Adjoint-based variational optimal mixed models for large-eddy simulation of turbulence

TL;DR

This paper introduces an adjoint-based variational optimal mixed model (VOMM) for large-eddy simulation of turbulence, improving accuracy, stability, and efficiency over existing models by integrating a priori turbulence statistics.

Contribution

The paper develops a novel VOMM model with adjoint-based optimization and minimal regularization, enhancing LES turbulence predictions and computational performance.

Findings

VOMM outperforms DSM, DMM, and ADM in turbulence statistics prediction.

VOMM achieves similar accuracy with only 30% of the computational time of DMM.

The model improves numerical stability and incorporates a priori turbulence information.

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.