a slowdown in the speed of the wave is observed; the modeling allows monitoring the distribution of the contaminant for all time. Therefore, the developed numerical model can be used to predict the distribution of contaminants in liquids.