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This study proposes a novel method for developing discretization-consistentclosure schemes for implicitly filtered Large Eddy Simulation (LES). Here, theinduced filter kernel, and thus the closure terms, are determined by theproperties of the grid and the discretization operator, leading to additionalcomputational subgrid terms that are generally unknown in a priori analysis. Inthis work, the task of adapting the coefficients of LES closure models is thusframed as a Markov decision process and solved in an a posteriori manner withReinforcement Learning (RL). This optimization framework is applied to bothexplicit and implicit closure models. The explicit model is based on anelement-local eddy viscosity model. The optimized model is found to adapt itsinduced viscosity within discontinuous Galerkin (DG) methods to homogenize thedissipation within an element by adding more viscosity near its center. For theimplicit modeling, RL is applied to identify an optimal blending strategy for ahybrid DG and Finite Volume (FV) scheme. The resulting optimized discretizationyields more accurate results in LES than either the pure DG or FV method andrenders itself as a viable modeling ansatz that could initiate a novel class ofhigh-order schemes for compressible turbulence by combining turbulence modelingwith shock capturing in a single framework. All newly derived models achieveaccurate results that either match or outperform traditional models fordifferent discretizations and resolutions. Overall, the results demonstratethat the proposed RL optimization can provide discretization-consistentclosures that could reduce the uncertainty in implicitly filtered LES.

Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning