Stochastic Backscatter for Grey-Area Mitigation in Hybrid RANS-LES Simulations

TL;DR

This paper develops and validates a stochastic backscatter (SBS) approach embedded in a hybrid RANS-LES framework (X-LES) to mitigate the grey-area problem in zone-based DES-like simulations. By blending a low-dissipation LD2 scheme with a first-order upwind flux and using a wall-distance–dependent shielding function, the method preserves stability while enabling selective LES in the flow domain. The SBS component injects energy back into resolved scales via a stochastic tensor driven by a Langevin-type process, with correlations tuned to preserve variance and avoid spurious noise production. Calibration on Decaying Isotropic Homogeneous Turbulence and application to wake-boundary-layer mixing demonstrate effective grey-area mitigation, improved spectral resolution, and closer agreement with experimental data, highlighting the practical potential for industrial aero- flows and aeroacoustic simulations.

Abstract

A scale-resolving simulation methodology that includes stochastic energy backscatter is incorporated into a proprietary block-structured compressible flow solver. Particular attention is devoted to the discretisation of the convective terms in the averaged/filtered governing equations. The objective is to achieve satisfactory dissipation and dispersion properties, while minimising the number of modifications to be made to the existing RANS solver, which employs, by default, a second-order accurate central scheme with Jameson-Schmidt-Turkel scalar artificial dissipation. A novel blending strategy, combining non-dissipative and strongly dissipative numerical discretisations, is proposed to enhance the overall numerical stability. First of all, the model is calibrated using the classic decay of isotropic homogeneous turbulence. Then, its effectiveness in mitigating the grey area is shown through the simulation of the mixing co-flow between the wake originating downstream of an airfoil at zero angle of attack and the zero-pressure-gradient turbulent boundary layer developing over a flat plate.

Figures (10)

• Figure 1: Probability density function of the $x$-component of the stochastic variable $\boldsymbol\xi$ in an X-LES block from the wake-boundary-layer mixing test case: first-order upwind scheme (a) vs. blended LD2–upwind scheme (b).
• Figure 2: Wall distance field for the cylinder test case: contour (a) and plot along a reference line (b). The reference line (solid black, square markers at its ends) is shown in (a).
• Figure 3: Wall distance field for the wake-boundary-layer mixing test case (see Section \ref{['subsec:mixing']}): contour (a) and plot along a reference line (b). The reference line (solid black, square markers at its ends) is shown in (a).
• Figure 4: Turbulent energy spectra at three time instances ($\boldsymbol{t^+ = 42, 98, 171}$): LD2 scheme (a) vs. JST scheme (b). Experimental data are represented by markers; solid lines denote computational results.
• Figure 5: Grid for the wake-boundary-layer mixing test case (a). Blocks simulated by X-LES + SBS in (b).