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Performance evaluation of standard second-order finite volume method for DNS solution of turbulent channel flow

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Abstract

DNS of turbulent flows is usually performed with high resolution meshes which demand high computational power. In addition, most classic studies use spectral methods due to its accuracy and lack of numerical dissipation. However, the effects of mesh refinement on turbulence structure was not much explored in the literature, mainly when finite volume methods (instead of usual spectral ones) are used to integrate the flow equations. In the present paper, DNS of a single phase channel flow is performed solving the primitive variables in space and time domains, using the Finite Volume Method and its influence on turbulence statistics is analyzed based on four different meshes. The results show some differences in turbulent statistics according to the resolution adopted and confirm that a turbulence analysis can be performed in domains without extreme refinement, at least, for lower order statistics.

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References

  1. Moser RD, Kim J, Mansour NN (1999) Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys Fluids 11(4):943–945

    Article  Google Scholar 

  2. Tryggvason G, Esmaeeli A, Lu J, Biswas S (2006) Direct numerical simulations of gas/liquid multiphase flows. Fluid Dyn Res 38(9):660–681

    Article  MathSciNet  Google Scholar 

  3. Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31(1):567–603

    Article  MathSciNet  Google Scholar 

  4. Argyropoulos C, Markatos N (2015) Recent advances on the numerical modelling of turbulent flows. Appl Math Model 39(2):693–732

    Article  MathSciNet  Google Scholar 

  5. Coleman GN, Sandberg RD (2010) A primer on direct numerical simulation of turbulence-methods, procedures and guidelines—Technical Report AFM-09/01a. Tech. rep., University of Southampton

  6. Patera AT (1984) A spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54(3):468–488

    Article  Google Scholar 

  7. Karniadakis G (1990) Spectral element-Fourier methods for incompressible turbulent flows. Comput Methods Appl Mech Eng 80(1–3):367–380

    Article  MathSciNet  Google Scholar 

  8. Vreman A, Kuerten JG (2014) Comparison of direct numerical simulation databases of turbulent channel flow at Reτ = 180. Phys Fluids 26(1):015102

    Article  Google Scholar 

  9. Füle P, Hernádi Z (2014) Investigation of turbulent channel flow using local mesh refinement. Period Polytech Mech Eng 58(1):7–13

    Article  Google Scholar 

  10. Cevheri M, McSherry R, Stoesser T (2016) A local mesh refinement approach for large-eddy simulations of turbulent flows. Int J Numer Methods Fluids 82(5):261–285

    Article  MathSciNet  Google Scholar 

  11. Avellaneda J, Bataille F, Toutant A (2019) DNS of turbulent low Mach channel flow under asymmetric high temperature gradient: effect of thermal boundary condition on turbulence statistics. Int J Heat Fluid Flow 77:40–47

    Article  Google Scholar 

  12. Girfoglio M, Quaini A, Rozza G (2019) A finite volume approximation of the Navier–Stokes equations with nonlinear filtering stabilization. Comput Fluids 187:27–45

    Article  MathSciNet  Google Scholar 

  13. Majander P, Siikonen T (2002) Evaluation of Smagorinsky-based subgrid-scale models in a finite-volume computation. Int J Numer Methods Fluids 40(6):735–774

    Article  Google Scholar 

  14. Eggels J, Unger F, Weiss M, Westerweel J, Adrian R, Friedrich R, Nieuwstadt F (1994) Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J Fluid Mech 268:175–210

    Article  Google Scholar 

  15. Iwamoto K, Kasagi N, Suzuki Y (2005) Direct numerical simulation of turbulent channel flow at Reτ = 2320. In: Proceedings of 6th Symp. Smart Control of Turbulence, pp 327–333

  16. Denner F, Evrard F, van Wachem B (2020) Conservative finite-volume framework and pressure-based algorithm for flows of incompressible, ideal-gas and real-gas fluids at all speeds. J Comput Phys 409:109348

    Article  MathSciNet  Google Scholar 

  17. Rhie CM, Chow WL (1983) Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J 21(11):1525–1532

    Article  Google Scholar 

  18. Bartholomew P, Denner F, Abdol-Azis MH, Marquis A, van Wachem BG (2018) Unified formulation of the momentum-weighted interpolation for collocated variable arrangements. J Comput Phys 375:177–208

    Article  MathSciNet  Google Scholar 

  19. Komen E, Camilo L, Shams A, Geurts BJ, Koren B (2017) A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows. J Comput Phys 345:565–595

    Article  MathSciNet  Google Scholar 

  20. Kim J, Moin P, Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133–166

    Article  Google Scholar 

  21. Trofimova AV, Tejada-Martínez AE, Jansen KE, Lahey RT Jr (2009) Direct numerical simulation of turbulent channel flows using a stabilized finite element method. Comput Fluids 38(4):924–938

    Article  Google Scholar 

  22. Rossi R (2009) Direct numerical simulation of scalar transport using unstructured finite-volume schemes. J Comput Phys 228(5):1639–1657

    Article  MathSciNet  Google Scholar 

  23. Vinuesa R, Prus C, Schlatter P, Nagib HM (2016) Convergence of numerical simulations of turbulent wall-bounded flows and mean cross-flow structure of rectangular ducts. Meccanica 51(12):3025–3042

    Article  MathSciNet  Google Scholar 

  24. Fulgosi M, Lakehal D, Banerjee S, De Angelis V (2003) Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface. J Fluid Mech 482:319–345

    Article  Google Scholar 

  25. Andrade JR, Martins RS, Thompson RL, Mompean G, da Silveira Neto A (2018) Analysis of uncertainties and convergence of the statistical quantities in turbulent wall-bounded flows by means of a physically based criterion. Phys Fluids 30(4):045106

    Article  Google Scholar 

  26. Bolotnov IA, Jansen KE, Drew DA, Oberai AA, Lahey RT Jr, Podowski MZ (2011) Detached direct numerical simulations of turbulent two-phase bubbly channel flow. Int J Multiph Flow 37(6):647–659

    Article  Google Scholar 

  27. Feng J, Bolotnov IA (2017) Evaluation of bubble-induced turbulence using direct numerical simulation. Int J Multiph Flow 93:92–107

    Article  MathSciNet  Google Scholar 

  28. John V, Roland M (2007) Simulations of the turbulent channel flow at Reτ = 180 with projection-based finite element variational multiscale methods. Int J Numer Methods Fluids 55(5):407–429

    Article  MathSciNet  Google Scholar 

  29. Pope SB (2001) Turbulent flows. IOP Publishing, Bristol

    MATH  Google Scholar 

  30. Moser R, Kim J, Mansour N. DNS data for turbulent channel flow. http://turbulence.oden.utexas.edu/MKM_1999.html. Accessed 20 July 2021

  31. Durran D, Weyn JA, Menchaca MQ (2017) Practical considerations for computing dimensional spectra from gridded data. Mon Weather Rev 145(9):3901–3910

    Article  Google Scholar 

  32. Tennekes H, Lumley JL, Lumley J et al (1972) A first course in turbulence. MIT Press, Cambridge

    Book  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper.

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Authors and Affiliations

  1. Department of Engineering and Technology, Federal Rural University of the Semi-arid Region, Av. Francisco Mota 572, Mossoró, RN, 59625900, Brazil

    Victor W. F. de Azevedo

  2. SINMEC Lab, Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, SC, 88040-900, Brazil

    Emilio E. Paladino

  3. Mechanical Process Engineering, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Fabian Denner & Fabien Evrard

Authors
  1. Victor W. F. de Azevedo
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  2. Fabian Denner
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  4. Emilio E. Paladino
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Correspondence to Victor W. F. de Azevedo.

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Technical Editor: Daniel Onofre de Almeida Cruz.

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de Azevedo, V.W.F., Denner, F., Evrard, F. et al. Performance evaluation of standard second-order finite volume method for DNS solution of turbulent channel flow. J Braz. Soc. Mech. Sci. Eng. 43, 513 (2021). https://doi.org/10.1007/s40430-021-03234-8

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  • DOI: https://doi.org/10.1007/s40430-021-03234-8

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