The performance of the nonlinearly stable flux reconstruction (NSFR) schemes for resolving subsonic viscous turbulent free-shear flows is investigated. The schemes are extensively verified for the direct numerical simulation (DNS) of the Taylor-Green Vortex (TGV) problem. Several under-resolved simulations of the TGV problem are conducted to assess the performance of NSFR for large eddy simulation that is implicitly filtered and fully implicit (ILES). Increasing the flux reconstruction correction parameter ensures that NSFR is stable and accurate for ILES while allowing for larger explicit time-steps. The entropy-stable schemes implemented with sum-factorization for tensor and Hadamard products are shown to be more cost-effective than classical DG with over-integration. The choice of the two-point (TP) numerical flux does not impact the solution and the use of standard eddy-viscosity-based sub-grid scale models does not yield improvements for the problem considered. From the DNS results, the pressure dilatation-based dissipation rate for the nonlinearly stable schemes is consistent with literature when computed from the kinetic energy (KE) budget terms, while spurious oscillations are seen when the term is directly computed. The magnitude of these oscillations is significantly lower for a collocated scheme and are effectively eliminated with the addition of Roe upwind dissipation to the TP numerical flux. Therefore, these oscillations are believed to be associated with the treatment of the face terms in nonlinearly stable schemes. It is shown that oversampling the velocity field is necessary for obtaining accurate turbulent KE (TKE) spectra and eliminates an apparent pile-up of TKE at the smallest resolved scales. Lastly, the TKE spectra for a decaying homogeneous isotropic turbulence case are in good agreement with experiment measurements and computational results in the literature.

翻译：本文研究了非线性稳定通量重构（NSFR）格式在解析亚音速粘性湍流自由剪切流中的性能。该格式在泰勒-格林涡（TGV）问题的直接数值模拟（DNS）中得到了广泛验证。通过开展TGV问题的若干欠分辨率模拟，评估了NSFR在隐式滤波全隐式大涡模拟（ILES）中的表现。增大通量重构修正参数可确保NSFR在ILES中保持稳定与精确，同时允许采用更大的显式时间步长。研究证明，针对张量与哈达玛积采用和分解实现的熵稳定格式，比传统超积分离散伽辽金方法更具成本效益。两点数值通量（TP）的选择不影响解的特性，而基于标准涡粘性的亚网格尺度模型对当前问题未见改进。DNS结果表明，通过动能收支项计算得到的非线性稳定格式压力膨胀耗散率与文献数据一致，而直接计算该项时会出现伪振荡。在并置格式中此类振荡幅值显著降低，且在TP数值通量中加入Roe迎风耗散后可完全消除，表明振荡与非稳定格式中界面项的处理方式相关。研究指出，对速度场进行过采样是获取精确湍动能（TKE）谱的必要条件，可消除最小分辨尺度处明显的TKE堆积现象。最后，衰减均匀各向同性湍流工况的TKE谱与实验测量值及文献计算结果高度吻合。