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.

翻译：本文研究非定常三维磁微极方程的无条件能量稳定数值格式，该方程描述了在磁场作用下导电流体中刚性微元结构的微观特性。第一个方案采用时间上的欧拉半隐式离散与空间上的协调有限元/稳定化有限元方法。第二个方案基于时间上的克兰克-尼科尔森离散及对非线性项的外推处理，以保持斜对称性质。我们证明了所提出的格式具有无条件能量稳定性。获得了速度场、磁场、微旋转场及流体压力的误差估计。此外，建立了若干一阶解耦数值格式。通过数值实验验证了理论收敛阶与无条件能量稳定性。