In this paper a characteristics-based open boundary condition (CBC) is proposed for the magnetohydrodynamic (MHD) system of equations. The algorithm is carefully designed and implemented in the context of a high-order flux reconstruction (FR) scheme under the Generalised Lagrange Multiplier (GLM)-MHD system of equations. It is implemented by adding the contribution of the characteristic equation directly to the corrected flux term in the FR scheme dispensing with solving time-dependent characteristic equations along boundary faces. The CBC method is shown to be more accurate and robust than commonly used zero normal derivative (ZND) and approximate Riemann solver boundary conditions (ARBC) in solving 1D, 2D, and 3D test problems. The CBC method is successfully applied to simulate challenging problems of magnetic reconnection for which other options failed to get stable results over long-period time integration.

中文翻译：

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非结构网格上磁流体动力学高阶解的开放边界条件

在本文中，为磁流体动力学 (MHD) 方程组提出了一种基于特征的开放边界条件 (CBC)。该算法是在广义拉格朗日乘子 (GLM)-MHD 方程系统下的高阶通量重建 (FR) 方案的上下文中精心设计和实现的。它是通过将特征方程的贡献直接添加到 FR 方案中的校正通量项来实现的，无需沿边界面求解瞬态特征方程。在解决 1D、2D 和 3D 测试问题时，CBC 方法被证明比常用的零正态导数 (ZND) 和近似黎曼求解器边界条件 (ARBC) 更准确和稳健。