This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered Large Eddy Simulation (LES). Here, 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. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with Reinforcement Learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and Finite Volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. 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：本研究提出了一种新颖方法，用于开发隐式滤波大涡模拟中离散一致的封闭格式。在此框架下，诱导滤波器核（进而封闭项）由网格属性和离散化算子共同决定，从而产生先验分析中通常未知的额外计算子网格项。为此，本文将大涡模拟封闭模型系数的自适应任务构建为马尔可夫决策过程，并采用强化学习以后验方式求解。该优化框架同时应用于显式和隐式封闭模型：显式模型基于单元局部涡黏模型，优化后的模型可在间断伽辽金方法中自适应调整诱导黏性，通过向单元中心增加黏性实现耗散均匀化；隐式建模则利用强化学习确定混合间断伽辽金与有限体积格式的最优混合策略。由此产生的优化离散化方案在大涡模拟中比纯间断伽辽金或有限体积方法获得更精确的结果，并作为一种可行的建模假说，通过将湍流建模与激波捕捉统一于单一框架，开创了可压缩湍流高阶格式的新类别。所有新推导模型在多种离散化与分辨率条件下均能达到与传统模型相当或更优的精确结果。总体而言，本研究表明所提出的强化学习优化方法能够提供离散一致的封闭格式，从而降低隐式滤波大涡模拟中的不确定性。