Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations
- Stanford Univ., CA (United States). Center for Turbulence Research
Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. Specifically, this metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O(107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally, it is demonstrated that the global Lyapunov exponent can be utilized as a metric to determine if the computational domain is large enough to adequately encompass the dynamic nature of the flow.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Organization:
- USDOE Office of Science (SC); Ford-Stanford Alliance
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1544369
- Alternate ID(s):
- OSTI ID: 1393708
- Journal Information:
- Physical Review Fluids (Online), Vol. 2, Issue 9; ISSN 2469-990X
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Ensemble Kalman Filter for Assimilating Experimental Data into Large-Eddy Simulations of Turbulent Flows
|
journal | December 2019 |
Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics
|
journal | October 2021 |
| Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence | text | January 2018 |
| Requirements Towards Predictive Simulations of Turbulent Reacting Flows | preprint | January 2020 |
Similar Records
Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents
LES SOFTWARE FOR THE DESIGN OF LOW EMISSION COMBUSTION SYSTEMS FOR VISION 21 PLANTS