Numerical continuation of high Reynolds number external flows

C. Wales*, A. L. Gaitonde, D. P. Jones, D. Avitabile, A. R. Champneys

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


A numerical continuation method for the compressible Reynolds-Averaged Navier-Stokes equation with the Spalart-Allmaras turbulence model is presented and applied to the flow around a 2D airfoil. Using continuation methods it is possible to study the steady flow states of a system as a parameter such as angle of attack is varied. This approach allows unstable solutions to be calculated, which are important for understanding the nonlinear dynamics of the system. Furthermore, this method can be used to find any multivalued solutions that exist at a single parameter value. The eigenvalues of the system are calculated using the Cayley transform to precondition the eigenvalue solver ARPACK. The eigenvalues are important as they show the stability of the solutions as well as accurately detect parameter values at which bifurcations take place.

Original languageEnglish
Pages (from-to)135-159
Number of pages25
JournalInternational Journal for Numerical Methods in Fluids
Issue number2
Publication statusPublished - 20 Jan 2012
Externally publishedYes


  • Bifurcation
  • Continuation
  • Eigenvalues
  • Navier-Stokes
  • Newton
  • Spalart-Allmaras


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