AN EFFECTIVE, LOCALLY EXACT FINITE-DIFFERENCE SCHEME FOR CONVECTION-DIFFUSION PROBLEMS

This article presents a new finite-difference scheme for convection-diffusion equations for numerical prediction of heat transfer and fluid flows. This scheme, called efficient finite differencing (EFD), is an extension of "locally exact" one-dimensional analytical methods. It takes into account more accurately the distribution of source term and diffusion coefficient within the control volume. EFD has been applied to the set of sample problems including one- and two-dimensional steady-state and transient convection-diffusion transport. A comparison with exact analytical solutions as well as the results obtained using other popular methods is also given. The EFD scheme has been shown to be more accurate while using a mesh system with fewer grid points. EFD also shows good stability for most of the problems considered.