- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Numerical Analysis
Volume 2010 (2010), Article ID 419021, 21 pages
Discontinuous Time Relaxation Method for the Time-Dependent Navier-Stokes Equations
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA
Received 17 July 2010; Accepted 16 September 2010
Academic Editor: William John Layton
Copyright © 2010 Monika Neda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Doklady Akademii Nauk SSSR, vol. 30, pp. 9–13, 1941.
- N. A. Adams and S. Stolz, “Deconvolution methods for subgrid-scale approximation in large eddy simulation,” in Modern Simulation Strategies for Turbulent Flow, R.T. Edwards, 2001.
- W. Layton and M. Neda, “Truncation of scales by time relaxation,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 788–807, 2007.
- L. C. Berselli, T. Iliescu, and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows, Scientific Computation, Springer, Berlin, Germany, 2006.
- V. John, Large Eddy Simulation of Turbulent Incompressible Flows, vol. 34 of Lecture Notes in Computational Science and Engineering, Springer, Berlin, Germany, 2004.
- B. J. Geurts, “Inverse modeling for large eddy simulation,” Physics of Fluids, vol. 9, pp. 3585–3587, 1997.
- P. Sagaut, Large Eddy Simulation for Incompressible Flows, Scientific Computation, Springer, Berlin, Germany, 2001.
- M. Germano, “Differential filters of elliptic type,” Physics of Fluids, vol. 29, no. 6, pp. 1757–1758, 1986.
- S. Stolz and N. A. Adams, “An approximate deconvolution procedure for large-eddy simulation,” Physics of Fluids, vol. 11, pp. 1699–1701, 1999.
- M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics, Bristol, UK, 1998.
- S. Stolz, N. A. Adams, and L. Kleiser, “The approximate deconvolution model for large-eddy simulation of compressible flows and its application to shock-turbulent-boundary-layer interaction,” Physics of Fluids, vol. 13, no. 10, pp. 2985–3001, 2001.
- S. Stolz, N. A. Adams, and L. Kleiser, “An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows,” Physics of Fluids, vol. 13, no. 4, pp. 997–1015, 2001.
- B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, vol. 35 of Frontiers in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 2008.
- V. J. Ervin, W. J. Layton, and M. Neda, “Numerical analysis of a higher order time relaxation model of fluids,” International Journal of Numerical Analysis and Modeling, vol. 4, no. 3-4, pp. 648–670, 2007.
- W. J. Layton, C. C. Manica, M. Neda, and L. G. Rebholz, “Helicity and energy conservation and dissipation in approximate deconvolution LES models of turbulence,” Advances and Applications in Fluid Mechanics, vol. 4, no. 1, pp. 1–46, 2008.
- V. Girault, B. Rivière, and M. F. Wheeler, “A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems,” Mathematics of Computation, vol. 74, no. 249, pp. 53–84, 2005.
- V. Girault, B. Rivière, and M. F. Wheeler, “A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations,” Mathematical Modelling and Numerical Analysis, vol. 39, no. 6, pp. 1115–1147, 2005.
- B. Cockburn, G. Kanschat, and D. Schotzau, “A locally conservative LDG method for the incompressible Navier-Stokes equations,” Mathematics of Computation, vol. 74, no. 251, pp. 1067–1095, 2005.
- S. Kaya and B. Rivière, “A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations,” SIAM Journal on Numerical Analysis, vol. 43, no. 4, pp. 1572–1595, 2005.
- M. F. Wheeler, “An elliptic collocation-finite element method with interior penalties,” SIAM Journal on Numerical Analysis, vol. 15, no. 1, pp. 152–161, 1978.
- Y. Epshteyn and B. Rivière, “Estimation of penalty parameters for symmetric interior penalty Galerkin methods,” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 843–872, 2007.
- C. C. Manica and S. K. Merdan, “Convergence analysis of the finite element method for a fundamental model in turbulence,” Tech. Rep. TR-MATH 06-12, University of Pittsburgh, Pittsburgh, Pa, USA, 2006.
- C. C. Manica, M. Neda, M. Olshanskii, and L. Rebholz, “Enabling numerical accuracy of Navier-Stokes-α through deconvolution and enhanced stability,” Mathematical Modelling and Numerical Analysis. In press.
- J. M. Connors, “Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes-alpha model,” Numerical Methods for Partial Differential Equations, vol. 26, pp. 1328–1350, 2010.
- A. Bowers and L. Rebholz, “Increasing accuracy and efficiency in FE computations of the Leray-deconvolution model,” Numerical Methods for Partial Differential Equations. In press.
- A. Dunca and Y. Epshteyn, “On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows,” SIAM Journal on Mathematical Analysis, vol. 37, no. 6, pp. 1890–1902, 2006.
- W. Layton, C. C. Manica, M. Neda, and L. G. Rebholz, “Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence,” Numerical Methods for Partial Differential Equations, vol. 24, no. 2, pp. 555–582, 2008.
- W. Layton, “A remark on regularity of an elliptic-elliptic singular perturbation problem,” Tech. Rep., University of Pittsburgh, Pittsburgh, Pa, USA, 2007.
- I. Stanculescu, “Existence theory of abstract approximate deconvolution models of turbulence,” Annali dell'Universitá di Ferrara, vol. 54, no. 1, pp. 145–168, 2008.
- M. Anitescu, F. Pahlevani, and W. J. Layton, “Implicit for local effects and explicit for nonlocal effects is unconditionally stable,” Electronic Transactions on Numerical Analysis, vol. 18, pp. 174–187, 2004.
- M. Crouzeix and P.-A. Raviart, “Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I,” RAIRO: Numerical Analysis, vol. 7, no. R-3, pp. 33–75, 1973.
- J. G. Heywood and R. Rannacher, “Finite-element approximation of the nonstationary Navier-Stokes problem. IV. Error analysis for second-order time discretization,” SIAM Journal on Numerical Analysis, vol. 27, no. 2, pp. 353–384, 1990.