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Study of the Spectral Difference Numerical Dissipation for Turbulent Flows Using Unstructured Grids

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Abstract

In this paper, the numerical dissipation properties of the Spectral Difference (SD) method are studied in the context of vortex dominated flows and wall-bounded turbulence, using uniform and distorted grids. First, the validity of using the SD numerical dissipation as the only source of subgrid dissipation (the so-called Implicit-LES approach) is assessed on regular grids using various polynomial degrees (namely, p = 3, p = 4, p = 5) for the Taylor-Green vortex flow configuration at R e = 5 000. It is shown that the levels of numerical dissipation greatly depend on the order of accuracy chosen and, in turn, lead to an incorrect estimation of the viscous dissipation levels. The influence of grid distortion on the numerical dissipation is then assessed in the context of finite Reynolds number freely-decaying and wall-bounded turbulence. Tests involving different amplitudes of distortion show that highly skewed grids lead to the presence of small-scale, noisy structures, emphasizing the need of explicit subgrid modeling or regularization procedures when considering coarse, high-order SD computations on unstructured grids. Under-resolved, high-order computations of the turbulent channel flow at R e τ = 1000 using highly-skewed grids are considered as well and present a qualitatively similar agreement to results obtained on a regular grid.

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References

  1. Kopriva, D.A., Kolias, J.H.: A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125(1), 244–261 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Liu, Y., Vinokur, M., Wang, Z.: Spectral difference method for unstructured grids I: basic formulation. J. Comput. Phys. 216(2), 780–801 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Van den Abeele, K., Lacor, C., Wang, Z: On the stability and accuracy of the spectral difference method. J. Sci. Comput. 37(2), 162–188 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ghosal, S.: An analysis of numerical errors in Large-Eddy simulations of turbulence. J. Comput. Phys. 125(1), 187–206 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chow, F., Moin, P.: A further study of numerical errors in Large-Eddy simulations. J. Comput. Phys. 184(2), 366–380 (2003)

    Article  MATH  Google Scholar 

  6. Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather Rev. 91(3), 99–164 (1963)

    Article  Google Scholar 

  7. Metais, O., Lesieur, M.: Spectral Large-Eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239(1), 157–194 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Sengupta, K., Jacobs, G., Mashayek, F.: Large-Eddy simulation of compressible flows using a spectral multidomain method. Int. J. Numer. Meth. Fluids 61(3), 311–340 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lodato, G., Castonguay, P., Jameson, A.: Discrete filter operators for Large-Eddy simulation using high-order Spectral Difference methods. Int. J. Numer. Meth. Fluids 72(2), 231–258 (2013)

    Article  MathSciNet  Google Scholar 

  10. Lodato, G., Castonguay, P., Jameson, A.: Structural Wall-modeled LES using a high-order spectral difference scheme for unstructured meshes. Flow Turb. Comb. 92 (1–2), 579–606 (2014)

    Article  Google Scholar 

  11. Chapelier, J.-B., Lodato, G.: A spectral-element dynamic model for the Large-Eddy simulation of turbulent flows. J. Comput. Phys. 321, 279–302 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Parsani, M., Ghorbaniasl, G., Lacor, C., Turkel, E.: An implicit high-order spectral difference approach for Large Eddy simulation. J. Comput. Phys. 229(14), 5373–5393 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Parsani, M., Bilka, M., Lacor, C.: Large Eddy Simulation of a Muffler with the High Order Spectral Difference Method. Spectral and High Order Methods for Partial Differential equations-ICOSAHOM 2012, pp. 337–347. Springer (2014)

  14. Mohammad, A.H., Wang, Z., Liang, C.: Large eddy simulation of flow over a cylinder using high-order spectral difference method. Adv. Appl. Math. Mech. 2(4), 451–466 (2010)

    MathSciNet  Google Scholar 

  15. Castonguay, P., Liang, C., Jameson, A.: Simulation of transitional flow over airfoils using the spectral difference method. AIAA Paper 2010–4626 (2010)

  16. Liang, C., Premasuthan, S., Jameson, A., Wang, Z.: Large eddy simulation of compressible turbulent channel flow with Spectral Difference method. AIAA Paper 2009–402 (2009)

  17. Grinstein, F.F., Margolin, L.G., Rider, W.J.: Implicit Large-Eddy Simulation: Computing Turbulent Fluid Dynamics. Cambridge University Press (2007)

  18. Chapelier, J.-B., Lodato, G., Jameson, A.: A study on the numerical dissipation of the Spectral Difference method for freely decaying and wall-bounded turbulence. Comp. Fluids 139, 261–280 (2016)

    Article  MathSciNet  Google Scholar 

  19. Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43(2), 357–372 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  20. Harten, A., Lax, P.D., Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25(1), 35–61 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  21. Sun, Y., Wang, Z. J., Liu, Y.: High-order multidomain Spectral Difference method for the Navier-Stokes equations on unstructured hexahedral grids. Commun. Comput. Phys. 2(2), 310–333 (2007)

    MathSciNet  MATH  Google Scholar 

  22. Gottlieb, S., Shu, C.: Total variation diminishing Runge-Kutta schemes. Math. Comput. 67(221), 73–85 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yee, H.C., Sandham, N.D., Djomehri, M.: Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150(1), 199–238 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K., Uno, A.: Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592(1), 335–366 (2007)

    MATH  Google Scholar 

  25. Yeung, P., Zhou, Y.: Universality of the Kolmogorov constant in numerical simulations of turbulence. Phys. Rev. E 56(2), 1746 (1997)

    Article  Google Scholar 

  26. Carton de Wiart, C., Hillewaert, K., Duponcheel, M., Winckelmans, G.: Assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number. Int. J. Numer. Meth. Fluids 74(7), 469–493 (2014)

    Article  MathSciNet  Google Scholar 

  27. Carton de Wiart, C., Hillewaert, K.: Development and Validation of a Massively Parallel High-Order Solver for DNS and LES of Industrial Flows, IDIHOM: Industrialization of High-Order Methods-A Top-Down Approach, pp. 251–292. Springer (2015)

  28. Graham, J., Kanov, K., Givelberg, E., Burns, R., Eyink, G., Szalay, A., Meneveau, C., Lee, M., Malaya, N., Moser, R.: A Web-Services accessible database for channel flow turbulence at R e τ = 1000. Bull. Am. Phys. Soc. 58 (2013)

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Acknowledgments

The use of the SD solver originally developed by Antony Jameson’s group at Stanford university, and joint financial support from the Agence Nationale de la Recherche (ANR) and Fondation de Recherche pour l’Aéronautique et l’Espace (FRAE) under Grant No. ANR-14-CE05-0029 are gratefully acknowledged. This work was granted access to the HPC resources of IDRIS-CNRS under the allocation i2015-2a7361. The Haute Normandie Computing center CRIANN is also acknowledged. The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. CORIA UMR6614, Normandie Université, CNRS, INSA et Université de Rouen, Saint-Étienne-du-Rouvray, France

    J.-B. Chapelier & G. Lodato

  2. School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    J.-B. Chapelier

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  1. J.-B. Chapelier
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  2. G. Lodato
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Correspondence to J.-B. Chapelier.

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Chapelier, JB., Lodato, G. Study of the Spectral Difference Numerical Dissipation for Turbulent Flows Using Unstructured Grids. Flow Turbulence Combust 99, 643–664 (2017). https://doi.org/10.1007/s10494-017-9847-5

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  • DOI: https://doi.org/10.1007/s10494-017-9847-5

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