标题： 基于多线性插值的参数化动态模态分解方法用于预测未见参数下Al₂O₃-水纳米流体的温度场 显示英文标题

标题： Parametric Dynamic Mode Decomposition with multi-linear interpolation for prediction of thermal fields of Al2O3-water nanofluid flows at unseen parameters

摘要： 该研究提出了一种数据驱动模型，该模型结合了动态模态分解与多线性插值，以预测未见过的雷诺数（Re）和粒子体积浓度（$\epsilon$）下的纳米流体流动的温度场。研究中考虑的流动是层流且不可压缩的。该研究采用自研的基于Fortran的求解器，通过二维矩形通道预测氧化铝（Al$_2$O$_3$）-水纳米流体流动的温度场，底部壁面受到均匀热通量的作用。研究考察了在一位和二维参数空间中运行的两种模型的性能。最初，使用基于动态模态分解与线性插值（DMD-LI）的求解器来预测任何Re $>$ 100时纳米流体的温度。基于DMD-LI的模型在Re =960时与基于CFD的求解器相比，预测的温度场的最大百分比差异仅为0.0273%，且$\epsilon$ =1.0%。平均努塞尔数的相应差异仅为0.39%。 在那之后，使用基于双线性插值的DMD（DMD-BLI）求解器来预测纳米流体在任何Re $>$ 100和 $\epsilon$ $>$ 0.5%的温度。 还检查了两种不同的数据堆叠方式的性能。 与基于CFD的模型相比，DMD-BLI-based模型在Re = 800和 $\epsilon$ = 1.35%时，预测温度场的最大百分比差异为0.21%。 平均努塞尔数预测的相应百分比差异仅为6.08%。 所有结果都详细报告了。 除了重要的结论外，研究的未来前景也列出来了。 显示英文摘要

摘要： The study proposes a data-driven model which combines the Dynamic Mode Decomposition with multi-linear interpolation to predict the thermal fields of nanofluid flows at unseen Reynolds numbers (Re) and particle volume concentrations ($\epsilon$). The flow, considered for the study, is laminar and incompressible. The study employs an in-house Fortran-based solver to predict the thermal fields of Al$_2$O$_3$-water nanofluid flow through a two-dimensional rectangular channel, with the bottom wall subjected to a uniform heat flux. The performance of two models operating in one- and two-dimensional parametric spaces are investigated. Initially, a DMD with linear interpolation (DMD-LI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100. The DMD-LI based model, predicts temperature fields with a maximum percentage difference of just 0.0273\%, in comparison with the CFD-based solver at Re =960, and $\epsilon$ = 1.0\%. The corresponding difference in the average Nusselt numbers is only 0.39\%. Following that a DMD with bi-linear interpolation (DMD-BLI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100 and $\epsilon$ $>$ 0.5\%. The performance of two different ways of stacking the data are also examined. When compared to the CFD-based model, the DMD-BLI-based model predicts the temperature fields with a maximum percentage difference of 0.21 \%, at Re = 800 and $\epsilon$ = 1.35\%. And the corresponding percentage difference in the average Nusselt number prediction is only 6.08\%. All the results are reported in detail. Along side the important conclusions, the future scope of the study is also listed.