Abstract: Computational fluid mechanics mainly studies how to solve the governing equations of fluid mechanics through numerical methods. In this paper, taking the incompressible Couette flow as an example, based on the theoretical analytical solution, the finite difference control equations of explicit method and implicit method are established, and the third method based on pressure correction method is proposed. The flow field distribution is solved by Matlab programming, and the effects of propulsion steps, equal fraction, time interval, and Reynolds number on the calculation error are studied. By studying the mechanical characteristics of classical flow phenomena, students can deepen their understanding of the basic methods and ideas of computational fluid mechanics, and cultivate the ability to integrate theory with practice.