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Title: Computation of bifurcations for the Navier-Stokes equations
Author: Zahed, Hanadi
ISNI:       0000 0004 2691 891X
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2010
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We investigate a two-dimensional boundary layer flow in a channel with a suction slot on the upper wall by solving the steady Navier-Stokes equations to compute steady state solutions and we investigate their stability using global stability analysis together with linear temporal simulation and a continuation method. Our primary aim in this work is to investigate bifurcations occurring in separated flows at large Reynolds numbers (R). Another motivation is to investigate the stability of a separated flow. The 2D steady Navier-Stokes equations in stream function(ψ)-vorticity (ω) are solved numerically using a hybrid finite difference and spectral method combined with pseudo arc length continuation techniques to track turning points and bifurcations. We are able to calculate two branches of solutions and the turning point bifurcation in this particular problem. Global stability results indicate that the first 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 is large, is unstable. The presence of the turning point is confirmed by the changing signs in the eigenvalue spectrum, as it moves from the lower, stable solution branch to the upper, unstable solution branch. The numerical simulation confirms the stability of the lower branch solutions and confirms that the upper branch is unstable; it is also in good agreement with global stability behaviour.
Supervisor: Gajjar, Jitesh Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available