Abstract
This paper presents an optimized discretization of the time derivative term for the dual-time stepping method. The proposed discretization is second order accurate and has a lower level of dissipation and dispersion errors than the conventional non-optimized second order discretization. Sample calculations demonstrate that the optimized scheme requires approximately 45–50% less time steps per unsteady cycle compared to the standard non-optimized scheme to resolve an unsteady flow within a certain margin of amplitude error. The number of time steps per cycle can be reduced by 10–15% to keep the phase error less than a certain level when the optimized scheme is used. Since time-accurate calculations are expensive, the proposed approach leads to significant savings of computational time and resources.
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
Jameson, A., Time Dependent Calculation Using Multigrid, with Application to Unsteady Flows Past Airfoils and Wings, AIAA Paper 91–1596, 1991.
Hu, F. Q., Hussaini, M. Y., and Manthey, J., Low-Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics, NASA Report, 1994.
Holmes, D. G., Mitchell, B. E., and Lorence, C. B., Three Dimensional Linearized Navier-Stokes Calculation for Flutter and Forced Response, Presented at the 8th ISUAAAT Conference, Sweden, 1997.
Melson, N. D., Sabetrik, M. D., and Atkins, H. L., Time-accurate Navier-Stokes Calculations with Multigrid Acceleration. Presented at the 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, April 4–9, 1993.
Tam, C. K. W. and Webb, J. C., Dispersion-Relation-Preserving Schemes for Computational Acoustics. Journal of Computational Physics, 107: 262–281, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Nyukhtikov, M., Smelova, N.V., Mitchell, B.E., Holmes, D.G. (2006). OPTIMIZED DUAL-TIME STEPPING TECHNIQUE FOR TIME-ACCURATE NAVIER-STOKES CALCULATIONS. In: Hall, K.C., Kielb, R.E., Thomas, J.P. (eds) UNSTEADY AERODYNAMICS, AEROACOUSTICS AND AEROELASTICITY OF TURBOMACHINES. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4605-7_33
Download citation
DOI: https://doi.org/10.1007/1-4020-4605-7_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4267-6
Online ISBN: 978-1-4020-4605-6
eBook Packages: EngineeringEngineering (R0)