This chapter introduces scale-resolving simulations (SRS), a class of turbulence modeling approaches that explicitly resolve a portion of the turbulent spectrum in space and time. The motivation for SRS is discussed in terms of the limitations of RANS-based methods in highly unsteady and non-equilibrium flows. Large Eddy Simulation (LES) is presented as the reference SRS approach, followed by a detailed discussion of subgrid-scale modeling, near-wall challenges, and practical LES variants. Hybrid RANS–LES methods are then introduced as industrially viable compromises for high-Reynolds-number flows.

Why Scale-Resolving Simulations Are Needed

RANS models:

Solve for mean flow quantities
Model all turbulent scales
Are fundamentally insensitive to instantaneous turbulence dynamics

However, many engineering flows are dominated by:

Large-scale unsteadiness
Coherent structures
Flow instabilities generating new turbulence

Examples include:

Bluff-body wakes
Strong separation
Swirling and rotating flows
Acoustics-driven problems
Unsteady FSI loads

In these cases:

The resolved turbulent structures matter more than the modeled averages.

Turbulence Spectrum and Modeling Philosophy

Turbulence consists of:

Large eddies: flow-dependent, geometry-sensitive, energy-containing
Small eddies: more universal, dissipative

Key observation (Kolmogorov):

Small scales tend to forget boundary conditions
Large scales retain flow history

This motivates resolving large eddies while modeling small ones

What “Scale-Resolving” Means

SRS refers to any approach that:

Resolves at least part of the turbulent spectrum
Produces physically meaningful unsteady flow structures

SRS includes:

Large Eddy Simulation (LES)
Wall-Modeled LES (WMLES)
Embedded LES (ELES)
Detached Eddy Simulation (DES, DDES, IDDES)
Scale-Adaptive Simulation (SAS)

DNS is excluded due to prohibitive cost.

Large Eddy Simulation (LES): Core Idea

LES applies a spatial filtering operation:

Large, grid-resolvable scales are computed directly
Small, subgrid scales are removed by filtering

After filtering:

New subgrid-scale (SGS) stress terms appear
These terms represent unresolved turbulence and must be modeled

Crucially:

LES does not model turbulence — it models dissipation.

Spatial Filtering and Grid Dependence

In practical CFD:

The filter width is proportional to the local grid size
The grid defines which scales are resolved

Implications:

LES is inherently grid-dependent
Refining the grid changes the resolved physics
LES solutions do not converge like RANS solutions

Instead:

Convergence is achieved in a statistical sense

Why Subgrid-Scale (SGS) Models Are Needed

Without an SGS model:

Energy cascades to unresolved scales
Energy accumulates near the grid cutoff
Simulation becomes unstable and unphysical

SGS models:

Remove energy at the grid scale
Ensure correct dissipation rate
Do not attempt to reconstruct small-scale turbulence

Common SGS Models in LES

8.1 Smagorinsky–Lilly Model

Algebraic eddy-viscosity model
Assumes local equilibrium of SGS turbulence

Limitations:

Requires case-dependent constant
Over-dissipative
Poor near walls and in laminar regions

8.2 Dynamic Smagorinsky Model

Determines model constant dynamically
Adapts to local flow conditions
Produces zero eddy viscosity in laminar regions

Advantages:

Less empirical
Better for transitional flows

Challenges:

Can produce noisy coefficients
Requires averaging for stability

8.3 WALE Model

Designed for near-wall behavior
Uses both strain and rotation rates
Naturally vanishes at walls without damping functions

Strengths:

Robust
Good default choice for wall-influenced LES
Handles transition well

8.4 SGS Transport Models

Solve a transport equation for SGS kinetic energy
More physically complete
Higher computational cost

Near-Wall Challenge in LES

In wall-bounded flows:

Turbulent eddies become extremely small near walls
Required grid resolution scales with Reynolds number

Fully resolving walls with LES:

Is infeasible for most industrial flows
Leads to billions of cells at high Re

This is the primary bottleneck of LES.

Wall-Modeled LES (WMLES)

WMLES:

Resolves outer turbulence
Models near-wall region using wall models

Key idea:

Only the log-layer and outer layer are resolved
Near-wall stresses are imposed, not resolved

Benefits:

Orders-of-magnitude cost reduction
Enables LES at industrial Reynolds numbers

Trade-off:

Wall shear stress accuracy depends on wall model quality

Embedded LES (ELES)

ELES combines:

RANS in regions of attached flow
LES in regions of interest (separation, mixing)

LES is:

Activated only in selected subdomains
Fed with synthetic turbulence at interfaces

This is particularly effective when:

Only part of the domain requires resolved turbulence
Computational resources are limited

Hybrid RANS–LES Models: Motivation

Hybrid models aim to:

Avoid LES resolution in boundary layers
Resolve turbulence in separated regions
Maintain reasonable cost

Core insight:

RANS and LES equations become formally identical once eddy viscosity is introduced.

The difference lies in how large the eddy viscosity is allowed to be.

Detached Eddy Simulation (DES)

DES:

Uses RANS near walls
Switches to LES mode in separated regions
Transition depends on grid size and turbulence length scale

Advantages:

Much cheaper than LES
Captures large-scale unsteadiness in wakes

Key risk:

Grid-Induced Separation (GIS)
Artificial LES activation inside boundary layers

Improved DES Variants

14.1 DDES (Delayed DES)

Shields boundary layers from LES limiter
Reduces grid-induced separation

Risk:

Over-shielding can suppress resolved turbulence

14.2 IDDES

Improved shielding
Enables wall-modeled LES behavior
Better balance between RANS and LES modes

IDDES is often the preferred DES variant in practice

Scale-Adaptive Simulation (SAS)

SAS:

Remains RANS-like in stable flows
Automatically resolves unsteadiness when flow becomes unstable

Key feature:

No explicit LES length scale
Resolution adapts based on flow physics

Strengths:

Very robust
No LES grid requirements

Limitations:

Does not fully resolve turbulence spectrum
May remain in RANS mode in weakly unstable flows

Selecting an SRS Approach

A practical classification:

Globally unstable flows
→ DES, IDDES, ELES, SAS
Locally unstable flows
→ WMLES, ELES, fine-grid DDES
Stable wall-bounded flows
→ RANS or ELES with synthetic turbulence

There is no universal best model.

Engineering Intuition

SRS resolves structures, not averages
LES accuracy depends more on grid and time step than model choice
Hybrid models rely on flow instability to work
Poor grids destroy SRS benefits
Post-processing requires statistical thinking

Rule of thumb:

If unsteady structures matter physically, SRS is worth the cost.

Study PrioritieS

If short on time, focus on:

Why RANS fails for unsteady turbulence
LES vs RANS philosophy
Role of SGS models
Near-wall limitation of LES
Difference between LES, DES, and SAS

Key Takeaways

Scale-resolving simulations explicitly compute turbulent structures.
LES resolves large eddies and models dissipation.
SGS models ensure correct energy removal.
Near-wall resolution is the main LES limitation.
WMLES and ELES make LES practical.
Hybrid RANS–LES models balance cost and fidelity.
Model selection must be driven by physics, not fashion.

Turbulence Chapter 5: Scale-Resolving Simulations (SRS)