改进的格子玻尔兹曼方法用于共轭磁流体动力学模拟
Improved lattice Boltzmann method for conjugate magnetohydrodynamic simulations
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中文总结 AI 辅助
针对共轭磁流体动力学模拟，提出改进的格子玻尔兹曼方法，通过将旋度-旋度项与简化散度项的差异作为源项处理，自动满足界面共轭约束，并用解析解验证了精度。
中文摘要 AI 辅助
在共轭磁流体动力学（MHD）流动的模拟中，当移动的导电流体在外加磁场作用下与边界导电壁动态相互作用时，解析流体-固体界面上的电导率跃迁会带来显著的数值挑战。在高磁雷诺数问题中，需要求解完整的磁感应方程，其中包含磁扩散的旋度-旋度项，而在原始的矢量格子玻尔兹曼方法（LBM）中，该项被简化为散度项。由此得到的LBM方案适用于模拟电导率恒定的流体域，其边界固体壁通过适当的边界条件进行建模。本研究表明，该方案同样适用于二维共轭MHD模拟，其中具有非零梯度的磁场分量垂直于电导率梯度。对于一般的共轭MHD模拟，我们通过考虑旋度-旋度项与简化散度形式之间的差异来改进LBM方案，该差异在LBM演化算法中被视为源项，并采用高效的LBM离散格式进行计算。改进的LBM方案通过两个相邻边界层内的体积积分自动满足流体-固体界面处所需的共轭约束。改进的LBM方案的准确性通过基准问题中流体-固体界面处电导率突变的逐段解析解进行了验证。
英文摘要
In the simulation of conjugate magnetohydrodynamic (MHD) flows, where a moving conducting fluid dynamically interacts with bounding conducting walls under the influence of an externally imposed magnetic field, resolving the electrical conductivity transition across the fluid-solid interface introduces significant numerical challenges. In problems with high magnetic Reynolds numbers, it is required to solve the full magnetic induction formulation that has a curl-of-curl term for the magnetic diffusion, which is simplified to a divergence term in the original vector-valued lattice Boltzmann method (LBM). The resulting LBM scheme is valid for simulating fluid domains with a constant conductivity where its bounding solid walls are modelled using appropriate boundary conditions. The current study shows that this scheme is also valid for two-dimensional conjugate MHD simulations where the magnetic field component with non-zero gradients is perpendicular to the conductivity gradient. For general conjugate MHD simulations, we improve the LBM scheme by considering the difference between the curl-of-curl term and the simplified divergence form, which is treated as a source term in the LBM evolution algorithm and computed using an efficient LBM discretisation scheme. The improved LBM scheme automatically satisfies the required conjugate constraints at the fluid-solid interface as a volume integral inside two adjacent boundary layers. The accuracy of the improved LBM scheme is verified by piecewise analytical solutions in benchmark problems with an abrupt conductivity jump across the fluid-solid interface.
发表机构
- Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（先进智能与计算研究所，科技研究局）
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