Comparative study of some numerical methods to solve a 3D advection-diffusion equation

Abstract

In this work, three finite difference methods have been used to solve a three dimensional advection-diffusion equation with given initial and boundary conditions. The three methods are fourth order finite difference method, Crank-Nicolson and Implicit Chapeau Function. We compare the performance of the methods by computing L2 error, L1 error and some performance indices such as mass distribution ratio (MDR), mass conservation ratio (MCR), total mass and R2 which is a measure of total variation in particle distribution.