Data-driven detached-eddy simulations based on explicit algebraic stress expressions for turbulent flows

TL;DR

This work introduces a data-driven DD-EAS-DDES framework that embeds an explicit algebraic stress model within a DDES switching context, using a neural network to map local flow invariants $\theta_j$ to coefficients $C_1$, $C_2$, and $C_{DES}$ trained with velocity data via an ensemble Kalman method. The algebraic closure ensures consistent tensor-basis coefficients $\beta_i$ across RANS and LES branches under the weak-equilibrium assumption, while augmenting the training with baseline coefficient values to preserve realistic switching. Validations on secondary flow in a square duct and separation over a bump demonstrate enhanced mean flow statistics, improved Reynolds-stress predictions, and more accurate switching behavior with an enlarged LES region, along with notable generalization to different Reynolds numbers and geometries. The approach maintains DES-level computational efficiency by avoiding additional transport equations and leveraging the algebraic closure, offering a practical path toward data-driven DES suitable for complex, massively separated flows.

Abstract

This work proposes a data-driven explicit algebraic stress-based detached-eddy simulation (DES) method. Despite the widespread use of data-driven methods in model development for both Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES), their applications to DES remain limited. The challenge mainly lies in the absence of modelled stress data, the requirement for proper length scales in RANS and LES branches, and the maintenance of a reasonable switching behaviour. The data-driven DES method is constructed based on the algebraic stress equation. The control of RANS/LES switching is achieved through the eddy viscosity in the linear part of the modelled stress, under the $\ell^2-ω$ DES framework. Three model coefficients associated with the pressure-strain terms and the LES length scale are represented by a neural network as functions of scalar invariants of velocity gradient. The neural network is trained using velocity data with the ensemble Kalman method, thereby circumventing the requirement for modelled stress data. Moreover, the baseline coefficient values are incorporated as additional reference data to ensure reasonable switching behaviour. The proposed approach is evaluated on two challenging turbulent flows, i.e., the secondary flow in a square duct and the separated flow over a bump. The trained model achieves significant improvements in predicting mean flow statistics compared to the baseline model. This is attributed to improved predictions of the modelled stress. The trained model also exhibits reasonable switching behaviour, enlarging the LES region to resolve more turbulent structures. Furthermore, the model shows satisfactory generalization capabilities for both cases in similar flow configurations.

Figures (23)

• Figure 1: Schematic of the present data-driven EAS-DDES method with the model coefficients represented by neural networks.
• Figure 2: Mean velocity in (a-c) $x$- and (f-h) $y$-directions and absolute prediction error contours in (d, e) $x$- and (i, j) $y$-directions in the third quadrant ($y<0$, $z<0$) for the square duct.
• Figure 3: Comparison of the mean and RMS velocity profiles between the DNS, the baseline EAS-DDES model, and the trained DD-EAS-DDES model at $z = -0.99$, $-0.8$, $-0.6$, $-0.4$, $-0.2$, $0$ for flows in the square duct.
• Figure 4: Comparisons of the normalized total stress between the (a-d) DNS, (e-h) the baseline EAS-DDES model, and (i-l) the trained DD-EAS-DDES model in the third quadrant ($y<0$, $z<0$) of the square duct.
• Figure 5: Comparisons of the shielding function $f_d$ and the turbulent viscosity ratio $\nu_t/\nu$ between the baseline EAS-DDES model and the trained DD-EAS-DDES model.