Journal of Scientific Computing

, Volume 67, Issue 1, pp 176–191 | Cite as

Comparison of Convective Flux Discretization Schemes in Detached-Eddy Simulation of Turbulent Flows on Unstructured Meshes

  • Andrey Kozelkov
  • Vadim Kurulin
  • Vladislav Emelyanov
  • Elena Tyatyushkina
  • Konstantin VolkovEmail author


Detached-eddy simulation (DES) of turbulent flows of viscous incompressible fluid is performed based on unstructured meshes. The common finite-difference schemes for discretization of convective fluxes are applied, and the DES model constants are calibrated for each of the numerical schemes presented. Results computed with the DES model on various types of meshes (block-structured, tetrahedral and polyhedral unstructured meshes, as well as a mesh with triangular prismatic elements) are analyzed. Efficiency of the discretization schemes selected for DES calculations is compared for different meshes. Calculations are performed for some benchmark test cases, decaying homogeneous isotropic turbulence and flow behind a backward-facing step. Recommendations to the selection of model constants and properties of various meshes are given for the DES calculations of turbulent flows of viscous incompressible fluid.


Finite difference scheme Detached-eddy simulation Unstructured mesh Finite volume method 

List of symbols

Latin symbols

\(C_{d1},C_{d2} \)

Empirical constants

\(C_{\mathrm{des}} \)

Empirical constant of DES model

\(C_f \)

Friction coefficient

\(C_{k\omega },\,C_{k\varepsilon } \)

Empirical constants of SST model

\(\hbox {C}_{\mathrm{SA}} \)

Empirical constant of SA model

\(\hbox {C}_\mathrm{S} \)

Smagorinsky constant

\(\hbox {C}_\mathrm{w} \)


\(d_\mathrm{w} \)

Distance to a wall

\(f_d \)

Empirical function of DDES model

\(\tilde{f}_{d}, \tilde{f}_{e}\)

Empirical functions of IDDES model

\(F_1 \)

Weighting function of SST model


Unit tensor

\(h_{\mathrm{max}} \)

Maximum cell size

\(h_{wn} \)

Size of cell normal to the streamlined surface


Turbulent kinetic energy

\(l_{\mathrm{rans}} \)

Linear scale of turbulence

\(l_{\mathrm{des}} \)

Hybrid linear scale of turbulence for DES model

\(l_{\mathrm{iddes}} \)

Hybrid linear scale of turbulence for IDDES model

\(l_{\mathrm{ddes}} \)

Hybrid linear scale of turbulence for DDES model



\(r_d \)

Boundary layer indicator

\(\hbox {S}\)

Strain rate tensor




Velocity vector

\(u,\, v,\, w\)

Velocity components

\(x,\,y,\, z\)

Cartesian coordinates

Greek symbols

\(\Delta \)

Filter width

\(\upvarepsilon \)

Dissipation rate

\({\upmu }\)

Molecular viscosity

\({\upmu }_t \)

Turbulent viscosity

\({\uprho }\)


\(\Omega \)

Vorticity tensor

\(\uptau \)

Viscous stress tensor

\({\upphi }\)

Unknown value





Sub-grid scale

\(\mu \)




Computational fluid dynamics


Detached-eddy simulation


Delayed DES


Direct numerical simulation


Improved DDES


Large-eddy simulation


Normalized variable diagram


Reynolds-averaged Navier–Stokes




Sub-grid scale


Shear stress transport



This work was supported by the Russian Foundation for Basic Research (Project 13-07-12079).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Andrey Kozelkov
    • 1
  • Vadim Kurulin
    • 1
  • Vladislav Emelyanov
    • 2
  • Elena Tyatyushkina
    • 1
  • Konstantin Volkov
    • 2
    Email author
  1. 1.Russian Federal Nuclear CenterSarovRussia
  2. 2.Baltic State Technical UniversitySaint PetersburgRussia

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