The 2nd, 4th, and 6th-Order Finite Difference Schemes for Pollutant Transport Equation

Abstract

In this paper, we study the pollutant transport phenomenon using an advection-diffusion equation. To solve the model numerically, we apply the finite difference method. Here we use the second, fourth, and sixth-order explicit finite difference schemes. To validate our numerical models, we compare the numerical results with the existing analytical solution. Further, we conclude that the methods can best approximate the exact solution when using a small Courant number and spatial grid partition. Amongst the three finite difference methods, we observe that the fourth-order FTCS is the best method to simulate the pollutant transport phenomena.