Comparison of finite difference and control volume methods for solving differential equations

Abstract

Comparisons are made between the finite difference method (FDM) and the control volume formulation (CVF). An analysis of truncation errors for the two methods is presented. Some rules-of-thumb related to the accuracy of the methods are included. It is shown that the truncation error is the same for both methods when the boundary conditions are of the Dirichlet type, the system equations are linear and represented in Cartesian coordinates. A technique to analyze the accuracy of the methods is presented. Two examples representing different physical situations are solved using the methods. The FDM failed to conserve mass for a small number of nodes when both boundary conditions include a derivative term (i.e. either a Robin or Neumann type boundary condition) whereas the CVF method did conserve mass for these cases. The FDM is more accurate than the CVF for problems with interfaces between adjacent regions. The CVF is (ΔX) order of accuracy for a Neumann type boundary condition whereas the FDM is (ΔX) 2 order.