Extension of high-order compact difference scheme for 3-D steady problem to unsteady problem

Based on our previous fourth-order compact difference scheme for the 3-D steady convection diffusion equation, a high-order compact implicit difference scheme for the 3-D unsteady convection diffusion equation is directly obtained. It is unconditionally stable and the local truncation error is second order for time and fourth order for space. Supporting numerical experiments are included to illustrate the high accuracy and robustness of present method.