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Convergence analysis of a fractional time-stepping technique for incompressible fluids with microstructure

We present and analyze a fully discrete fractional time stepping technique 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 scheme uncouples the computation of the linear and angular velocity and the pressure. It is unconditionally stable and delivers optimal convergence rates.