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A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers

van Rees, Wim M. and Leonard, Anthony and Pullin, D. I. and Koumoutsakos, Petros (2011) A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers. Journal of Computational Physics, 230 (8). pp. 2794-2805. ISSN 0021-9991. https://resolver.caltech.edu/CaltechAUTHORS:20110421-100240833

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Abstract

We present a validation study for the hybrid particle-mesh vortex method against a pseudo-spectral method for the Taylor–Green vortex at Re_Γ = 1600 as well as in the collision of two antiparallel vortex tubes at Re_Γ = 10,000. In this study we present diagnostics such as energy spectra and enstrophy as computed by both methods as well as point-wise comparisons of the vorticity field. Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases. For the Taylor–Green vortex, the vorticity contours computed by both methods around the time of the energy dissipation peak overlap. The energy spectrum shows that only the smallest length scales in the flow are not captured by the vortex method. In the second flow case, where we compute the collision of two anti-parallel vortex tubes at Reynolds number 10,000, the vortex method results and the pseudo-spectral method results are in very good agreement up to and including the first reconnection of the tubes. The maximum error in the effective viscosity is about 2.5% for the vortex method and about 1% for the pseudo-spectral method. At later times the flows computed with the different methods show the same qualitative features, but the quantitative agreement on vortical structures is lost.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2010.11.031DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/B6WHY-51NG4SF-1/2/03b7270941c1982961c3ac95de74a280PublisherUNSPECIFIED
Additional Information:© 2010 Elsevier Inc. Received 13 August 2010; revised 18 November 2010; accepted 19 November 2010. Available online 9 December 2010. We wish to acknowledge many helpful discussions with Yue Yang (Caltech) during the course of this work.
Group:GALCIT
Subject Keywords:Vortex method; Pseudo-spectral method; Vortical flow; Vortex reconnection
Issue or Number:8
Record Number:CaltechAUTHORS:20110421-100240833
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110421-100240833
Official Citation:Wim M. van Rees, Anthony Leonard, D.I. Pullin, Petros Koumoutsakos, A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers, Journal of Computational Physics, Volume 230, Issue 8, 20 April 2011, Pages 2794-2805, ISSN 0021-9991, DOI: 10.1016/j.jcp.2010.11.031.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23408
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:21 Apr 2011 21:39
Last Modified:03 Oct 2019 02:46

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