Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations

In this paper, the first-order and second-order semi-discrete predictormulticorrector (PMC) algorithms to solve the 2D/3D unsteady incompressible micropolar fluid equations (IMNSE) are proposed. In the algorithms, the first-order and second-order BDF formulas are adopted to approximate the time derivative terms. At each time step, two elliptical sub-problems with Dirichlet conditions are solved at the prediction step, the strategy of projection about linear momentum equation with additional viscosity term and the elliptical sub-problems about angular momentum are solved at the multicorrection step. Furthermore, the unconditional stability and error estimates of the first-order scheme are proved theoretically. Numerical experiments are carried out to show the effectiveness of the algorithms.