We propose a novel method for developing discretization-consistent closure schemes for implicitly filtered Large Eddy Simulation (LES). In implicitly filtered LES, the induced filter kernel, and thus the closure terms, are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. Therefore, the task of adapting the coefficients of LES closure models is formulated as a Markov decision process and solved in an a posteriori manner with Reinforcement Learning (RL). This allows to adjust the model to the actual discretization as it also incorporates the interaction between the discretization and the model itself. This optimization framework is applied to both explicit and implicit closure models. An element-local eddy viscosity model is optimized as the explicit model. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid discontinuous Galerkin (DG) and finite volume scheme. All newly derived models achieve accurate and consistent results, either matching or outperforming classical state-of-the-art models for different discretizations and resolutions. Moreover, the explicit model is demonstrated to adapt its distribution of viscosity within the DG elements to the inhomogeneous discretization properties of the operator. In the implicit case, the optimized hybrid scheme renders itself as a viable modeling ansatz that could initiate a new class of high order schemes for compressible turbulence. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.

翻译：我们提出了一种面向隐式滤波大涡模拟（LES）的离散化一致闭合方案开发新方法。在隐式滤波LES中，诱导滤波核及其闭合项由网格与离散化算子特性共同决定，导致在先验分析中通常未知的附加计算子网格项。为此，我们将LES闭合模型系数调整任务建模为马尔可夫决策过程，并采用强化学习（RL）以后验方式求解。该方法通过纳入离散化与模型本身的交互作用，使模型能够自适应调整至实际离散化特性。该优化框架同时适用于显式与隐式闭合模型：显式模型中优化了单元局部涡黏模型；隐式建模中则应用RL识别混合间断伽辽金（DG）与有限体积格式的最优混合策略。所有新推导模型均能获得精确且一致的结果，在不同离散化与分辨率条件下，其性能可比肩甚至超越经典先进模型。此外，显式模型展现了在DG单元内根据算子非均匀离散化特性自适应调整涡粘性分布的能力。在隐式情况下，优化的混合格式展现出作为可行建模方案的潜力，有望催生可压缩湍流新型高阶格式。总体而言，研究结果表明，所提出的RL优化可提供离散化一致的闭合模型，从而降低隐式滤波LES中的不确定性。