AI 中文总结
本研究对比三种ROM方法（ROM-FULL、ROM-DEIM、ROM-RBF），在两种基准流动中验证后，为选择合适的ROM策略提供了指南。
AI 中文摘要
本研究对比了三种针对由Carreau流变模型描述的广义牛顿流体流动模拟的降阶建模（ROM）方法。所有三种方法均依赖于在流变参数空间中使用全阶模型（FOM）生成离线快照，随后对快照矩阵进行本征正交分解（POD）以获取降阶基，但它们在在线阶段针对新参数值重构解的方式存在差异。所研究的三种ROM方法为：（i）侵入式Galerkin投影至降阶基并完整重组装算子（ROM-FULL）；（ii）使用离散经验插值法结合GappyPOD处理非线性项的侵入式超降阶Galerkin投影（ROM-DEIM）；（iii）使用径向基函数插值的非侵入式插值方法（ROM-RBF）。我们在两种基准流动上验证了这三种ROM方法： lid驱动腔和封闭容器中的沉降球，涵盖边界驱动和力驱动流动。ROM-FULL精度最高，但需在在线阶段重组装全阶非线性算子；ROM-RBF完全非侵入式，其精度与数据可用性密切相关，在训练数据范围外会下降；ROM-DEIM在效率与精度间实现平衡，即便数据稀疏时也表现良好。研究结果为基于求解器可及性、计算效率和所需精度选择合适的ROM策略提供了指南。
英文摘要
This study compares three reduced-order modeling (ROM) approaches for flow simulations of generalized Newtonian fluids described by the Carreau rheological model. All three methods rely on offline snapshot generation in the rheological parameter space using the full-order model (FOM), followed by a proper orthogonal decomposition (POD) of the snapshot matrix to obtain a reduced basis, but they differ in how they reconstruct the solution for new parameter values in the online phase. The three ROM approaches examined are: (i) intrusive Galerkin projection onto the reduced basis with full operator reassembly (ROM-FULL), (ii) intrusive hyper-reduced Galerkin projection using the discrete empirical interpolation method with GappyPOD for the nonlinear term (ROM-DEIM), and (iii) a non-intrusive interpolation approach using radial basis function interpolation (ROM-RBF). We demonstrate these three ROM approaches on two benchmark flows: a lid-driven cavity and a sphere settling in a closed container, spanning boundary-driven and force-driven flows. ROM-FULL achieves the highest accuracy but requires reassembling the full-order nonlinear operator during the online phase, whereas ROM-RBF is fully non-intrusive, and its accuracy is closely tied to data availability and deteriorates outside the training data range. ROM-DEIM offers a balance between efficiency and accuracy, even when data are sparse. The results provide guidelines for selecting an appropriate ROM strategy based on solver accessibility, computational efficiency, and desired accuracy.
