An effective, locally exact finite-difference scheme for convection-diffusion problems

This article presents a new finite-difference scheme for convection-diffusi on equations for numerical prediction of heat transfer and fluid flows. Thi s scheme, called efficient finite differencing (EFD), is an extension of "l ocally exact" one-dimensional analytical methods. It takes into account mor e accurately the distribution of source term and diffusion coefficient with in the control volume. EFD has been applied to the set of sample problems i ncluding one- and two-dimensional steady-state and transient convection-dif fusion transport. A comparison with exact analytical solutions as well as t he results obtained using other popular methods is also gir,en. The EFD sch eme has been shown to be more accurate while using a mesh system with Sewer grid points. EFD also shows good stability for most of the problems consid ered.