Zhang Zhe, Su Haiyan, Feng Xinlong
College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China.
Entropy (Basel). 2022 Aug 19;24(8):1159. doi: 10.3390/e24081159.
We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge-Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations.
本文提出并分析了一种用于非稳态热耦合磁流体动力学方程的有效解耦算法。所提出的方法是时间推进中的一阶速度校正投影算法，包括标准速度校正和旋转速度校正，它可以完全解耦模型中的所有变量。同时，该格式不仅是线性的，在每个时间步仅需求解一系列常系数线性偏微分方程，而且标准速度校正算法可为压力场产生诺伊曼边界条件，而旋转速度校正算法可产生一致边界，提高了压力场的精度。从而提高了我们的计算效率。然后，我们给出了算法的能量稳定性并给出了详细证明。建立旋转速度校正算法稳定性结果的关键思想是借助规范 - 乌扎瓦公式将旋转项转化为伸缩对称形式。最后，数值实验表明旋转速度校正投影算法能有效地求解热耦合磁流体动力学方程。
