Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

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

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

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

Constant

\(d_\mathrm{w} \) :

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

I :

Unit tensor

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

Maximum cell size

\(h_{wn} \) :

Size of cell normal to the streamlined surface

k :

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

p :

Pressure

\(r_d \) :

Boundary layer indicator

\(\hbox {S}\) :

Strain rate tensor

t :

Time

u :

Velocity vector

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

Velocity components

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

Cartesian coordinates

\(\Delta \) :

Filter width

\(\upvarepsilon \) :

Dissipation rate

\({\upmu }\) :

Molecular viscosity

\({\upmu }_t \) :

Turbulent viscosity

\({\uprho }\) :

Density

\(\Omega \) :

Vorticity tensor

\(\uptau \) :

Viscous stress tensor

\({\upphi }\) :

Unknown value

t :

Turbulent

sgs:

Sub-grid scale

\(\mu \) :

Viscous

CFD:

Computational fluid dynamics

DES:

Detached-eddy simulation

DDES:

Delayed DES

DNS:

Direct numerical simulation

IDDES:

Improved DDES

LES:

Large-eddy simulation

NVD:

Normalized variable diagram

RANS:

Reynolds-averaged Navier–Stokes

SA:

Spalart–Allmaras

SGS:

Sub-grid scale

SST:

Shear stress transport

References

  1. Mozer, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re\(_{\tau }=590\). Phys. Fluids 11(4), 943–945 (1999)

    Article  Google Scholar 

  2. Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics. Springer, New York (2002)

    Book  MATH  Google Scholar 

  3. Spalart P.R., Jou W.-H., Strelets M., Allmaras S.R.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Proceedings of the First AFOSR International Conference on DND/LES, 4–8 August 1997, Ruston, Louisiana, USA, pp. 137–147. Greyden Press, Columbus (1997)

  4. Spalart, P.R.: Strategies for turbulence modeling and simulations. Int. J. Heat Fluid Flow 21(3), 252–263 (2000)

    Article  Google Scholar 

  5. Travin, A., Shur, M., Strelets, M., Spalart, P.R.: Physical and numerical upgrades in the detached-eddy simulation of complex turbulent flows. Advances in LES of Complex Flows, pp. 239–254. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  6. Zhang, Z., Zhang, W., Zhai, Z., Chen, Q.: Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD. Part 2. Comparison with experimental data from literature. HVAC&R Res. 13(6), 1–18 (2007)

    Article  Google Scholar 

  7. Chevalier, M., Peng, S.H.: Detached eddy simulation of turbulent flow in a highly offset intake diffuser. Notes Numer. Fluid Mech. Multidiscip. Des. 111, 111–121 (2010)

    Article  Google Scholar 

  8. Sohail, M.A., Chao, Y., Husain, M.: Comparison of detached eddy simulations with turbulence modeling. Int. J. Mech. Mater. Eng. 2(1), 869–875 (2011)

    Google Scholar 

  9. Travin, A., Shur, M., Strelets, M., Spalart, P.: Detached-eddy simulations past a circular cylinder. Flow Turbul. Combust. 63(1–4), 293–313 (2000)

    Article  MATH  Google Scholar 

  10. Garbaruk A., Niculin D., Strelets M., Dyadkin A., Krylov A., Stekenius K.: Comparative study of different turbulence modelling approaches to prediction of transonic and supersonic flows past a re-entry capsule with balance flaps. In: Proceedings of the 4th European Conference for Aerospace Sciences, 4–8 July 2011, Saint Petersburg, Russia (2011)

  11. Morgut, M., Nobile, E.: Influence of grid type and turbulence model on the numerical prediction of the flow around marine propellers working in uniform inflow. Ocean Eng. 42, 26–34 (2012)

    Article  Google Scholar 

  12. Weinman, K.A., Valentino, M.: Comparison of Hybrid RANS-LES Calculations Within the Framework of Compressible and Incompressible Unstructured Solvers. Progress in Hybrid RANS-LES, pp. 329–338. Springer, Berlin (2010)

    Google Scholar 

  13. Strelets M.: Detached eddy simulation of massively separated flows. AIAA Paper 2001–0879

  14. Ubbink O.: Numerical prediction of two fluid systems with sharp interfaces. PhD Thesis, University of London, Imperial College of Science, Technology & Medicine (1997)

  15. Gaskell, P.H.: Curvature-compensated convective-transport: SMART, a new boundedness-preserving transport algorithm. Int. J. Numer. Methods Fluids 8(6), 617–641 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jasak, H., Weller, H.G., Gosman, A.D.: High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Methods Fluids 31(2), 431–449 (1999)

    Article  MATH  Google Scholar 

  17. Salvetti M.V., Camarri S., Dervieux A., Koobus B., Ouvrard H., Wornom S.: A numerical method for large-eddy simulation on unstructured grids. In: Proceedings of Contact Forum KVAB (Flamish Science Academy), Modern Techniques for Solving Partial Differential Equations, 19 June 2008, Brussels, Belgium (2008)

  18. Morton S.A., Forsythe J.R., Squires K.D., Wurtzler K.E.: Assessment of unstructured grids for detached-eddy simulation of high Reynolds number separated flows. In: Proceedings of the 8th International Society for Grid Generation, June 2002, Honolulu (2002)

  19. Cummings, R.M., Schutte, A.: Detached-eddy simulation of the vortical flow field about the VFE-2 delta wing. Aerosp. Sci. Technol. 24(1), 66–76 (2013)

    Article  Google Scholar 

  20. Gritskevich, M.S., Garbaruk, A.V., Menter, F.R.: Fine-tuning of DDES and IDDES formulations to the k-\(\omega \) shear stress transport model. Prog. Flight Phys. 5, 23–42 (2013)

    Article  Google Scholar 

  21. Revell, A., Craft, T.J., Laurence, D.P.R.: Turbulence modeling of strongly detached flows: the circular cylinder. Notes Numer. Fluid Mech. Multidiscip. Des. 97, 279–288 (2008)

    Article  MathSciNet  Google Scholar 

  22. Spalart P.R.: Young-Person’s guide to detached-eddy simulation grids. NASA Technical Report, CR-2001-211032 (2001)

  23. Spalart, P.R., Strelets, MKh, Travin, A.: Expectations in the wall region of a large-eddy simulation. ERCOFTAC Ser. Qual. Reliab. Large Eddy Simul. 12(3), 189–191 (2008)

    Google Scholar 

  24. Betelin, V.B., Shagaliev, V.B., Aksenov, V.B., Belyakov, I.M., Deryuguin, YuN, Korchazhkin, D.A., Kozelkov, A.S., Nikitin, V.F., Sarazov, A.V., Zelenskiy, D.K.: Mathematical simulation of hydrogen–oxygen combustion in rocket engines using LOGOS code. Acta Astronaut. 96, 53–64 (2014)

    Article  Google Scholar 

  25. Emelyanov, V.N., Karpenko, A.G., Volkov, K.N.: Development of advanced computational fluid dynamics tools and their application to simulation of internal turbulent flows. Prog. Flight Phys. 7, 247–268 (2015)

    Article  Google Scholar 

  26. Wesseling, P.: Principles of Computational Fluid Dynamics. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  27. Leonard, B.P.: A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19(1), 59–98 (1979)

    Article  MATH  Google Scholar 

  28. Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337 (1971)

    Article  Google Scholar 

  29. Winkler C.M., Dorgan A.J., Mani M.: The effect of unstructured grid topology and resolution on simulations of decaying turbulence. In: Proceedings of the 27th International Congress on Aeronautical Sciences (ICAS 2010), 19-24 September, Nice, France (2010)

  30. Swanson R.C., Rumsey C.L., Rubinstein R., Balakumar P., Zang T.A.: Parametric study of decay of homogeneous isotropic turbulence using large eddy simulation. NASA Technical Report, TM-2012-217593 (2012)

  31. Vogel, J.C., Eaton, J.K.: Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step. J. Heat Transf. 107(4), 922–929 (1985)

    Article  Google Scholar 

  32. Kuzmin, D., Mierka, O., Turek, S.: On the implementation of the \(k-\varepsilon \) turbulence model in incompressible flow solvers based on a finite element discretisation. Int. J. Comput. Sci. Math. 1(2–4), 193–201 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  33. Casarsa, L., Giannattasio, P.: Three-dimensional features of the turbulent flow through a planar sudden expansion. Phys. Fluids 20, 015103 (2008)

    Article  MATH  Google Scholar 

  34. Wang, W., Zhang, L., Yan, Y.: Large eddy simulation of turbulent flow downstream of a backward-facing step. Proc. Eng. 31, 16–22 (2012)

    Article  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. Russian Federal Nuclear Center, Sarov, Russia

    Andrey Kozelkov, Vadim Kurulin & Elena Tyatyushkina

  2. Baltic State Technical University, Saint Petersburg, Russia

    Vladislav Emelyanov & Konstantin Volkov

Authors
  1. Andrey Kozelkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vadim Kurulin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladislav Emelyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Elena Tyatyushkina
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Konstantin Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Konstantin Volkov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kozelkov, A., Kurulin, V., Emelyanov, V. et al. Comparison of Convective Flux Discretization Schemes in Detached-Eddy Simulation of Turbulent Flows on Unstructured Meshes. J Sci Comput 67, 176–191 (2016). https://doi.org/10.1007/s10915-015-0075-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-015-0075-7

Keywords

Search

Navigation