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I. Stojanovic, S. Braun:
"On the non-uniqueness of marginally separated boundary layer flows";
in: "Proceedings in Applied Mathematics and Mechanics (PAMM)", 20 (1); GAMM Gesellschaft für angewandte Mathematik und Mechanik, 2020, 2 pages.

A stationary or time dependent, laminar flow with a locally separated boundary layer is considered. The Navier-Stokes equations are analysed with the method of matched asymptotic expansions. The resulting integro-differential equation, known as the fundamental equation of marginal separation, is solved numerically by means of a spectral method based on Chebyshev polynomials. The critical value of the parameter controlling the magnitude of the adverse pressure gradient is associated with a bifurcation of the stability characteristics of the locally separated shear layer. The solution behaviour of the integro-differential equation in the corresponding parameter space is investigated. Special emphasis is placed on the observed non-uniqueness of solutions and the associated branch points.

laminar separation bubble, integro-differential equation, spectral methods, bifurcation analysis

http://dx.doi.org/10.1002/pamm.202000154