Free Access
Volume 48, Number 3, May-June 2014
Page(s) 765 - 793
Published online 01 April 2014
  1. N. Adams and A. Leonard, Deconvolution of subgrid scales for the simulation of shock-turbulence interaction, in Direct and Large Eddys Simulation III, edited by N.S.P. Voke and L. Kleiser. Kluwer, Dordrecht (1999) 201. [Google Scholar]
  2. N. Adams and S. Stolz, Deconvolution methods for subgrid-scale approximation in large-eddy simulation, Modern Simulation Strategies for Turbulent Flow, edited by R.T. Edwards (2001). [Google Scholar]
  3. N. Adams and S. Stolz, A subgrid-scale deconvolution approach for shock capturing. J. Comput. Phys. 178 (2002) 391–426. [CrossRef] [MathSciNet] [Google Scholar]
  4. G.A. Baker, V.A. Dougalis and O.A. Karakashian, On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations. Math. Comput. 39 (1982) 339–375. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Barbato, L.C. Berselli and C.R. Grisanti, Analytical and numerical results for the rational large eddy simulation model. J. Math. Fluid Mech. 9 (2007) 44–74. [CrossRef] [MathSciNet] [Google Scholar]
  6. L.C. Berselli, On the large eddy simulation of the Taylor-Green vortex. J. Math. Fluid Mech. 7 (2005) S164–S191. [CrossRef] [Google Scholar]
  7. J.P. Boyd, Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: preserving boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys. 143 (1998) 283–288. [CrossRef] [Google Scholar]
  8. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics. Springer-Verlag, New York (1994). [Google Scholar]
  9. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral methods, Evolution to complex geometries and applications to fluid dynamics. Scientific Computation. Springer, Berlin (2007). [Google Scholar]
  10. A. Chorin, Numerical solution for the Navier-Stokes equations. Math. Comput. 22 (1968) 745–762. [CrossRef] [MathSciNet] [Google Scholar]
  11. J. Connors and W. Layton, On the accuracy of the finite element method plus time relaxation. Math. Comput. 79 (2010) 619–648. [CrossRef] [Google Scholar]
  12. A. Dunca, Investigation of a shape optimization algorithm for turbulent flows, tech. rep., Argonne National Lab, report number ANL/MCS-P1101-1003 (2002). Available at [Google Scholar]
  13. A. Dunca, Space averaged Navier Stokes equations in the presence of walls. Ph.D. thesis, University of Pittsburgh (2004). [Google Scholar]
  14. A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows. SIAM J. Math. Anal. 37 (2006) 1890–1902. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Emmrich, Error of the two-step BDF for the incompressible Navier-Stokes problem. M2AN: M2AN 38 (2004) 757–764. [CrossRef] [EDP Sciences] [Google Scholar]
  16. V. Ervin, W. Layton and M. Neda, Numerical analysis of a higher order time relaxation model of fluids. Int. J. Numer. Anal. Model. 4 (2007) 648–670. [Google Scholar]
  17. V. Ervin, W. Layton and M. Neda, Numerical analysis of filter based stabilization for evolution equations. SINUM 50 (2012) 2307–2335. [CrossRef] [Google Scholar]
  18. P. Fischer and J. Mullen, Filter-based stabilization of spectral element methods. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 265–270. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Garnier, N. Adams and P. Sagaut, Large eddy simulation for compressible flows. Sci. Comput. Springer, Berlin (2009). [Google Scholar]
  20. V. Girault and P.-A. Raviart, Finite element approximation of the Navier-Stokes equations, in vol. 749 of Lect. Notes Math. Springer-Verlag, Berlin (1979). [Google Scholar]
  21. M.D. Gunzburger, Finite element methods for viscous incompressible flows, A guide to theory, practice, and algorithms. Computer Science and Scientific Computing. Academic Press Inc., Boston, MA (1989). [Google Scholar]
  22. F. Hecht and O. Pironneau, Freefem++, webpage: [Google Scholar]
  23. J.G. Heywood and R. Rannacher, Finite-element approximation of the nonstationary Navier-Stokes problem. IV. Error analysis for second-order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [CrossRef] [MathSciNet] [Google Scholar]
  24. V. John, Large eddy simulation of turbulent incompressible flows, Analytical and numerical results for a class of LES models, in vol. 34 of Lect. Notes Comput. Sci. Engrg. Springer-Verlag, Berlin (2004). [Google Scholar]
  25. V. John and W.J. Layton, Analysis of numerical errors in large eddy simulation. SIAM J. Numer. Anal. 40 (2002) 995–1020. [CrossRef] [MathSciNet] [Google Scholar]
  26. W. Layton, Superconvergence of finite element discretization of time relaxation models of advection. BIT 47 (2007) 565–576. [CrossRef] [MathSciNet] [Google Scholar]
  27. W. Layton, The interior error of van Cittert deconvolution is optimal. Appl. Math. 12 (2012) 88–93. [Google Scholar]
  28. W. Layton, C. Manica, M. Neda and L. Rebholz, Helicity and energy conservation and dissipation in approximate deconvolution LES models of turbulence. Adv. Appl. Fluid Mech. 4 (2008) 1–46. [MathSciNet] [Google Scholar]
  29. W. Layton and M. Neda, Truncation of scales by time relaxation. J. Math. Anal. Appl. 325 (2007) 788–807. [CrossRef] [Google Scholar]
  30. W. Layton, L.G. Rebholz and C. Trenchea, Modular nonlinear filter stabilization of methods for higher Reynolds numbers flow. J. Math. Fluid Mech. (2011) 1–30. [Google Scholar]
  31. W. Layton, L. Röhe and H. Tran, Explicitly uncoupled VMS stabilization of fluid flow. Comput. Methods Appl. Mech. Engrg. 200 (2011) 3183–3199. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Mathew, R. Lechner, H. Foysi, J. Sesterhenn and R. Friedrich, An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15 (2003). [CrossRef] [Google Scholar]
  33. J.S. Mullen and P.F. Fischer, Filtering techniques for complex geometry fluid flows. Commun. Numer. Methods Engrg. 15 (1999) 9–18. [CrossRef] [Google Scholar]
  34. S. Ravindran, Convergence of extrapolated BDF2 finite element schemes for unsteady penetrative convection model. Numer. Funct. Anal. Optim. 33 (2011) 48–79. [CrossRef] [Google Scholar]
  35. P. Rosenau, Extending hydrodynamics via the regularization of the Chapman-Enskog expansion. Phys. Rev. A 40 (1989) 7193. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. M. Schäfer and S. Turek, Benchmark computations of laminar flow around cylinder, in Flow Simulation with High-Performance Computers II, vol. 52. Edited by H. EH. Vieweg (1996) 547–566. [Google Scholar]
  37. S. Schochet and E. Tadmor, The regularized Chapman-Enskog expansion for scalar conservation laws. Arch. Rat. Mech. Anal. 119 (1992) 95. [CrossRef] [Google Scholar]
  38. I. Stanculescu, Existence theory of abstract approximate deconvolution models of turbulence. Ann. Univ. Ferrara Sez. VII Sci. Mat. 54 (2008) 145–168. [CrossRef] [MathSciNet] [Google Scholar]
  39. S. Stolz and N. Adams, On the approximate deconvolution procedure for LES. Phys. Fluids, II (1999) 1699–1701. [Google Scholar]
  40. S. Stolz, N. Adams and L. Kleiser, An approximate deconvolution model for large eddy simulation with application to wall-bounded flows. Phys. Fluids 13 (2001) 997–1015. [CrossRef] [Google Scholar]
  41. S. Stolz, N. Adams and L. Kleiser, The approximate deconvolution model for LES of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys. Fluids 13 (2001) 2985. [CrossRef] [Google Scholar]
  42. S. Stolz, N. Adams and L. Kleiser, The approximate deconvolution model for compressible flows: isotropic turbulence and shock-boundary-layer interaction,Advances in LES of Complex Flows, in vol. 65 of Fluid Mechanics and Its Applications. Edited by R. Friedrich and W. Rodi. Springer, Netherlands (2002) 33–47. [Google Scholar]
  43. D. Tafti, Comparison of some upwind-biased high-order formulations with a second-order central-difference scheme for time integration of the incompressible Navier-Stokes equations. Comput. Fluids 25 (1996) 647–665. [CrossRef] [MathSciNet] [Google Scholar]
  44. G. Taylor, On decay of vortices in a viscous fluid. Phil. Mag. 46 (1923) 671–674. [CrossRef] [Google Scholar]
  45. G.I. Taylor and A.E. Green, Mechanism of the production of small eddies from large ones, Proc. Royal Soc. London Ser. A 158 (1937) 499–521. [NASA ADS] [CrossRef] [Google Scholar]
  46. M. Visbal and D. Rizzetta, Large-eddy simulation on general geometries using compact differencing and filtering schemes, AIAA Paper (2002) 2002–288. [Google Scholar]
  47. X. Wang, An efficient second order in time scheme for approximating long time statistical properties of the two dimensional Navier–Stokes equations. Numer. Math. 121 (2012) 753–779. [CrossRef] [MathSciNet] [Google Scholar]
  48. E. Zeidler, Applied functional analysis, vol. 108 of Appl. Math. Sci. Springer-Verlag, New York (1995). [Google Scholar]

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