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

Year 2020, Volume: 4 Issue: 3, 145 - 154, 30.09.2020

Mustafa Ağgül

https://doi.org/10.30939/ijastech..729443

Cited By: 1

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.

Keywords

Approximate Deconvolution , Crank-Nicholson , Stability , Accuracy , Turbulence Models , Space Filter

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.