In this paper, a one-level operator splitting method (OOSM) and a two-level operator splitting method (TOSM) for the two-dimensional or three-dimensional (2D/3D) unsteady incompressible micropolar fluid equations with double diffusion convection (IMFDDC) are proposed and analyzed. Firstly, a OOSM is constructed, which consists of five steps. The projection strategy is adopted to get the values of linear velocity and pressure in the first two steps, then the three elliptic subproblems about the angular velocity, the temperature, and the concentration variables are solved in the last three steps. The original variables with the predefined boundary conditions need to be solved separately in each step. Next, in order to solve the problem efficiently, a TOSM is presented, which only solves the nonlinear equations in the coarse level subspaces and the Oseen type linearized equations in the fine level. The numerical analysis of stability and error estimates of the fully discrete methods show that TOSM can reach the same accuracy as the OOSM with . Numerical examples are provided to confirm the effectiveness and reliability of the proposed methods.

中文翻译：

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双扩散对流非定常不可压缩微极性流体方程的一级和二级算子分裂方法


本文提出了二维或三维（2D/3D）非定常不可压缩微极性流体双扩散对流方程（IMFDDC）的一级算子分裂法（OOSM）和二级算子分裂法（TOSM） ）提出并分析。首先构建OOSM，分为五个步骤。采用投影策略在前两步中得到线速度和压力值，然后在后三步中求解关于角速度、温度和浓度变量的三个椭圆子问题。具有预定义边界条件的原始变量需要在每个步骤中单独求解。接下来，为了有效地求解该问题，提出了一种TOSM，它仅求解粗级子空间中的非线性方程和精细级中的Oseen型线性化方程。全离散方法稳定性和误差估计的数值分析表明，TOSM 可以达到与 OOSM 相同的精度。提供数值例子来证实所提出方法的有效性和可靠性。