Skip to main content
Log in

Numerical and Physical Instabilities in Massively Parallel LES of Reacting Flows

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

Abstract

LES of reacting flows is rapidly becoming mature and providing levels of precision which can not be reached with any RANS (Reynolds Averaged) technique. In addition to the multiple subgrid scale models required for such LES and to the questions raised by the required numerical accuracy of LES solvers, various issues related to the reliability, mesh independence and repetitivity of LES must still be addressed, especially when LES is used on massively parallel machines. This talk discusses some of these issues: (1) the existence of non physical waves (known as ‘wiggles’ by most LES practitioners) in LES, (2) the effects of mesh size on LES of reacting flows, (3) the growth of rounding errors in LES on massively parallel machines and more generally (4) the ability to qualify a LES code as ‘bug free’ and ‘accurate’. Examples range from academic cases (minimum non-reacting turbulent channel) to applied configurations (a sector of an helicopter combustion chamber).

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abarbanel, S.S., Chertock, A.E.: Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, I. J. Comput. Phys. 160, 42–66 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Boudier, G., Gicquel, L.Y.M., Poinsot, T., Bissières, D., Bérat, C.: Effect of mesh resolution on large eddy simulation of reacting flows in complex geometry combustors. Combust. Flame 155(1–2), 196–214 (2008)

    Article  Google Scholar 

  3. Chaitin-Chatelin, F., Frayssé, V.: Lectures on Finite Precision Computations. SIAM, Philadelphia (1996)

    Book  MATH  Google Scholar 

  4. Clavin, P.: Dynamics of combustion fronts in premixed gases: from flames to detonations. Proc. Combust. Inst. 28, 569–586 (2000)

    Article  Google Scholar 

  5. Colin, O., Rudgyard, M.: Development of high-order Taylor-Galerkin schemes for unsteady calculations. J. Comput. Phys. 162(2), 338–371 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 24th National Conference of the ACM, pp. 157–172 (1969)

    Google Scholar 

  7. Di Mare, F., Jones, W.P., Menzies, K.: Large eddy simulation of a model gas turbine combustor. Combust. Flame 137, 278–295 (2004)

    Article  Google Scholar 

  8. Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, London (1981)

    MATH  Google Scholar 

  9. Freitag, M., Janicka, J.: Investigation of a strongly swirled premixed flame using LES. Proc. Combust. Inst. 31, 1477–1485 (2007)

    Article  Google Scholar 

  10. Ghosal, S., Moin, P.: The basic equations for the large eddy simulation of turbulent flows in complex geometry. J. Comput. Phys. 118, 24–37 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Giauque, A., Selle, L., Poinsot, T., Buechner, H., Kaufmann, P., Krebs, W.: System identification of a large-scale swirled partially premixed combustor using LES and measurements. J. Turbul. 6(21), 1–20 (2005)

    Article  MathSciNet  Google Scholar 

  12. Hanrot, G., Lefèvre, V., Stehlé, D., Zimmermann, P.: Worst cases for a periodic function with large arguments. In: Kornerup, P., Muller, J.-M. (eds.) Proceedings of the 18th IEEE Symposium on Computer Arithmetic, pp. 133–140. IEEE Computer Society Press, Los Alamitos (2007)

    Chapter  Google Scholar 

  13. Hirsch, C.: Numerical Computation of Internal and External Flows. Wiley, New York (1988)

    MATH  Google Scholar 

  14. Ho, C.M., Huerre, P.: Perturbed free shear layers. J. Fluid Mech. 16, 365 (1984)

    Article  Google Scholar 

  15. Klein, M.: An attempt to assess the quality of large eddy simulations in the context of implicit filtering. Flow Turbul. Combust. 75(1–4), 131–147 (2005)

    Article  MATH  Google Scholar 

  16. Lele, S.K.: Compact finite difference schemes with spectral like resolution. J. Comput. Phys. 103, 16–42 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu, W.-H., Sherman, A.H.: Comparative analysis of the Cuthill—McKee and the reverse Cuthill-Mckee ordering algorithms for sparse matrices. SIAM J. Numer. Anal. 13(2), 198–213 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197(1), 215–240 (2004)

    Article  MATH  Google Scholar 

  19. Martin, C., Benoit, L., Sommerer, Y., Nicoud, F., Poinsot, T.: LES and acoustic analysis of combustion instability in a staged turbulent swirled combustor. AIAA J. 44(4), 741–750 (2006)

    Article  Google Scholar 

  20. Meyers, J., Geurts, B.J., Baelmans, M.: Database analysis of errors in large-eddy simulation. Phys. Fluids 15(9), 2740–2755 (2003)

    Article  Google Scholar 

  21. Moureau, V., Lartigue, G., Sommerer, Y., Angelberger, C., Colin, O., Poinsot, T.: Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys. 202(2), 710–736 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 2nd edn. R.T. Edwards, Ann Arbor (2005)

    Google Scholar 

  23. Poinsot, T., Echekki, T., Mungal, M.G.: A study of the laminar flame tip and implications for premixed turbulent combustion. Combust. Sci. Technol. 81(1–3), 45–73 (1992)

    Article  Google Scholar 

  24. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  25. Pope, S.B.: Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35 (2004)

    Article  Google Scholar 

  26. Prière, C., Gicquel, L.Y.M., Gajan, P., Strzelecki, A., Poinsot, T., Bérat, C.: Experimental and numerical studies of dilution systems for low emission combustors. AIAA J. 43(8), 1753–1766 (2005)

    Article  Google Scholar 

  27. Rayleigh, L.: The explanation of certain acoustic phenomena. Nature 18, 319–321 (1878)

    Article  Google Scholar 

  28. Richard, S., Colin, O., Vermorel, O., Benkenida, A., Angelberger, C., Veynante, D.: Towards large eddy simulation of combustion in spark ignition engines. Proc. Combust. Inst. 31, 3059–3066 (2007)

    Article  Google Scholar 

  29. Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Scientific Computation Series. Springer, Berlin (2000)

    Google Scholar 

  30. Schmitt, P., Poinsot, T.J., Schuermans, B., Geigle, K.: Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high pressure burner. J. Fluid Mech. 570, 17–46 (2007)

    Article  MATH  Google Scholar 

  31. Schønfeld, T., Rudgyard, M.: Steady and unsteady flows simulations using the hybrid flow solver avbp. AIAA J. 37(11), 1378–1385 (1999)

    Article  Google Scholar 

  32. Selle, L., Benoit, L., Poinsot, T., Nicoud, F., Krebs, W.: Joint use of compressible large-eddy simulation and Helmholtz solvers for the analysis of rotating modes in an industrial swirled burner. Combust. Flame 145(1–2), 194–205 (2006)

    Article  Google Scholar 

  33. Sengupta, T.K.: Fundamentals of Computational Fluid Dynamics. Universities Press, Hyderabad (2004)

    Google Scholar 

  34. Sengupta, T.K., Ganerwal, G., Dipankar, A.: High accuracy compact schemes and Gibbs’ phenomenon. J. Sci. Comput. 21(3), 253–268 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  35. Senoner, J.-M., García, M., Mendez, S., Staffelbach, G., Vermorel, O., Poinsot, T.: Growth of rounding errors and repetitivity of large eddy simulations. AIAA J. 46(7), 1773–1781 (2008)

    Article  Google Scholar 

  36. Sommerer, Y., Galley, D., Poinsot, T., Ducruix, S., Lacas, F., Veynante, D.: Large eddy simulation and experimental study of flashback and blow-off in a lean partially premixed swirled burner. J. Turbul. 5 (2004)

  37. Stoer, J.S., Bulirsch, R.: An Introduction to Numerical Analysis. Springer, Berlin (1980)

    Google Scholar 

  38. Taylor, V.E., Nour-Omid, B.: A study of the factorization fill-in for a parallel implementation of the finite element method. Int. J. Numer. Methods Eng. 37, 3809–3823 (1994)

    Article  MATH  Google Scholar 

  39. Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, Cambridge (1972)

    Google Scholar 

  40. Vichnevetsky, R., Bowles, J.B.: Fourier Analysis of Numerical Approximations of Hyperbolic Equations. SIAM Studies in Applied Mechanics. SIAM, Philadelphia (1982)

    Google Scholar 

  41. Vreman, A.W., Geurts, B.J., Kuerten, J.G.M.: A priori tests of large eddy simulation of the compressible plane mixing layer. J. Eng. Mathods 29, 299–327 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  42. Vreman, B., Geurts, B., Kuerten, H.: Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. Int. J. Numer. Methods Fluids 22, 297–311 (1996)

    Article  MATH  Google Scholar 

  43. Williams, F.A.: Combustion Theory. Benjamin Cummings, Menlo Park (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. Poinsot.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poinsot, T., Garcia, M., Senoner, J.M. et al. Numerical and Physical Instabilities in Massively Parallel LES of Reacting Flows. J Sci Comput 49, 78–93 (2011). https://doi.org/10.1007/s10915-010-9432-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-010-9432-8

Keywords

Navigation