This work introduces a novel schemes that combines scalar auxiliary variable (SAV) and pressure-correction (PC) method to solve the magneto-hydrodynamic (MHD) equations. Prove that the first-order and the second-order PC-SAV scheme are unconditionally energy stable. Moreover, the results obtained by our numerical experiments can well verify the effectiveness of the schemes. Finally, the PC-SAV adaptive time-stepping method is given that improve efficiency.

中文翻译：

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基于标量辅助变量法的MHD方程压力校正新方案

这项工作介绍了一种结合标量辅助变量 (SAV) 和压力校正 (PC) 方法来求解磁流体动力学 (MHD) 方程的新方案。证明一阶和二阶 PC-SAV 方案是无条件能量稳定的。此外，我们的数值实验结果可以很好地验证方案的有效性。最后给出了提高效率的PC-SAV自适应时间步长方法。