In the present contribution, we analyze the non-stationary, incompressible, laminar, natural convection flow in a rectangular enclosure filled with a micropolar-nanofluid (Al₂O₃/water) in the presence of a magnetic field, using Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) method. DMD method utilizes numerically or experimentally obtained data (often generated by nonlinear dynamics) to compute the eigenvalues and the eigenmodes of an approximated linear model, and the growth/decay (damp) rates, frequencies and spatial structures for each mode. POD provides the energy content measure for different modes. DMD and POD method have been applied in the study, optimization and control of large-scale dynamical systems. They can be used supplementary to each other or separately for cross comparison. We propose an efficient way to (i) snapshots sampling (ii) select the optimal number for analysis and (iii) define the grid resolution (grid density) for obtaining a grid independent solution for the DMD analysis. We numerically solve the flow equations using a meshless point collocation method (MPCM), using the Moving Least Square (MLS) method to approximate the unknown field functions and their spatial derivatives. We demonstrate stability of the system using the Ritz and dynamic spectrum along with the phase portrait of time coefficients of the most dominant DMD modes. We estimate the energy contents of the captured modes for various Hartman (Ha) and Rayleigh (Ra) numbers, nanoparticles volume fractions ($\phi$), magnetic field ($\xi$) and square enclosure angles ($\gamma$). The energy content of each mode for Al₂O₃/water nanofluid is associated with the corresponding eigenvalue and discloses its contribution to the total energy. The results show that the above mentioned parameters significantly affect the energy contents of the captured modes.

在当前的贡献中，我们分析了填充有微极性纳米流体（Al ₂ O _3）的矩形外壳中的非平稳，不可压缩，层流，自然对流/水）在磁场存在下，使用动态模式分解（DMD）和适当的正交分解（POD）方法。DMD方法利用数值或实验获得的数据（通常由非线性动力学生成）来计算近似线性模型的本征值和本征模，以及每种模的增长/衰减（阻尼）速率，频率和空间结构。POD提供了针对不同模式的能量含量度量。DMD和POD方法已被应用于大型动力系统的研究，优化和控制。它们可以相互补充使用，也可以单独用于交叉比较。我们提出了一种有效的方法来（i）快照采样（ii）选择最佳数量进行分析，以及（iii）定义网格分辨率（网格密度），以获得用于DMD分析的与网格无关的解决方案。我们使用无网格点配点法（MPCM）在数值上求解流动方程，并使用移动最小二乘（MLS）方法来近似未知场函数及其空间导数。我们使用Ritz和动态频谱以及最主要的DMD模式的时间系数的相图来证明系统的稳定性。我们估算了各种Hartman（Ha）和Rayleigh（Ra）数，纳米粒子体积分数（$\phi$），磁场（$\xi$）和方围角（$\gamma$）。Al ₂ O ₃ /水纳米流体的每种模式的能量含量与相应的特征值相关，并公开了其对总能量的贡献。结果表明，上述参数显着影响捕获模式的能量含量。