Continuation methods applied to the 2D Navier-Stokes equations at high Reynolds numbers

C. Wales*, A. L. Gaitonde, D. P. Jones

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two-dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two-dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright (c) 2012 John Wiley & Sons, Ltd.

Translated title of the contributionContinuation methods applied to the 2D Navier-Stokes equations at high Reynolds numbers
Original languageEnglish
Pages (from-to)1258-1289
Number of pages32
JournalInternational Journal for Numerical Methods in Fluids
Volume70
Issue number10
DOIs
Publication statusPublished - 10 Dec 2012

Bibliographical note

Other: Accepted May 2011

Keywords

  • nonlinear solvers
  • Newton
  • stability
  • RANS: Reynolds averaged Navier-Stokes
  • compressible flow
  • turbulence models
  • PATTERN MULTIFRONTAL METHOD
  • TURBULENCE MODELS
  • BIFURCATION-ANALYSIS
  • PERIODIC-SOLUTIONS
  • STABILITY ANALYSIS
  • AIRFOIL
  • FLOWS
  • COMPUTATION
  • MATRICES
  • SYSTEMS

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