Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction
Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction
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DOI：
10.1063/1.4898641
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发表时间：
2014-10
影响因子：
4.6
通讯作者：
S. Hickel;Christian P. Egerer;J. Larsson
中科院分区：
文献类型：
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作者：
S. Hickel;Christian P. Egerer;J. Larsson
我们推导并分析了隐式大涡模拟（LES）的可压缩流，适用于一个广泛的马赫数范围内，特别是有效的LES激波湍流相互作用的模型。遵循整体建模理念，物理上健全的湍流建模和未解析亚网格尺度（SGS）的数值建模完全合并，其方式与传统隐式LES方法截然不同。隐式亚网格模型的设计使得在低马赫数限制下与不可压湍流理论的渐近一致性得以保持。可压缩性的影响是适当占了一个新的数值通量函数，它可以捕捉到强激波在超音速流动，也确保了光滑波和湍流的准确表示没有过多的数值耗散。对激波管问题、Noh三维内爆问题、大尺度强迫和衰减三维均匀各向同性湍流、超音速湍流边界层流动和马赫数为2.88的压缩-膨胀斜坡流的模拟表明了SGS模型的良好性能;在这个流动范围内，预测结果与理论、直接数值模拟和实验参考数据非常吻合。隐式LES的典型的冲击-湍流相互作用的结果进行了比较显式LES使用动态Smagorinsky模型的结果。分析表明，用于激波捕获的数值方法的细节明显超过了显式和隐式LES中不同湍流建模策略的影响。隐式LES模型恢复了用快速畸变理论预测的激波捕捉误差的理想二阶网格收敛。动态Smagorinsky模型与混合方法相结合，该方法将六阶中心差分与七阶加权基本无振荡方案相结合，得到与隐式LES结果非常相似的湍流统计数据。然而，虽然显式LES需要一个定制的高阶低耗散数值方法，适用于数值耗散只在冲击法向，没有这样的特设调整是必要的建议隐式LES方法。
We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence statistics that are very similar to the implicit LES results. However, while the explicit LES requires a tailored high-order low-dissipative numerical method that applies numerical dissipation only in shock normal direction, no such ad hoc adjustments are necessary with the proposed implicit LES method.