Perpustakaan Digital ITB

Pollutant transport phenomenon has been a concerning problem in our efforts to preserve the environment. Mathematically, this phenomenon is usually portrayed by the advection diffusion equation which is derived from Fick’s first law and the continuation equation. In this study, the mathematical model is observed in one and two dimensions which is then solved using four different numerical methods. We use the 2nd, 4th and 6th order Forward Time Centered Space and Forward Time Backwards Space Centered Space to solve the mathematical methods. Later, this study further examines the methods by determining the stability conditions, consistency and the order of accuracy by using the Von Neumann stability analysis and Taylor series. To follow that, we confirm each method and its properties by comparing the numerical results with an existing analytical problems and solutions. From those experiments, we can conclude that every method is able to represent the analytical solution. However, in each dimension and each method possesses different stability conditions and orders of accuracy. In obtaining this result, we believe that this study could illustrate the pollutant transport phenomenon.