采用FE-HMM方法的局部受限非线性涡流问题的磁场适配多尺度格式
Magnetic Field Conforming Multiscale Formulations for Locally-Confined Nonlinear Eddy Current Problems Using the FE-HMM Method
- Univ. Grenoble Alpes, CNRS, Grenoble INP, G2ELab（格勒诺布尔阿尔卑斯大学）
- Monash University（蒙纳士大学）
- KU Leuven（荷语鲁汶大学）
- University of Liège（列日大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出适配h-conforming的磁性复合材料多尺度HMM格式，采用双中尺度问题与松弛NR方案，经二维三维软磁复合材料验证可缓解非线性涡流问题的收敛问题
AI中文摘要：
用于电能转换的磁性复合材料通常包含彼此绝缘的铁磁夹杂，以减轻涡流损耗。这类复合材料的数值模型需足够稳健，以应对非线性铁磁夹杂及单元内存在显著受限涡流时可能出现的收敛问题。本文在周期性框架下提出一种适配h- conforming的磁性复合材料多尺度格式，所提方法采用异质多尺度方法（Heterogeneous Multiscale Method, HMM），包含两个中尺度问题：用于上尺度化 homogenized 磁通量密度$\boldsymbol{B}_M$的磁准静态问题，以及用于上尺度化宏观增量磁阻率$(\boldsymbol{\nabla} \boldsymbol{B}_M/\boldsymbol{\nabla} \boldsymbol{H}_M)$的静磁问题。此外，该方法在宏观和中尺度层面均采用松弛牛顿-拉夫逊（Newton--Raphson）格式，以缓解与h-conforming格式中非线性BH本构律相关的著名NR收敛问题。通过具有线性和非线性BH曲线的二维及三维理想化周期性软磁复合材料，评估该格式的精度与性能。此外，本文还证明磁准静态中尺度问题可替换为静磁问题
英文摘要：
Magnetic composites used for the conversion of electrical energy often incorporate ferromagnetic inclusions insulated from each other to mitigate eddy current losses. Numerical models for these composites must be robust enough to address potential convergence issues arising from the presence of nonlinear magnetic inclusions and presence of significant confined eddy currents in the cell. This paper introduces an $\mathbf{h}$-conforming multiscale formulation for magnetic composites in a periodic framework. The proposed method uses the Heterogeneous Multiscale Method (HMM) with two mesoscale problems: a magnetoquasistatic problem for upscaling the homogenized magnetic flux density $\mathbf{B}_M$ and a magnetostatic problem for upscaling the macroscale incremental reluctivity $(\partial \mathbf{B}_M/\partial \mathbf{H}_M)$. Additionally, the method uses relaxed Newton--Raphson schemes at both macro and mesoscale levels to mitigate the well-known NR convergence issue linked to nonlinear BH constitutive laws in $\mathbf{h}$-conforming formulations. The accuracy and performance of the formulation are evaluated using 2D and 3D idealized periodic soft magnetic composites with linear and nonlinear BH curves. Furthermore, the paper demonstrates that the magnetoquasistatic mesoscale problem can be replaced by a magnet a
