High-Order Compact Difference Scheme for Convection–Diffusion Problems on Nonuniform Grids

In this study, a high-order compact (HOC) scheme for solving the convection–diffusion equation (CDE) under a nonuniform grid setting is developed. To eliminate the difficulty in dealing with convection terms through traditional numerical methods, an upwind function is provided to turn the steady CDE into its equivalent diffusion equation (DE). After obtaining the HOC scheme for this DE through an extension of the optimal difference method to a …