Stojanovic, I., & Braun, S. (2021). On the non‐uniqueness of marginally separated boundary layer flows. Proceedings in Applied Mathematics and Mechanics, 20(1), Article e202000154. https://doi.org/10.1002/pamm.202000154
spectral methods; Management, Monitoring, Policy and Law; Geography, Planning and Development; laminar separation bubble; integro-differential equation; bifurcation analysis
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Abstract:
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.
