Computation of Bifurcations for the Navier-Stokes Equations

UoM administered thesis: Phd

  • Authors:
  • Hanadi Zahed

Abstract

We investigate a two-dimensional boundary layer flow in a channel with a suctionslot on the upper wall by solving the steady Navier-Stokes equations to computesteady state solutions and we investigate their stability using global stability analysistogether with linear temporal simulation and a continuation method. Ourprimary aim in this work is to investigate bifurcations occurring in separatedflows at large Reynolds numbers (R). Another motivation is to investigate thestability of a separated flow. The 2D steady Navier-Stokes equations in streamfunction(ψ)-vorticity (ω) are solved numerically using a hybrid finite differenceand spectral method combined with pseudo arc length continuation techniquesto track turning points and bifurcations.We are able to calculate two branches of solutions and the turning pointbifurcation in this particular problem. Global stability results indicate that thefirst solution on the lower branch, where the separation bubble is short, is stable,while the second solution on the upper branch, where the separation bubble islarge, is unstable. The presence of the turning point is confirmed by the changingsigns in the eigenvalue spectrum, as it moves from the lower, stable solutionbranch to the upper, unstable solution branch. The numerical simulation confirmsthe stability of the lower branch solutions and confirms that the upper branch isunstable; it is also in good agreement with global stability behaviour.

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Original languageEnglish
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Award date1 Aug 2010