Pressure‐correction projection methods for the time‐dependent micropolar fluids

The unsteady micropolar Navier–Stokes equations (MNSE) is a system which describes the evolution of an incompressible fluid whose material particles possess both translational and rotational degrees of freedom. In this article, both the first order and second order pressure‐correction (PC) projection method for the MNSE are proposed. The unconditionally stability analysis corresponding to the temporal semidiscrete version and the fully discrete version of the PC projection method are proved, and the first order error estimation for the temporal semidiscrete version is deduced. Some numerical simulation results are presented to show the effect of PC projection method. In this paper, the method is extended to non‐homogeneous boundary value problems, especially, the lubrication problem of coaxial bearings. In the case of different rotational angular velocities, the fluid field is still smooth, indicating that the lubrication performance is effective.