Improved Delayed Detached Eddy Simulation (IDDES)

• IDDES is a hybrid turbulence model that combines RANS and LES methodologies to predict wall-bounded turbulent flows with high fidelity.
• It employs a dynamic switching mechanism using a shielding function and hybrid length scale to transition smoothly between RANS and LES regimes.
• Applications span high-Mach propulsion, iced aerodynamics, and separated flows, offering improved accuracy over traditional turbulence models.

Improved Delayed Detached Eddy Simulation (IDDES) is an advanced hybrid turbulence modeling strategy that blends Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) methodologies for high-fidelity simulation of wall-bounded turbulent flows. IDDES introduces key enhancements over its predecessors (DES, DDES) to address the grid-induced separation problem and "grey area" errors, providing a robust framework for accurate prediction of turbulence in both attached and massively separated flows across a wide range of engineering applications, including high-Mach propulsion systems, iced aerodynamics, and canonical turbulence test cases (Plewacki et al., 22 Nov 2025, Zhou et al., 21 Jul 2025, Xiao et al., 2022, Herr et al., 2023, Arolla, 2014).

1. Mathematical Formulation and Hybridization Framework

At its core, IDDES employs a hybridized transport equation approach in which the destruction term of the modeled turbulence quantity—such as the working variable $\tilde\nu$ in Spalart–Allmaras (SA) or the TKE $k$ in SST $k$–$\omega$ or RSM—is governed by a hybrid length scale $l_{\mathrm{IDDES}}$. This length scale mediates the mode of operation (RANS or LES) according to the local flow and grid characteristics:

$$l_{\mathrm{IDDES}} = l_{\mathrm{RANS}} - f_d\,\max(0,\;l_{\mathrm{RANS}} - C_{\mathrm{DES}}\,\Delta)$$

Here, $l_{\mathrm{RANS}}$ is the wall-distance or turbulence-model-based RANS scale, $\Delta$ is the local grid filter width, $C_{\mathrm{DES}}$ is a calibration constant (typically $\sim 0.65$ for SA and SST), and $f_d$ is the delay ("shielding") function that prevents premature activation of LES near walls. The transition to LES is thus dynamically determined and grid-adaptive (Plewacki et al., 22 Nov 2025, Arolla, 2014, Yousif et al., 2020).

In IDDES with Reynolds-stress backgrounds, a scalar eddy-viscosity subgrid model (Boussinesq) replaces pure Reynolds-stress closure in the LES region to ensure sufficient dissipation, while full anisotropy-resolving RSM equations are retained in RANS zones (Herr et al., 2023).

2. Shielding, Switching, and Near-Wall Treatment

A principal innovation in IDDES is the continual and smooth LES/RANS blending achieved by the shielding function $f_d$, which uses a strain-rate–based local sensor:

$$f_d = 1 - \tanh\!\left[(8\,r_d)^3\right], \quad r_d = \frac{\tilde\nu}{\kappa^2\,d^2\,\sqrt{S_{ij}S_{ij}}}$$

This functional form ensures that $f_d \to 0$ in the viscous sublayer, preserving RANS closure, and $f_d \to 1$ in the log layer and outer flow where the grid can support LES (Plewacki et al., 22 Nov 2025, Yousif et al., 2020). In generalized frameworks, additional blending terms (e.g., $f_B$, $f_e$) support wall-modeled LES and reduce log-layer mismatch (Herr et al., 2023, Zhou et al., 21 Jul 2025).

Recent advances in wall modeling incorporate data-driven ML wall functions using KDTree lookups of wall-resolved IDDES training data, enabling accurate imposition of wall stress, $k$, and $\epsilon$ in coarse-grid near-wall layers. This data-driven approach maintains prediction accuracy within 3–5% of low-Re IDDES but at roughly half the mesh cost (Davidson, 23 Oct 2024).

3. LES Region Subgrid Closure and Anisotropy Adaptation

In the pure LES regions, IDDES rectifies subgrid closure deficiencies using various strategies:

• Scalar eddy-viscosity modeling (e.g., $\nu_t = k/\omega$),
• Minimum-dissipation length scales, and
• Shear-layer–specific adaptivity.

Anisotropic minimum-dissipation (AMD) IDDES modifies the LES length scale to

$$\Delta_{\mathrm{AMD}} = \left[-\,\Delta_k\,g_{ik}\;\Delta_\ell\,g_{j\ell}\;S_{ij}\;g_{mn}\,g_{mn}\right]^{1/2}$$

with $C_{\mathrm{DES,AMD}}\sim 2.4$, which ensures correct inertial-range energy drain and improved prediction of Kelvin-Helmholtz structures on anisotropic meshes (Zhou et al., 21 Jul 2025).

Shear-layer–adapted (SLA) subgrid scales employ a projection of the grid size onto the local vorticity-normal plane and apply a vortex-tilting measure to minimize dissipation in separated shear layers:

$\Delta_{\rm SL} = \Delta_4\,F_{KH}(\mathrm{VTM})$

This reduction in $\ell_{LES}$ by one to two orders of magnitude in planar shear layers dramatically improves the prediction of KH instability and physical rollup (Xiao et al., 2022).

4. Implementation in Multiphysics and Complex Geometries

IDDES is routinely deployed in compressible, multiphysics environments, as exemplified by Mach-10 scramjet simulations where IDDES is coupled with a 12-species, 27-reaction finite-rate chemistry (FRC) model. The Favre-averaged transport equations (mass, momentum, energy, and species) are closed with the IDDES turbulence model and evaluated without explicit turbulence–chemistry interaction modeling (Plewacki et al., 22 Nov 2025). This results in accurate shock/autoignition location and combustion patterns that agree with experimental diagnostics within uncertainty.

Data-driven wall functions and mesh strategies with merged near-wall cells (e.g., $20<y^+<60$ in first off-wall cell) have been developed for efficiency, preserving low-Re LES resolution outside the first cell and maintaining $C_f$, $C_p$, and velocity profile accuracy across separated diffuser, hump, channel, and flat-plate flows (Davidson, 23 Oct 2024).

5. Performance, Validation, and Limitations

IDDES and its advanced variants have been validated over a range of canonical cases:

• Channel flows at $Re_\tau$ up to $98,300$: friction velocity and mean profile errors within $\pm2$%, total shear stress matching DNS (Herr et al., 2023, Davidson, 23 Oct 2024).
• Flat-plate boundary layers: time-averaged skin friction $c_f$ matches low-$Re$ IDDES results, although a plateau in $c_f(x)$ is observed, potentially due to synthetic turbulence injection (Herr et al., 2023).
• Decaying isotropic turbulence: AMD-IDDES recovers the $k^{-5/3}$ law on anisotropic grids, while standard DES suffers grey-area errors (Zhou et al., 21 Jul 2025).
• Iced wing flows: Shear-layer–adapted scales accelerate KH breakdown, reducing plateau length and restoring correct reattachment locations, with integrated $C_L$, $C_D$ within 1–10% of experiments (Xiao et al., 2022, Zhou et al., 21 Jul 2025).

Standard IDDES tends to overpredict eddy viscosity in initial separated shear layers, suppressing physical instability growth. SLA and AMD modifications mitigate this with minimal additional computational complexity. Performance in wall-bounded separated flows is now dictated primarily by subgrid modeling and synthetic-turbulence/initialization strategies (Xiao et al., 2022, Herr et al., 2023).

6. Applications, Best Practices, and Outlook

IDDES and its recent improvements are employed in high-$Re$ wall-bounded and separated flow scenarios, including hypersonic propulsion, sweeps on iced wings, wall-mounted bluff bodies, and benchmark validation flows. Recommendations include:

• Maintain $y^+ < 1$–$15$ in critical wall regions to ensure accurate mode blending (Yousif et al., 2020).
• Couple low-dissipation numerical fluxes (e.g., KEC, Ducros shock sensor) with higher-order implicit time integration (e.g., BDF2) to suppress under-resolution errors in stiff multiphysics environments (Plewacki et al., 22 Nov 2025).
• Use physically motivated or data-driven wall boundary treatments on coarse grids to reduce cost while preserving near-wall accuracy (Davidson, 23 Oct 2024).
• Apply subgrid scale adaptivity—AMD or SLA especially—in regions of strong anisotropy or shear-layer separation.

Limiting factors remain in plateaued $c_f$ predictions, long-range influence of synthetic turbulence, and possible resolved-stress overprediction in ML wall function approaches, motivating future developments in mode switching, wall modeling, and subgrid closure (Herr et al., 2023, Davidson, 23 Oct 2024).

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References:

(Plewacki et al., 22 Nov 2025) Hybrid RANS-LES simulation of transverse fuel injection in a Mach-10 scramjet engine (Zhou et al., 21 Jul 2025) A numerical investigation of sweep effects on turbulent flow over iced wings (Xiao et al., 2022) Enhanced Prediction of Three-dimensional Finite Iced Wing Separated Flow Near Stall (Herr et al., 2023) Improved Delayed Detached Eddy Simulation with Reynolds-Stress Background Modeling (Davidson, 23 Oct 2024) Hybrid LES/RANS for flows including separation: A new wall function using Machine Learning based on binary search trees (Arolla, 2014) A hybrid RANS/LES framework to investigate spatially developing turbulent boundary layers (Yousif et al., 2020) On the characteristics of the turbulent wake behind a wall-mounted square cylinder