Non-Markovian Closure Models for Large Eddy Simulations using the Mori-Zwanzig Formalism
Non-Markovian Closure Models for Large Eddy Simulations using the Mori-Zwanzig Formalism
复制标题
使用 Mori-Zwanzig 形式进行大涡模拟的非马尔可夫闭合模型
DOI：
10.1103/physrevfluids.2.014604
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K. Duraisamy
中科院分区：
文献类型：
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作者：
E. Parish;K. Duraisamy
这项工作使用 Mori-Zwanzig (M-Z) 形式主义（一个源自非平衡统计力学的概念）作为开发粗粒度湍流模型的基础。考虑了广义朗之万方程 (GLE) 的力学原理，并将从正交动力学方程中获得的见解用作模型开发的起点。考虑一类子网格模型，它们通过有限记忆近似表示非局部行为（Stinis，P.，“不确定性量化的 Mori-Zwanzig 简化模型 I：参数不确定性”，\textit{arXiv：1211.4285}，2012。），其长度是使用与解析变量的雅可比行列式谱半径相关的启发式确定的。所得模型与基础数值分辨率密切相关，并且能够逼近非马尔可夫效应。 Burgers 方程的数值实验表明，基于 M-Z 的模型可以准确预测不同网格分辨率下总动能和总耗散率的时间演化。对于粗粒度适中的情况，可以准确预测相空间中每个解析模式的轨迹。均匀各向同性湍流的 LES 和泰勒格林涡表明，基于 M-Z 的模型能够提供出色的预测，准确捕获子网格对能量传递的贡献。最后，完全开发的河道流的 LES 证明了基于 M-Z 的模型对非衰减问题的适用性。值得注意的是，闭包的形式不是由建模者强加的，而是源自粗粒度的数学，突出了基于 M-Z 的技术定义 LES 闭包的潜力。
This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from non-equilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of sub-grid models is considered which represent non-local behavior via a finite memory approximation (Stinis, P., "Mori-Zwanzig reduced models for uncertainty quantification I: Parametric uncertainty," \textit{arXiv:1211.4285}, 2012.), the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase-space is accurately predicted for cases where the coarse-graining is moderate. LES of homogeneous isotropic turbulence and the Taylor Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the sub-grid contribution to energy transfer. Lastly, LES of fully developed channel flow demonstrate the applicability of M-Z-based models to non-decaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse-graining, highlighting the potential of M-Z-based techniques to define LES closures.