Journal of Applied Mathematics
Volume 2013 (2013), Article ID 596218, 10 pages
http://dx.doi.org/10.1155/2013/596218
Research Article

Comparison Study on the Performances of Finite Volume Method and Finite Difference Method

Renwei Liu,1 Dongjie Wang,1 Xinyu Zhang,1 Wang Li,1,2 and Bo Yu1

1National Engineering Laboratory for Pipeline Safety and Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, China
2PetroChina Southwest Pipeline Company, Chengdu 610041, China

Received 26 March 2013; Revised 9 June 2013; Accepted 9 June 2013

Academic Editor: Shuyu Sun

Copyright © 2013 Renwei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDM with variant mesh densities, discrete forms, and treatments of boundary condition. It is indicated that FVM is superior to FDM from the perspective of accuracy, stability of convection term, robustness, and calculation efficiency. Particularly ,when the mesh is coarse and taken as , the results of FDM suffer severe oscillation and even lose physical meaning.