The study of Large-Eddy Simulations (LES) in turbulent flows continues to be a critical area of research, particularly in understanding the behavior of small-scale turbulence structures and their impact on resolved scales. In this study, we focus on the LES of turbulent flows, particularly the one-dimensional Stochastic Burgers Equation (SBE), using fully conservative higher-order schemes. The interaction between spatial discretization and SubGrid-Scale (SGS) modeling is explored rigorously by validating these schemes against analytical solutions for both the Linear Advection-Diffusion (LAD) equation and the Non-Linear Burgers (NLB) equation under laminar conditions. This ensures robustness before applying the approach to LES of stochastic turbulence. The study investigates how second-order and fourth-order discretization schemes influence the dynamic coefficients of various SGS models, including Constant Smagorinsky (CS), Dynamic Smagorinsky (DS), Dynamic Wong-Lilly (DWL), 1.5-order Turbulent Kinetic Energy Deardorff (TKED), Equilibrium Heinz (EH), and Dynamic Heinz (DH) models. The second-order scheme was found to amplify fluctuations in dynamic SGS coefficients due to its higher numerical dissipation, contrasting with the more stable behavior observed with the fourth order scheme, which better captures resolved scales and results in smaller dynamic coefficients. Despite inherent differences in SGS models and discretization schemes, the final velocity distributions in one dimensional turbulence simulations were remarkably consistent, suggesting a limited influence of SGS modeling on large-scale structures in simplified turbulence scenarios. However, notable variations in resolved-scale kinetic energy were uncovered, emphasizing the importance of accurately capturing small-scale turbulence structures for precise energy dissipation predictions in LES.

翻译：大涡模拟（LES）在湍流研究领域始终是至关重要的研究方向，特别是在理解小尺度湍流结构行为及其对可解析尺度的影响方面。本研究聚焦于湍流的大涡模拟，特别针对一维随机Burgers方程（SBE），采用完全守恒高阶数值格式进行求解。通过将线性对流扩散方程（LAD）和非线性Burgers方程（NLB）在层流条件下的解析解作为基准，系统验证了空间离散格式与亚格子尺度（SGS）模型之间的相互作用机制，确保该方法在应用于随机湍流大涡模拟前具有鲁棒性。研究深入探讨了二阶与四阶离散格式对多种SGS模型动态系数的影响，包括常系数Smagorinsky模型（CS）、动态Smagorinsky模型（DS）、动态Wong-Lilly模型（DWL）、1.5阶湍动能Deardorff模型（TKED）、平衡Heinz模型（EH）以及动态Heinz模型（DH）。研究发现，二阶格式因其较高的数值耗散会放大动态SGS系数的波动，而四阶格式则表现出更稳定的特性，能更好地捕捉可解析尺度并产生更小的动态系数。尽管SGS模型与离散格式存在本质差异，一维湍流模拟中的最终速度分布却表现出高度一致性，这表明在简化湍流场景中SGS建模对大尺度结构的影响有限。然而，研究揭示了可解析尺度动能的显著变化，强调了大涡模拟中准确捕捉小尺度湍流结构对于精确预测能量耗散的重要性。