A High-Order Compact ADI Scheme for the 3D Unsteady Convection-Diffusion Equation

In this paper, we developed a high-order compact ADI scheme for solving the three-dimensional (3D) unsteady convection-diffusion equation. By using fourth-order compact schemes for spatial derivatives and the Crank-Nicolson method for temporal derivative, the present ADI scheme is fourth-order accurate in space and second-order accurate in time. The solution procedure consists of a number of tridiagonal matrix operations, which makes the computation cost effective. The unconditionally stability of the method is verified by means of the discrete Fourier analysis. Two typical numerical experiments are given to demonstrate the high accuracy of the present method and to compare it with the classical Douglas ADI scheme and the Karaa´s fourth-order ADI scheme.