A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system
A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system
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DOI：
10.1016/j.jcp.2013.08.004
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Zhang;M. Ni
中科院分区：
文献类型：
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作者：
J. Zhang;M. Ni
具有复杂边界的磁流体力学(MHD)流动的数值模拟一直是聚变反应堆包层发展中非常感兴趣的课题，因为难以准确地模拟沿任意几何形状的Hartmann层和侧层。为了模拟MHD流动，开发了一种一致守恒型格式的自适应版本。此外，本文还首次尝试在自适应网格加密(AMR)技术下，更灵活、更方便地实现了不规则壁面MHD流动的割胞方法。它采用流体体积(VOF)方法来表示流体-导电壁的界面，使得解决流固耦合的磁场问题成为可能，重点讨论了当切割单元中的导电性不连续时如何实现电场求解。对于不规则切割单元，采用守恒插值法计算单元中心的洛伦兹力。另一方面，将展示当使用AMR技术时，如何在细/粗网格边界上实施一致和保守的格式。然后，通过五个试验模拟对所应用的数值格式进行了验证，所有所考虑的情况都获得了很好的一致性，同时表现出了良好的一致性和保守性。
The numerical simulation of Magnetohydrodynamics (MHD) flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the Hartmann layers and side layers along arbitrary geometries. An adaptive version of a consistent and conservative scheme has been developed for simulating the MHD flows. Besides, the present study forms the first attempt to apply the cut-cell approach for irregular wall-bounded MHD flows, which is more flexible and conveniently implemented under adaptive mesh refinement (AMR) technique. It employs a Volume-of-Fluid (VOF) approach to represent the fluid–conducting wall interface that makes it possible to solve the fluid–solid coupling magnetic problems, emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut-cell. For the irregular cut-cells, the conservative interpolation technique is applied to calculate the Lorentz force at cell-center. On the other hand, it will be shown how consistent and conservative scheme is implemented on fine/coarse mesh boundaries when using AMR technique. Then, the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered, simultaneously showed good consistency and conservative properties.