Analysis of Convection-Diffusion Problems at Various Peclet Numbers Using Finite Volume and Finite Difference Schemes

Abstract

Convection-diffusion problems arise frequently in many areas of applied sciences and engineering. In this paper, we solve a convection-diffusion problem by central differencing scheme, upwinding differencing scheme (which are special cases of finite volume scheme) and finite difference scheme at various Peclet numbers. It is observed that when central differencing scheme is applied, the solution changes rapidly at high Peclet number because when velocity is large, the flow term becomes large, and the convection term dominates. Similarly, when velocity is low, the diffusion term dominates and the solution diverges, i.e., mathematically the system does not satisfy the criteria of consistency. On applying upwinding differencing scheme, we conclude that the criteria of consistency is satisfied because in this scheme the flow direction is also considered. To support our study, a test example is taken and comparison of the numerical solutions with the analytical solutions is done.

Keywords: Finite volume method, Partial differential equation