In the framework of a mixed finite element method, a structure-preserving formulation for incompressible MHD equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the fluid part from the Maxwell part by means of staggered discrete time sequences and, in doing so, partially linearizes the system. Conservation and dissipation properties of the formulation before and after the decoupling are analyzed. We demonstrate optimal spatial and second-order temporal error convergence and conservation and dissipation properties of the proposed method using manufactured solutions, and apply it to the benchmark Orszag-Tang and lid-driven cavity test cases.

翻译：在混合有限元方法框架下，本文提出了适用于一般边界条件的不可压缩磁流体动力学方程的保结构数值格式。通过采用交错离散时间序列的蛙跳型时间推进方案，该格式实现了流体部分与麦克斯韦部分的完全解耦，并在此过程中实现了系统的部分线性化。本文分析了该格式在解耦前后的守恒与耗散特性。通过构造精确解验证了所提方法在空间上具有最优收敛阶、在时间上具有二阶收敛精度，并展示了其守恒与耗散特性。最后，将该方法应用于Orszag-Tang基准算例和盖驱动方腔流动测试案例。