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).
Similar content being viewed by others
References
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)
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)
Chaitin-Chatelin, F., Frayssé, V.: Lectures on Finite Precision Computations. SIAM, Philadelphia (1996)
Clavin, P.: Dynamics of combustion fronts in premixed gases: from flames to detonations. Proc. Combust. Inst. 28, 569–586 (2000)
Colin, O., Rudgyard, M.: Development of high-order Taylor-Galerkin schemes for unsteady calculations. J. Comput. Phys. 162(2), 338–371 (2000)
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)
Di Mare, F., Jones, W.P., Menzies, K.: Large eddy simulation of a model gas turbine combustor. Combust. Flame 137, 278–295 (2004)
Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, London (1981)
Freitag, M., Janicka, J.: Investigation of a strongly swirled premixed flame using LES. Proc. Combust. Inst. 31, 1477–1485 (2007)
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)
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)
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)
Hirsch, C.: Numerical Computation of Internal and External Flows. Wiley, New York (1988)
Ho, C.M., Huerre, P.: Perturbed free shear layers. J. Fluid Mech. 16, 365 (1984)
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)
Lele, S.K.: Compact finite difference schemes with spectral like resolution. J. Comput. Phys. 103, 16–42 (1992)
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)
Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197(1), 215–240 (2004)
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)
Meyers, J., Geurts, B.J., Baelmans, M.: Database analysis of errors in large-eddy simulation. Phys. Fluids 15(9), 2740–2755 (2003)
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)
Poinsot, T., Veynante, D.: Theoretical and Numerical Combustion, 2nd edn. R.T. Edwards, Ann Arbor (2005)
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)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)
Pope, S.B.: Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35 (2004)
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)
Rayleigh, L.: The explanation of certain acoustic phenomena. Nature 18, 319–321 (1878)
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)
Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Scientific Computation Series. Springer, Berlin (2000)
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)
Schønfeld, T., Rudgyard, M.: Steady and unsteady flows simulations using the hybrid flow solver avbp. AIAA J. 37(11), 1378–1385 (1999)
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)
Sengupta, T.K.: Fundamentals of Computational Fluid Dynamics. Universities Press, Hyderabad (2004)
Sengupta, T.K., Ganerwal, G., Dipankar, A.: High accuracy compact schemes and Gibbs’ phenomenon. J. Sci. Comput. 21(3), 253–268 (2004)
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)
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)
Stoer, J.S., Bulirsch, R.: An Introduction to Numerical Analysis. Springer, Berlin (1980)
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)
Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, Cambridge (1972)
Vichnevetsky, R., Bowles, J.B.: Fourier Analysis of Numerical Approximations of Hyperbolic Equations. SIAM Studies in Applied Mechanics. SIAM, Philadelphia (1982)
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)
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)
Williams, F.A.: Combustion Theory. Benjamin Cummings, Menlo Park (1985)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10915-010-9432-8