Convergence Analysis of Fractional Time-Stepping Techniques for Incompressible Fluids with Microstructure

We present and analyze fully discrete fractional time stepping techniques for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material particles possess both translational and rotational degrees of freedom. The proposed schemes uncouple the computation of the linear and angular velocity and the pressure. We develop a first order scheme which is unconditionally stable and delivers optimal convergence rates, and an almost unconditionally stable second order scheme.