On One Dimensional Advection -- Diffusion Equation with Variable Diffusivity
In this paper, we address a time-dependent one-dimensional linear advection-diffusion equation with Dirichlet homogeneous boundary conditions. The equation is solved both analytically, using separation of variables, and numerically, employing the finite difference method. The computational output includes three dimensional (3D) plots for solutions, focusing on pollutants such as Ammonia, Carbon monoxide, Carbon dioxide, and Sulphur dioxide. Concentrations, along with their respective diffusivities, are analyzed through 3D plots and actual calculations. To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air, the domain is divided into two halves. The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity, and vice versa, using 2D and 3D plots. This task is crucial for effective pollution control strategies, and safeguarding the environment and public health.