用于三相界面流的谱嵌入算子学习：三元 Cahn-Hilliard-Navier-Stokes 基准测试
Spectral-Embedded Operator Learning for Three-Phase Interfacial Flow: A Ternary Cahn-Hilliard-Navier-Stokes Benchmark
- University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究构建三相界面流基准，对比 DeepONet 变体，发现谱嵌入的 SEDONet 可显著降低预测误差，对三相流强非周期结构适配性更优。
中文摘要 AI 辅助
算子学习替代模型大多在单场、单界面问题上进行基准测试，尚不清楚这些场景中验证的架构选择是否适用于受约束的多相流。我们引入三相界面流基准测试，以研究主干坐标表示是否对多通道、界面主导的目标重要。该配置为：在有界壁约束域内，气泡上升穿过水，刺破水-油界面，并将水羽流卷吸入油中。参考数据采用保结构三元 Cahn-Hilliard-Navier-Stokes 求解器生成，该求解器代数上保持单纯形约束。从在九维参数空间上采样的 1024 个 Sobol 模拟中，我们学习从物理参数到五通道时空场的映射。我们比较仅主干表示不同的三个参数匹配的 DeepONet 变体：原始坐标（DeepONet）、随机傅里叶特征（FEDONet）和固定张量积切比雪夫字典（SEDONet）。与 FEDONet 相比，SEDONet 将测试相对 L2 误差降低了 16.8%，与 DeepONet 相比降低了 24.0%，同时改善了所有五个输出通道。时空误差分析将主要增益定位于扩散界面附近和气泡穿透后区域。结果表明，切比雪夫表示对该三相流强非周期性的壁法向和时间结构特别有效。
英文摘要
Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices validated in those settings transfer to constrained, multiphase flows. We introduce a three-phase interfacial-flow benchmark to examine whether the trunk coordinate representation matters for a multi-channel, interface-dominated target. The configuration consists of an air bubble rising through water, piercing a water-oil interface, and entraining a water plume into the oil within a bounded, wall-confined domain. Reference data are generated using a structure-preserving ternary Cahn-Hilliard-Navier-Stokes solver that algebraically preserves the simplex constraint. From 1,024 Sobol-sampled simulations spanning a nine-dimensional parameter space, we learn the mapping from physical parameters to five-channel space-time fields. We compare three parameter-matched DeepONet variants differing only in trunk representation: raw coordinates (DeepONet), random Fourier features (FEDONet), and a fixed tensor-product Chebyshev dictionary (SEDONet). SEDONet reduces the test relative L2 error by 16.8% compared with FEDONet and by 24.0% compared with DeepONet, while improving all five output channels. Spatial and temporal error analyses localize the principal gains near the diffuse interfaces and after bubble breakthrough. The results indicate that the Chebyshev representation is particularly effective for the strongly non-periodic wall-normal and temporal structure of this three-phase flow.
