A high-order low dissipative numerical framework is discussed to tackle simultaneously the modeling of unresolved sub-grid scale flow turbulence and the capturing of shock waves. The flows around two different airfoil profiles are simulated using a Spectral Difference discretisation scheme. First, a transitional, almost incompressible, low Reynolds number flow over a Selig-Donovan 7003 airfoil. Second, a high Reynolds number flow over a RAE2822 airfoil under transonic conditions. These flows feature both laminar and turbulent flow physics and are thus particularly challenging for turbulence sub-grid scale modeling. The accuracy of the recently developed Spectral Element Dynamic Model, specifically capable of detecting spatial under-resolution in high-order flow simulations, is evaluated. Concerning the test in transonic conditions, the additional complexity due to the presence of shock waves has been handled using an artificial viscosity shock-capturing technique based on bulk viscosity. To mitigate the impact of the shock-capturing on turbulence dissipation, it was necessary to combine the high-order modal-type shock detection with a usual sensor measuring the local flow compressibility.

讨论了一个高阶低耗散数值框架，以同时解决未解析的子网格尺度流湍流的建模和冲击波的捕获。使用“频谱差异”离散化方案模拟了两个不同翼型轮廓周围的气流。首先，过渡的，几乎不可压缩的低雷诺数流经过Selig-Donovan 7003机翼。其次，跨音速条件下，高雷诺数流过RAE2822机翼。这些流动既具有层流物理特性，又具有湍流物理特性，因此对于湍流子网格规模建模尤其具有挑战性。评估了最近开发的“光谱元素动态模型”的准确性，该模型特别能够检测高阶流模拟中的空间分辨率不足。关于跨音速条件下的测试，由于存在冲击波，因此额外的复杂性已使用基于体粘度的人工粘度冲击捕获技术进行了处理。为了减轻震荡捕获对湍流消散的影响，有必要将高阶模态震荡检测与测量局部流可压缩性的常规传感器相结合。