A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients

ABSTRACT

Advection-diffusion equation with constant and variable coefficients has a wide range of practical and industrial applications. Due to the importance of advection-diffusion equation the present paper, solves and analyzes these problems using a new finite difference equation as well as a numerical scheme. The developed scheme is based on a mathematical combination between Siemieniuch and Gradwell approximation for time and Dehghan's approximation for spatial variable. In the proposed scheme a special discretization for the spatial variable is made in such away that when applying the finite difference equation at any time level (j + 1) two nodes from both ends of the domain are left. After that the unknowns at the two nodes adjacent to the boundaries are obtained from the interpolation technique. The results are compared with some available analytical solutions and show a good agreement.

Keywords:

Advection-diffusion equation, Explicit finite difference techniques, Implicit finite difference techniques, Interapolation techniques.