用虚拟域扩展解决神经算子流场模拟边界条件难题
Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operator
- 构建虚拟域扩展框架，将边界条件转化为虚拟域上场值的设定
- 在多个数值例子中验证，虚拟域方法可实现高精度流场预测
- 适合希望复用预训练神经算子的工程仿真研究人员
本文提出一种虚拟域扩展（VDE）框架，用于在预训练局部神经算子（LNO）进行流场模拟时施加边界条件（BC）。通过在输入函数上构建扩展的虚拟域，补偿LNO推理过程中计算域的腐蚀特性，将边界条件施加转化为对扩展域上场值的确定。提出了多种场值计算策略，包括填充操作、直接施加、压力对称性及反向传播优化，并与传统求解器的边界处理方式对比。研究发现，LNO的大时间间隔导致需处理的近边界区域较宽，仅在靠近边界的少数节点施加边界条件（如传统浸入边界法）难以保证高精度。通过在扩展虚拟域上合理赋值，VDE能准确施加边界条件，获得合理的流场预测结果。该工作为可靠施加边界条件提供了指导，有助于推动预训练LNO在更多场景中的应用。
原文摘要 · Abstract (English)
This paper builds up a virtual domain extension (VDE) framework for imposing boundary conditions (BCs) in flow simulation using pre-trained local neural operator (LNO). It creates extended virtual domains to the input function to compensate for the corrosion nature of computational domains during LNO inference, thus turns the implementation of BC into the determination of field values on the extended domain. Several strategies to calculate the field values are proposed and validated in solving numerical examples, including padding operation, direct imposition, pressure symmetry, and optimization by backpropagation, and compared with boundary imposition in traditional solvers. It is found that the large time interval of LNO induces a relatively wide near-boundary domain to be processed, thus imposing BC on only a few nodes near the boundary following the immersed boundary conception in traditional solvers can hardly achieve high accuracy. With appropriate values assigned on the extended virtual domains, VDE can accurately impose BCs and lead to reasonable flow field predictions. This work provides a guidance for imposing BCs reliably in LNO prediction, which could facilitate the reuse of pre-trained LNO in more applications.
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