Adjoint-based variational optimal mixed models for large-eddy simulation of turbulence
arXiv:2301.08423 · doi:10.1063/5.0155184
Abstract
An adjoint-based variational optimal mixed model (VOMM) is proposed for subgrid-scale (SGS) closure in large-eddy simulation (LES) of turbulence. The stabilized adjoint LES equations are formulated by introducing a minimal regularization to address the numerical instabilities of the long-term gradient evaluations in chaotic turbulent flows. The VOMM model parameters are optimized by minimizing the discrepancy of energy dissipation spectra between LES calculations and a priori knowledge of direct numerical simulation (DNS) using the gradient-based optimization. The a posteriori performance of the VOMM model is comprehensively examined in LES of three turbulent flows, including the forced homogeneous isotropic turbulence, decaying homogenous isotropic turbulence, and temporally evolving turbulent mixing layer. The VOMM model outperforms the dynamic Smagorinsky model (DSM), dynamic mixed model (DMM) and approximate deconvolution model (ADM) in predictions of various turbulence statistics, including the velocity spectrum, structure functions, statistics of velocity increments and vorticity, temporal evolutions of the turbulent kinetic energy, dissipation rate, momentum thickness and Reynolds stress, as well as the instantaneous vortex structures at different grid resolutions and times. In addition, the VOMM model only takes up 30% time of the DMM model for all flow scenarios. These results demonstrate that the proposed VOMM model improves the numerical stability of LES and has high a posteriori accuracy and computational efficiency by incorporating the a priori information of turbulence statistics, highlighting that the VOMM model has a great potential to develop advanced SGS models in the LES of turbulence.
arXiv comment77 pages, 29 figures, 9 tables
References in corpus (21)
- Turbulence Modeling in the Age of Data
- Deep Neural Networks for Data-Driven Turbulence Models
- Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach
- Sub-grid modelling for two-dimensional turbulence using neural networks
- Searching for turbulence models by artificial neural network
- RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
- A neural network approach for the blind deconvolution of turbulent flows
- Scientific multi-agent reinforcement learning for wall-models of turbulent flows
- Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning
- Ensemble Kalman method for learning turbulence models from indirect observation data
- Deconvolutional artificial neural network models for large eddy simulation of turbulence
- Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations
- Synchronization to big-data: nudging the Navier-Stokes equations for data assimilation of turbulent flows
- Embedded training of neural-network sub-grid-scale turbulence models
- Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
- The drag-adjoint field of a circular cylinder wake at Reynolds numbers 20, 100 and 500
- Multiple Shooting Shadowing for Sensitivity Analysis of Chaotic Dynamical Systems
- A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation
- A Lagrangian relaxation towards equilibrium wall model for large eddy simulation
- A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows
- Temporally sparse data assimilation for the small-scale reconstruction of turbulence