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

Abstract

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 L 2 error, L ∞ error and some performance indices such as mass distribution ratio (MDR), mass conservation ratio (MCR), total mass and R 2 which is a measure of total variation in particle distribution.