Abstract
In this paper we compare a second-order accurate finite volume method and a fourth-order approach for a direct numerical simulation of the flow in a cubical driven cavity at Re = 10, 000. Experimental results are available for comparison. The fourth-order method turns out to be the superior method. For a driven cavity with spanwise aspect ratio 0.5 at Re = 10, 000, along with experimental results also the results of a LES (with a dynamic mixed subgrid-scale model) are available. We will demonstrate the challenge of turbulence modelling by comparing this LES on a 64 × 64 × 32 grid, a fourth-order DNS on a 503 grid and an experiment. Finally, using the fourth-order simulation method, a DNS of a turbulent flow in a cubical cavity at Re = 50,000 is performed using a 1923 grid. Mean velocities, turbulence intensities and power spectra are computed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fasel, H.F. (1990) Numerical simulation of instability and transition in boundary layer flows, Laminar-Turbulent Transition, D. Arnal & R. Michel (eds.). Springer-Verlag, Berlin.
Harlow, F.H. and Welsh, J.E. (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics of Fluids, 8, pp. 2182–2189.
Joslin, R.D., Streett, C.L. and Chang, C.L. (1992) Validation of three-dimensional incompressible spatial direct numerical simulation code — a comparison with linear theory and parabolic stability equation theories for boundary layer transition on a flat plate, NASA Technical Paper 3205.
Liu, Z. and Liu, C. (1994) Fourth order finite difference and multigrid methods for modeling instabilities in flat plate boundary layers — 2D and 3D approaches, Computers & Fluids, 7, pp. 955–982.
Prasad, A.K. and Koseff, J.R. (1989) Reynolds number and end-wall effects on a liddriven cavity flow, Physics of Fluids A, 1, pp. 208–218.
Rai M. and Moin P. (1989) On direct simulations of turbulent flow using finite-difference schemes, AIAA-89-0369.
Verstappen, R.W.C.P. and Veldman, A.E.P. (1994) Direct numerical simulation of a 3D turbulent flow in a driven cavity at Re=10,000, Computational Fluid Dynamics ’94, S. Wagner et al. (eds.), John Wiley & Sons, Chichester pp. 558–565.
Verstappen, R.W.C.P. and Veldman, A.E.P. (1996) A fourth-order finite volume method for direct numerical simulation of turbulence at higer Reynolds numbers, Computational Fluid Dynamics ’96, J.A. Désidéri et al. (eds.), John Wiley & Sons, Chichester pp. 1073–1079.
Zang, Y.Z., Street, R.L. and Koseff, J.R. (1993) A dynamic mixed subgrid-scale model and its application to turbulent recirculating flow, Physics of Fluids A, 5, pp. 3186–3196.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Verstappen, R.W.C.P., Veldman, A.E.P. (1997). A Comparison of Low-Order DNS, High-Order DNS and LES. In: Chollet, JP., Voke, P.R., Kleiser, L. (eds) Direct and Large-Eddy Simulation II. ERCOFTAC Series, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5624-0_9
Download citation
DOI: https://doi.org/10.1007/978-94-011-5624-0_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6370-8
Online ISBN: 978-94-011-5624-0
eBook Packages: Springer Book Archive