Unconditionally energy stable numerical schemes for the three-dimensional magneto-micropolar equations

Abstract: In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some magnetic field. The first scheme is comprised of the Euler semi-implicit discretization in time and conforming finite element/stabilizedfinite element in space. The second one is based on Crank-Nicolson discretization in time and extrapolated treatment of the nonlinear terms such that skew-symmetry properties are retained. We prove that the proposed schemes are unconditionally energy stable. Some error estimates for the velocity field, the magnetic field, the micro-rotation field and the fluid pressure are obtained. Furthermore, we establish some first-order decoupled numerical schemes. Numerical tests are provided to check the theoretical rates and unconditionally energy stable.