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Research Article

A dynamic closure modeling framework for large eddy simulation using approximate deconvolution: Burgers equation

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Article: 1464368 | Received 28 Jul 2017, Accepted 06 Apr 2018, Published online: 27 Apr 2018

References

  • Adams, N. A., & Stolz, S. (2002). A subgrid-scale deconvolution approach for shock capturing. Journal of Computational Physics, 178(2), 391–426.
  • Berland, J., Lafon, P., Daude, F., Crouzet, F., Bogey, C., & Bailly, C. (2011). Filter shape dependence and effective scale separation in large-eddy simulations based on relaxation filtering. Computers & Fluids, 47(1), 65–74.
  • Berselli, L. C., Iliescu, T., & Layton, W. J. (2006). Mathematics of large eddy simulation of turbulent flows. New York, NY: Springer-Verlag.
  • Biemond, J., Lagendijk, R. L., & Mersereau, R. M. (1990). Iterative methods for image deblurring. Proceedings of the IEEE, 78(5), 856–883.
  • Bogey, C., & Bailly, C. (2004). A family of low dispersive and low dissipative explicit schemes for flow and noise computations. Journal of Computational Physics, 194(1), 194–214.
  • Bogey, C., & Bailly, C. (2006a). Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering. Computers & Fluids, 35(10), 1344–1358.
  • Bogey, C., & Bailly, C. (2006b). Large eddy simulations of transitional round jets: Influence of the Reynolds number on flow development and energy dissipation. Physics of Fluids, 18(6), 065101.
  • Boris, J. P., Grinstein, F. F., Oran, E. S., & Kolbe, R. L. (1992). New insights into large eddy simulation. Fluid Dynamics Research, 10(4–6), 199–228.
  • Bouffanais, R., Deville, M. O., & Leriche, E. (2007). Large-eddy simulation of the flow in a lid-driven cubical cavity. Physics of Fluids, 19(5), 055108.
  • Bull, J. R., & Jameson, A. (2016). Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation. Journal of Computational Physics, 306, 117–136.
  • Carati, D., Winckelmans, G. S., & Jeanmart, H. (2001). On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. Journal of Fluid Mechanics, 441, 119–138.
  • De Stefano, G., & Vasilyev, O. V. (2002). Sharp cutoff versus smooth filtering in large eddy simulation. Physics of Fluids, 14(1), 362–369.
  • Dunca, A. A. (2011). On the existence of global attractors of the approximate deconvolution models of turbulence. Journal of Mathematical Analysis and Applications, 389(2), 1128–1138.
  • Dunca, A. A., & Epshteyn, Y. (2006). On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows. SIAM Journal on Mathematical Analysis, 37(6), 1890–1902.
  • Dunca, A. A., & Lewandowski, R. (2014). Error estimates in approximate deconvolution models. Communications in Mathematical Sciences, 12(4), 757–778.
  • Falkovich, G., & Sreenivasan, K. R. (2006). Lessons from hydrodynamic turbulence. Physics Today, 59(4), 43–49.
  • Fauconnier, D., De Langhe, C., & Dick, E. (2009). A family of dynamic finite difference schemes for large-eddy simulation. Journal of Computational Physics, 228(6), 1830–1861.
  • Galperin, B., & Orszag, S. A. (1993). Large eddy simulation of complex engineering and geophysical flows. New York: Cambridge University Press.
  • Germano, M. (1986). Differential filters for the large eddy numerical simulation of turbulent flows. Physics of Fluids, 29, 1755–1756.
  • Germano, M. (2009). A new deconvolution method for large eddy simulation. Physics of Fluids, 21, 045107.
  • Germano, M. (2015). The similarity subgrid stresses associated to the approximate Van Cittert deconvolutions. Physics of Fluids, 27(3), 035111.
  • Germano, M., Piomelli, U., Moin, P., & Cabot, W. H. (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids, 3, 1760–1765.
  • Gottlieb, S., & Shu, C. W. (1998). Total variation diminishing Runge-Kutta schemes. Mathematics and Computers, 67(221), 73–85.
  • Gullbrand, J., & Chow, F. K. (2003). The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. Journal of Fluid Mechanics, 495(1), 323–341.
  • Habisreutinger, M. A., Bouffanais, R., Leriche, E., & Deville, M. O. (2007). A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation. Journal of Computational Physics, 224(1), 241–266.
  • Jahne, B. (1997). Digital image processing: Concepts, algorithms, and scientific aplications. Berlin, Heildelberg: Springer-Verlag.
  • Jameson, A. (2008). The construction of discretely conservative finite volume schemes that also globally conserve energy or entropy. Journal of Scientific Computing, 34(2), 152–187.
  • Jordan, S. A., & Ragab, S. A. (1996). A large-eddy simulation of the shear-driven cavity flow using dynamic modeling. International Journal of Computational Fluid Dynamics, 6(4), 321–335.
  • Layton, W. (2016). Energy dissipation in the Smagorinsky model of turbulence. Applied Mathematics Letters, 59, 56–59.
  • Layton, W., & Lewandowski, R. (2006). Residual stress of approximate deconvolution models of turbulence. Journal of Turbulence, 7, 1–21.
  • Layton, W., & Neda, M. (2007). A similarity theory of approximate deconvolution models of turbulence. Journal of Mathematical Analysis and Applications, 333(1), 416–429.
  • Layton, W. J., & Rebholz, L. (2012). Approximate deconvolution models of turbulence: analysis, phenomenology and numerical analysis. Berlin: Springer-Verlag.
  • Lele, S. K. (1992). Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103(1), 16–42.
  • Lesieur, M., & Metais, O. (1996). New trends in large-eddy simulations of turbulence. Annual Review of Fluid Mechanics, 28(1), 45–82.
  • Lilly, D. K. (1992). A proposed modification of the Germano subgrid-scale closure method. Physics of Fluids, 4, 633–635.
  • Love, M. D. (1980). Subgrid modelling studies with Burgers’ equation. Journal of Fluid Mechanics, 100(01), 87–110.
  • Lund, T. S. (2003). The use of explicit filters in large eddy simulation. Computers & Mathematics with Applications, 46(4), 603–616.
  • Mathew, J., Foysi, H., & Friedrich, R. (2006). A new approach to LES based on explicit filtering. International Journal of Heat and Fluid Flow, 27(4), 594–602.
  • Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J., & Friedrich, R. (2003). An explicit filtering method for large eddy simulation of compressible flows. Physics of Fluids, 15(8), 2279–2289.
  • Maulik, R., & San, O. (2017a). A dynamic subgrid-scale modeling framework for boussinesq turbulence. International Journal of Heat and Mass Transfer, 108, 1656–1675.
  • Maulik, R., & San, O. (2017b). A novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows. Computers & Mathematics with Applications, 74, 420–445.
  • Maulik, R., & San, O. (2017c). A stable and scale-aware dynamic modeling framework for subgrid-scale parameterizations of two-dimensional turbulence. Computers & Fluids, 158, 11–38.
  • Meneveau, C., & Katz, J. (2000). Scale-invariance and turbulence models for large-eddy simulation. Annual Review of Fluid Mechanics, 32(1), 1–32.
  • Mullen, J. S., & Fischer, P. F. (1999). Filtering techniques for complex geometry fluid flows. Communications in Numerical Methods in Engineering, 15(1), 9–18.
  • Najafi-Yazdi, A., Najafi-Yazdi, M., & Mongeau, L. (2015). A high resolution differential filter for large eddy simulation: Toward explicit filtering on unstructured grids. Journal of Computational Physics, 292, 272–286.
  • Najjar, F. M., & Tafti, D. K. (1996). Study of discrete test filters and finite difference approximations for the dynamic subgrid-scale stress model. Physics of Fluids, 8, 1076–1088.
  • Orszag, S. A. (1971). On the elimination of aliasing in finite-difference schemes by filtering high-wavenumber components. Journal of the Atmospheric Sciences, 28(6), 1074–1074.
  • Piomelli, U. (1999). Large-eddy simulation: achievements and challenges. Progress in Aerospace Sciences, 35(4), 335–362.
  • Press, W., Teukolsky, S., Vetterling, W., & Flannery, B. (1992). Numerical recipes in FORTRAN: The art of scientific computing. New York: Cambridge University Press.
  • Pruett, C. D., & Adams, N. A. (2000). A priori analyses of three subgrid-scale models for one-parameter families of filters. Physics of Fluids, 12, 1133–1142.
  • Rebholz, L. G. (2007). Conservation laws of turbulence models. Journal of Mathematical Analysis and Applications, 326(1), 33–45.
  • Ritchmyer, R. D., & Morton, K. W. (1967). Difference methods for initial-value problems. New York: Interscience.
  • Sagaut, P. (2006). Large eddy simulation for incompressible flows: an introduction. New York: Springer-Verlag.
  • Sagaut, P., & Grohens, R. (1999). Discrete filters for large eddy simulation. International Journal for Numerical Methods in Fluids, 31(8), 1195–1220.
  • San, O. (2016). Analysis of low-pass filters for approximate deconvolution closure modeling in one-dimensional decaying Burgers turbulence. International Journal of Computational Fluid Dynamics, 30, 20–37.
  • Sarghini, F., Piomelli, U., & Balaras, E. (1999). Scale-similar models for large-eddy simulations. Physics of Fluids, 11(6), 1596–1607.
  • Smagorinsky, J. (1963). General circulation experiments with the primitive equations. I. The basic experiments. Monthly Weather Review, 91(3), 99–164.
  • Smagorinsky, J. (1993). Some historical remarks on the use of nonlinear viscosities. In B. Galperin & S. A. Orszag (Eds.), Large eddy simulation of complex engineering and geophysical flows (pp. 3–36). New York: Cambridge University Press.
  • Stanculescu, I. (2008). Existence theory of abstract approximate deconvolution models of turbulence. Annali dell’Universita di Ferrara, 54(1), 145–168.
  • Stolz, S., & Adams, N. A. (1999). An approximate deconvolution procedure for large-eddy simulation. Physics of Fluids, 11, 1699–1701.
  • Stolz, S., Adams, N. A., & Kleiser, L. (2001). An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Physics of Fluids, 13, 997–1015.
  • Vasilyev, O. V., Lund, T. S., & Moin, P. (1998). A general class of commutative filters for LES in complex geometries. Journal of Computational Physics, 146(1), 82–104.
  • Zang, Y., Street, R. L., & Koseff, J. R. (1993). A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Physics of Fluids, 5(12), 3186–3196.