论文标题
使用直接数字模拟的大型模拟对大型仿真的数值和建模误差评估
Numerical and modeling error assessment of large-eddy simulation using direct-numerical-simulation-aided large-eddy simulation
论文作者
论文摘要
我们研究各向同性和壁构成的湍流中大涡模拟（LES）的数值误差。引入了使用过滤后的DNS数据计算LES的亚网格尺度（SGS）项的直接数字模拟（DNS）辅助级公式。我们首先验证该公式在过滤器和数值算法的分化操作员之间没有换向误差的情况下，该公式的误差为零。此方法允许评估与LE相关的网格分辨率上各种数值方案的数值误差的时间演变。分析表明，数值错误与建模误差的数量级相同，并且经常相互取消。这支持了以下想法：经过过滤的DNS数据培训的监督机学习算法可能不适用于强大的SGS模型开发，因为这种方法无视随着时间的推移积累的系统中存在数值错误。湍流通道流中误差的评估还确定了接近墙壁占主导地位的数值误差，这对墙模型的发展具有影响。
We study the numerical errors of large-eddy simulation (LES) in isotropic and wall-bounded turbulence. A direct-numerical-simulation (DNS)-aided LES formulation, where the subgrid-scale (SGS) term of the LES is computed by using filtered DNS data is introduced. We first verify that this formulation has zero error in the absence of commutation error between the filter and the differentiation operator of the numerical algorithm. This method allows the evaluation of the time evolution of numerical errors for various numerical schemes at grid resolutions relevant to LES. The analysis shows that the numerical errors are of the same order of magnitude as the modeling errors and often cancel each other. This supports the idea that supervised machine learning algorithms trained on filtered DNS data might not be suitable for robust SGS model development, as this approach disregards the existence of numerical errors in the system that accumulates over time. The assessment of errors in turbulent channel flow also identifies that numerical errors close to the wall dominate, which has implications for the development of wall models.
