We propose a new neural network based large eddy simulation framework for the incompressible Navier-Stokes equations based on the paradigm "discretize first, filter and close next". This leads to full model-data consistency and allows for employing neural closure models in the same environment as where they have been trained. Since the LES discretization error is included in the learning process, the closure models can learn to account for the discretization. Furthermore, we introduce a new divergence-consistent discrete filter defined through face-averaging. The new filter preserves the discrete divergence-free constraint by construction, unlike general discrete filters such as volume-averaging filters. We show that using a divergence-consistent LES formulation coupled with a convolutional neural closure model produces stable and accurate results for both a-priori and a-posteriori training, while a general (divergence-inconsistent) LES model requires a-posteriori training or other stability-enforcing measures.

翻译：我们提出了一种新的基于神经网络的大涡模拟框架，用于不可压缩纳维-斯托克斯方程，其范式为“先离散，再滤波并闭合”。这实现了模型与数据的完全一致性，并允许在训练环境中直接部署神经闭合模型。由于大涡模拟的离散误差被纳入学习过程，闭合模型能够学会补偿离散化带来的影响。此外，我们引入了一种通过面平均定义的新型散度一致离散滤波器。与体积平均滤波器等通用离散滤波器不同，该新滤波器在构造上保持了离散无散约束。我们证明，采用散度一致的大涡模拟公式结合卷积神经闭合模型，在先验训练和后验训练中均能产生稳定且准确的结果，而通用（非散度一致）的大涡模拟模型则需要后验训练或其他稳定性增强措施。