A new implicit finite difference method with a compact correction term for solving unsteady convection diffusion equations

A new implicit finite difference method with a compact correction term is established for solving unsteady convection-diffusion equations. The correction terms by connecting classical and compact finite difference formulas are proposed for improving the accuracies of numerical solutions. This new method with fourth order accuracy can be used for the numerical calculations of convection diffusion equation on both uniform and nonuniform grid systems. It can be extended not only from one-dimensional to multi-dimensional equations, but also from steady to unsteady convection-diffusion equations. Several convection-diffusion problems are stimulated for verifying the flexibility and high accuracy of this method.