A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order time discretization of a perturbed system which approximates the MHD system. The main results are that the convergence for the velocity and the magnetic field are strongly second-order in time while that for the pressure is strongly first-order in time. Some numerical tests are performed to illustrate the theoretical predictions and demonstrate the efficiency of the proposed scheme.

中文翻译：

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时变磁流体动力学方程的高阶压力分离方案

提出了时间相关不可压缩磁流体动力学 (MHD) 方程的高阶压力分离方案。该方案允许我们在每个时间步将 MHD 系统解耦为两个子问题。首先，求解速度和磁场的耦合线性椭圆系统。然后，对压力处理 Poisson-Neumann 问题。通过将此分离方案解释为近似 MHD 系统的扰动系统的高阶时间离散化来分析稳定性并完成误差分析。主要结果是速度和磁场的收敛在时间上是强二阶的，而压力的收敛在时间上是强一阶的。