Abstract
Compact finite difference methods are nowadays very popular for the simulation of compressible turbulent flows, see for instance (Lele, 1992) and (Boersma, 2005). Due to the low dissipation and dispersion errors of the compact finite difference schemes, they can be used for various type of problems including large eddy and direct numerical simulation of turbulent flow and laminar turbulent transition. However due to the low numerical dissipation compact finite difference have the tendency to be numerically quite unstable. In practice this instability issue is solved by applying a spatial filter to the calculated solution or by using a staggered layout of the flow variables. The latter is of course more appealing. In this paper we will extend the staggered formulation we have developed for compressible flow, see (Boersma, 2005) to the incompressible flow case.
Keywords
- Direct Numerical Simulation
- Laminar Turbulent Transition
- Dispersion Error
- Compact Difference Scheme
- Compact Finite Difference Scheme
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Boersma, B.J., 2005, A staggered compact finite difference formulation for the compressible Navier-Stokes equations, J. of Comp. Phys, 208, 675–690.
Lele, S.K., 1992, Compact finite difference schemes with spectral like resolution, J. of Comp. Phys., 103, 16–42.
Harlow, F.H., & Welch, J.E., 1965, Numerical calculatios of time-dependent viscous incompressible flow of fluid with a free surface, Phys. of Fluids, 8, 2182–2189.
Gavrilakis, S., 1992, Numerical simulation of low-Reynolds number turbulent flow through a straight square duct, J. of Fluid Mech., 244, 101–129.
Huser, A., & Biringen, S., 1993, Direct numerical simulation of turbulent flow in a square duct, J. of Fluid Mech., 257, 65–95.
van der Vorst, H.A., & Vuik, C., 1994, GMRESR: a Family of Nested GMRES Methods, Num. Lin. Alg. Appl., 1, 369–386.
Niederschulte, M.A., 1989, Turbulent flow through a rectangular channel, PhD thesis, University of Illinois, Urbana-Champaign.
Gear, C.W., 1971, Numerical initial value problems in ordinary differential equations, Prentice Hall, New Jersey, USA.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this paper
Cite this paper
Boersma, B.J. (2011). On the development of a 6th order accurate compact finite difference scheme for incompressible flow. In: Kuerten, H., Geurts, B., Armenio, V., Fröhlich, J. (eds) Direct and Large-Eddy Simulation VIII. ERCOFTAC Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2482-2_11
Download citation
DOI: https://doi.org/10.1007/978-94-007-2482-2_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2481-5
Online ISBN: 978-94-007-2482-2
eBook Packages: EngineeringEngineering (R0)