Summary Chart of Incompressible Flow Turbulence Models
Created by John M. Cimbala
• The order is from least complex to most complex.
• Consider incompressible flow without buoyancy, but the flow is three-dimensional.
• DNS is included for completeness, even though it is not a turbulence model.
Model
Classification
Number of
additional
transport eqs.
Algebraic models
(zero-equation
models)
0
One-equation
models
1
Two-equation
models
2
Algebraic
Reynolds stress
models (ASM)
Reynolds stress
models (RSM)
& Anisotropic
Dissipation Rate
models
2
7
additional
Detached Eddy
Simulation (DES) equations in
& similar hybrid RANS regions
only
models (PANS)
0 (algebraic)
Large Eddy
or 1 (transport)
Simulation (LES)
for smallest
scales only
Direct Numerical
Simulation (DNS)
0
Assumptions/Approximations/Models
Mixing
length
Boussinesq eddy viscosity
model,
− ρ uiu j ≈ − 23 ρ Kδ ij + 2 µe Sij
Nonlinear extension of Boussinesq
eddy viscosity model,
− ρ uiu j ≈ − 23 ρ Kδ ij + 2 µe Sij +
additional higher-order terms
Solve for ensemble-averaged
quantities only (no details about
time-dependent turbulence
quantities)
Model all turbulent scales,
but only in RANS regions
“Exact” time-dependent
solution of large scales
Model small-scale
turbulence
“Exact” - solve all scales of
turbulence (small to large)