Leray and LANS-α modelling of turbulent mixing
Leray and LANS-α modelling of turbulent mixing
复制标题
湍流混合的 Leray 和 LANS-α 建模
DOI：
10.1080/14685240500501601
复制
发表时间：
2005
影响因子：
1.9
通讯作者：
Darryl D. Holm
中科院分区：
文献类型：
--
作者：
B. Geurts;Darryl D. Holm
在Navier-Stokes方程的非线性项的数学正则化被发现提供了一个系统的方法来推导亚网格封闭湍流的数值模拟。通过构造，这些次网格闭包意味着相应的模型方程组强解的存在性和唯一性。我们将考虑两个这样的数学正则化原理，即Leray和局域网-α正则化的大涡解释。勒雷原理引入了一个平滑的传输速度作为正则化对流非线性的一部分。局域网-α原理以一种自然的方式扩展了Leray公式，其中包含平滑传输速度的滤波开尔文环流定理显式满足。这些正则化原则引起隐含的子网格封闭，实现在大涡模拟湍流混合。与过滤直接数值模拟数据和预测从流行的动态涡粘性模型的比较表明，这些数学正则化模型提供了更高的精度在一个较低的计算成本比动态的方法。特别是，正则化模型在捕获较小分辨率尺度的流动特征特性方面表现得特别好。空间分辨率和雷诺数的变化表明，Leray模型比局域网-α模型更稳健，但精度略低。局域网-α模式在解析解中保留了更多的小尺度变异性。然而，这需要相应地增加所需的空间分辨率。当使用二阶有限体积离散化时，通过使用不大于该模型定义中出现的长度尺度α的网格间距，可以实现隐含的局域网-α模型的潜在精度。本文是与焦点问题级联动力学：基础和建模。
Mathematical regularization of the nonlinear terms in the Navier–Stokes equations is found to provide a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large-eddy interpretation of two such mathematical regularization principles, i.e. Leray and LANS-α regularization. The Leray principle introduces a smoothed transport velocity as part of the regularized convective nonlinearity. The LANS-α principle extends the Leray formulation in a natural way in which a filtered Kelvin circulation theorem, incorporating the smoothed transport velocity, is explicitly satisfied. These regularization principles give rise to implied subgrid closures which are implemented in large eddy simulations of turbulent mixing. Comparison with filtered direct numerical simulation data and with predictions obtained from popular dynamic eddy-viscosity modelling shows that these mathematical regularization models provide considerably more accuracy at a lower computational cost than the dynamic approaches. In particular, the regularization models perform especially well in capturing the flow features characteristic of the smaller resolved scales. Variations in spatial resolution and Reynolds number establish that the Leray model is more robust but also slightly less accurate than the LANS-α model. The LANS-α model retains more of the small-scale variability in the resolved solution. However, this requires a corresponding increase in the required spatial resolution. When using second-order finite volume discretization, the potential accuracy of the implied LANS-α model is found to be realized by using a grid spacing that is not larger than the length scale α that appears in the definition of this model. This paper is associated with the focus-issue Cascade Dynamics: Fundamentals and Modelling.