In this paper, we incorporate the EMAC formulation into the Ladyzhenskaya model (LM), a large eddy simulation (LES) of incompressible flows. The EMAC formulation, which conserves energy, linear momentum, and angular momentum even with weak enforcement of incompressibility, has been shown to provide tangible benefits over the popular skew-symmetric for direct numerical simulation and regularized models of the Navier Stokes equations (NSE). The combination of EMAC with the LM addresses the known over-dissipation issues associated with the classical Smagorinsky model (SM). We develop a finite element discretization for the EMAC-LM system and analyze its stability and derive numerical error estimates, showing improved long-time behavior compared to the standard LM approach, particularly due to EMAC's favorable Gronwall constant independent of the Reynolds number. Benchmark simulations demonstrate that the EMAC-LM model yields more accurate flow structures, especially at high Reynolds numbers.

翻译：本文在 Ladyzhenskaya 模型（LM）——一种用于不可压缩流动的大涡模拟（LES）——中引入了 EMAC 格式。EMAC 格式即使在弱不可压缩性条件下也能保持能量、线性动量及角动量守恒，已被证明在直接数值模拟和 Navier-Stokes 方程（NSE）的正则化模型中，相比常用的斜对称格式具有显著优势。将 EMAC 与 LM 结合，旨在解决经典 Smagorinsky 模型（SM）已知的过度耗散问题。我们为 EMAC-LM 系统开发了有限元离散方案，分析了其稳定性并推导了数值误差估计，结果表明相较于标准 LM 方法，该方案具有更优的长时间行为，这主要得益于 EMAC 格式具有与雷诺数无关的有利 Gronwall 常数。基准模拟验证了 EMAC-LM 模型能够产生更精确的流动结构，在高雷诺数条件下尤为明显。