The double-tree method: An O(n) unsteady aerodynamic lifting surface method

Bryn Jones*, Peter Dunning, Alireza Maheri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
3 Downloads (Pure)


Two new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time-saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n log n) tree methods together results in an O(n) method, called the double-tree method. Other case studies show that the trade-off between accuracy and speed can be easily and reliably controlled by the agglomeration cut-off distance. For a flat plate with 5x200 panels analysed over 20 time steps, the double-tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full-aircraft analysis within optimisation or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.
Original languageEnglish
Pages (from-to)1394-1414
Number of pages21
JournalInternational Journal for Numerical Methods in Fluids
Issue number10
Early online date15 Apr 2020
Publication statusPublished - Oct 2020

Bibliographical note

Open Access via Wiley agreement.

Some results in this work were obtained using the Maxwell High Performance Computing Cluster of the University of Aberdeen IT Service (, provided by Dell Inc. and supported by Alces Software.
The lead author would also like to thank the University of Aberdeen for their research scholarship funding.


  • aerodynamics
  • incompressible flow
  • parallelization
  • subsonic
  • model
  • reduction
  • time integration


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