A Comparative Study of Numerical Schemes for Convection-diffusion Equation

In this paper, three different numerical schemes are described to approximate the solution of the convection-diffusion equation. The methods are based on differential quadrature and finite difference. In the first scheme, time derivative is approximated using forward difference and the space derivatives using polynomial based differential quadrature method (PDQM). In the second scheme, the discretization of the time and space derivatives are done using PDQM and central difference respectively, while in the third scheme only PDQM is used for the discretization of both time and space derivatives. The validation and comparison of the schemes are done through the simulation of two classic examples of convection-diffusion problem having known exact solution. It is found that the numerical schemes are in excellent agreement with the exact solution. We conclude with the realization that the third scheme, i.e. PDQM in time and space produce more accurate results among these three schemes.