Research Article
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Year 2020, , 145 - 154, 30.09.2020
https://doi.org/10.30939/ijastech..729443

Abstract

References

  • [1] Sagaut, P. (2006). Large eddy simulation for incompressible flows. Scientific Computation, Springer Verlag.
  • [2] John, V. (2004). Large eddy simulation of turbulent incom-pressible flows. Lecture Notes in Computational Science and Engineering, Springer Verlag.
  • [3] Berselli, L.C. and Iliescu, T., and Layton, W.J. (2006). Mathematics of large eddy simulation of turbulent flows. Sci-entific Computation, Springer Verlag.
  • [4] Adams, N.A. and Stolz, S. (2001). Deconvolution methods for subgrid-scale approximation in large-eddy simulation. Modern Simulation Strategies for Turbulent Flow, B. Geurts (editor), pp. 21-41, R. T. Edwards.
  • [5] Adams, N.A., Stolz, S., Kleiser, L. (2006). The Approximate Deconvolution Model for Compressible Flows: Isotropic Turbulence and Shock-Boundary-Layer Interaction. Fluid Mechanics and Its Applications. Advances in LES of Com-plex Flows, vol. 65, 2006, pp. 33-47, Springer Netherlands.
  • [6] Cardoso Manica, C., and Merdan, S. K. (2007). Finite ele-ment error analysis of a zeroth order approximate deconvolu-tion model based on a mixed formulation. JMAA, vol. 331, no. 1, pp. 669-685.
  • [7] Layton, W. and Lewandowski, R. (2006). Residual stress of approximate deconvolution models of turbulence. Journal of Turbulence, vol. 7, Issue 46, p. 1-21.
  • [8] Labovsky, A., Trenchea, C. (2011). Large Eddy Simulation for Turbulent Magnetohydrodynamic Flows. JMMA, vol. 377, pp.516-533.
  • [9] Labovsky, A., Trenchea, C. (2010). A family of Approxi-mate Deconvolution Models for MagnetoHydroDynamic Turbulence. Numerical Functional Analysis and Optimiza-tion, vol.31(12), pp.1362-1385.
  • [10] Dunca, A. and Epshteyn, Y. (2006). On the Stolz-Adams deconvolution model for the large eddy simulation of turbu-lent flows. SIAM J. Math. Anal., Vol. 37(6), pp. 1890-1902.
  • [11] Gunzburger, M., Labovsky A. (2012). High Accuracy Method for Turbulent Flow Problems. Mathematical Models and Methods in Applied Sciences, vol. 22 (6).
  • [12] Aggul, M., Kaya, S., Labovsky, A. (2019). Two approach-es to creating a turbulence model with increased temporal ac-curacy. Applied Mathematics and Computations, vol. 358, pp. 25-36.
  • [13] Girault, V., Raviart, P.A. (1979). Finite element approxima-tion of the Navier-Stokes equations. Lecture notes in mathe-matics, no. 749, Springer-Verlag.
  • [14] Schäfer M., Turek S., Durst F., Krause E., Rannacher R. (1996). Benchmark Computations of Laminar Flow Around a Cylinder. Flow Simulation with High-Performance Com-puters II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag.
  • [15] John, V. (2004). Reference values for drag and lift of a two dimensional time-dependent flow around a cylinder. Interna-tional Journal for Numerical Methods in Fluids, 44:777–788.
  • [16] Bowers, A. L., Rebholz, L.G., Takhirov A., Trenchea C. (2012). Improved accuracy in regularization models of in-compressible flow via adaptive nonlinear filtering. Int. J. Numer. Meth. Fluids, 70: 805-828.

Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation

Year 2020, , 145 - 154, 30.09.2020
https://doi.org/10.30939/ijastech..729443

Abstract

This report presents a method with high spatial and temporal accuracy for estimating solutions of Navier-Stokes equations at high Reynolds number. It employs Crank-Nicolson time discretization along with the zeroth-order ap-proximate deconvolution model of turbulence to regularize the flow prob-lem; solves a deviation of the Navier Stokes equation instead. Both theoreti-cal and computational findings of this report illustrate that the model pro-duces a high order of accuracy and stability. Furthermore, measurements of the drag and lift coefficients of a benchmark problem verify the potential of the model in this kind of computations.

References

  • [1] Sagaut, P. (2006). Large eddy simulation for incompressible flows. Scientific Computation, Springer Verlag.
  • [2] John, V. (2004). Large eddy simulation of turbulent incom-pressible flows. Lecture Notes in Computational Science and Engineering, Springer Verlag.
  • [3] Berselli, L.C. and Iliescu, T., and Layton, W.J. (2006). Mathematics of large eddy simulation of turbulent flows. Sci-entific Computation, Springer Verlag.
  • [4] Adams, N.A. and Stolz, S. (2001). Deconvolution methods for subgrid-scale approximation in large-eddy simulation. Modern Simulation Strategies for Turbulent Flow, B. Geurts (editor), pp. 21-41, R. T. Edwards.
  • [5] Adams, N.A., Stolz, S., Kleiser, L. (2006). The Approximate Deconvolution Model for Compressible Flows: Isotropic Turbulence and Shock-Boundary-Layer Interaction. Fluid Mechanics and Its Applications. Advances in LES of Com-plex Flows, vol. 65, 2006, pp. 33-47, Springer Netherlands.
  • [6] Cardoso Manica, C., and Merdan, S. K. (2007). Finite ele-ment error analysis of a zeroth order approximate deconvolu-tion model based on a mixed formulation. JMAA, vol. 331, no. 1, pp. 669-685.
  • [7] Layton, W. and Lewandowski, R. (2006). Residual stress of approximate deconvolution models of turbulence. Journal of Turbulence, vol. 7, Issue 46, p. 1-21.
  • [8] Labovsky, A., Trenchea, C. (2011). Large Eddy Simulation for Turbulent Magnetohydrodynamic Flows. JMMA, vol. 377, pp.516-533.
  • [9] Labovsky, A., Trenchea, C. (2010). A family of Approxi-mate Deconvolution Models for MagnetoHydroDynamic Turbulence. Numerical Functional Analysis and Optimiza-tion, vol.31(12), pp.1362-1385.
  • [10] Dunca, A. and Epshteyn, Y. (2006). On the Stolz-Adams deconvolution model for the large eddy simulation of turbu-lent flows. SIAM J. Math. Anal., Vol. 37(6), pp. 1890-1902.
  • [11] Gunzburger, M., Labovsky A. (2012). High Accuracy Method for Turbulent Flow Problems. Mathematical Models and Methods in Applied Sciences, vol. 22 (6).
  • [12] Aggul, M., Kaya, S., Labovsky, A. (2019). Two approach-es to creating a turbulence model with increased temporal ac-curacy. Applied Mathematics and Computations, vol. 358, pp. 25-36.
  • [13] Girault, V., Raviart, P.A. (1979). Finite element approxima-tion of the Navier-Stokes equations. Lecture notes in mathe-matics, no. 749, Springer-Verlag.
  • [14] Schäfer M., Turek S., Durst F., Krause E., Rannacher R. (1996). Benchmark Computations of Laminar Flow Around a Cylinder. Flow Simulation with High-Performance Com-puters II. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag.
  • [15] John, V. (2004). Reference values for drag and lift of a two dimensional time-dependent flow around a cylinder. Interna-tional Journal for Numerical Methods in Fluids, 44:777–788.
  • [16] Bowers, A. L., Rebholz, L.G., Takhirov A., Trenchea C. (2012). Improved accuracy in regularization models of in-compressible flow via adaptive nonlinear filtering. Int. J. Numer. Meth. Fluids, 70: 805-828.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mustafa Ağgül 0000-0003-4013-9907

Publication Date September 30, 2020
Submission Date April 29, 2020
Acceptance Date July 2, 2020
Published in Issue Year 2020

Cite

APA Ağgül, M. (2020). Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation. International Journal of Automotive Science And Technology, 4(3), 145-154. https://doi.org/10.30939/ijastech..729443
AMA Ağgül M. Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation. ijastech. September 2020;4(3):145-154. doi:10.30939/ijastech.729443
Chicago Ağgül, Mustafa. “Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation”. International Journal of Automotive Science And Technology 4, no. 3 (September 2020): 145-54. https://doi.org/10.30939/ijastech. 729443.
EndNote Ağgül M (September 1, 2020) Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation. International Journal of Automotive Science And Technology 4 3 145–154.
IEEE M. Ağgül, “Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation”, ijastech, vol. 4, no. 3, pp. 145–154, 2020, doi: 10.30939/ijastech..729443.
ISNAD Ağgül, Mustafa. “Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation”. International Journal of Automotive Science And Technology 4/3 (September 2020), 145-154. https://doi.org/10.30939/ijastech. 729443.
JAMA Ağgül M. Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation. ijastech. 2020;4:145–154.
MLA Ağgül, Mustafa. “Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation”. International Journal of Automotive Science And Technology, vol. 4, no. 3, 2020, pp. 145-54, doi:10.30939/ijastech. 729443.
Vancouver Ağgül M. Crank-Nicholson Scheme of the Zeroth-Order Approximate Deconvolution Model of Turbulence Based On a Mixed Formulation. ijastech. 2020;4(3):145-54.

International Journal of Automotive Science and Technology (IJASTECH) is published by Society of Automotive Engineers Turkey


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