Numerical Solutions Based on Finite Difference Techniques for Two Dimensional Advection-Diffusion Equation
Muhannad A. M. Shallal *
Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq.
Borhan F. Jumaa
Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq.
*Author to whom correspondence should be addressed.
Abstract
In this article, the two dimensional Advection- Diffusion equation has been solved by two finite difference techniques. In the first technique an Alternating Direction Implicit scheme (ADI) is used, this technique is a second order accurate in time and space. In the second technique a Crank Nicolson (CN) method is adapted. This method is known to be of order two in space and time, implicit in time, unconditionally stable and has higher order of accuracy. The numerical results are compared with the analytic solution to illustrate the performance and the efficiency of the methods.
Keywords: Advection-Diffusion equation, Crank-Nicolson method, ADI method, parabolic equation.