A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem

Anand Shukla, Akhilesh Kumar Singh, P. Singh
2012 American Journal of Computational and Applied Mathematics  
Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being used for solving these governing equations here we are describing comparative study of Finite volume
more » ... Finite volume method and finite difference method. air. For solving these types of problems, authors presented an iterative, non-overlapping domain decomposition method for solving these problems. A reformulation of the problem leads to an equivalent problem, where the unknowns are on the boundary of the sub-domains [3] .The solving of this interface problem by a Krylov type algorithm [4] , was done by the solving of independent problems in each subdomain, which permits to use efficiently parallel computation. In order to have very fast convergence, C. Japhet et. al use differential interface conditions of order one in the normal direction and of order two in the tangential direction to the interface, which was optimized approximations of absorbing boundary conditions [5] . The present paper deals with the description of the finite volume method for solving differential equations. The comparison is done between the analytical solutions (AS), the solutions obtained by implementing finite volume method and the finite difference method (FDM).
doi:10.5923/j.ajcam.20110102.13 fatcat:tebwxtlirzagnajdnn2fmeobmq