Numerical bifurcation analysis for 3‐dimensional sudden expansion fluid dynamic problem

Summary This paper deals with bifurcation analysis methods based on the Asymptotic Numerical Method [35, 19]. It is used to investigate three-dimensional instabilities in a sudden expansion. To do so, high performance computing is implemented in ELMER an open-source multi-physical software. In this work, velocity-pressure mixed vectors are used with ANM based methods, remarks are made for the branch-switching method in the case of symmetry breaking bifurcation and new three-dimensional instabilities results are presented for the sudden expansion ratio E=3. Critical Reynolds numbers for primary bifurcations are studied with the evolution of a geometric parameter. New values are computed which reveal new trends that complete the work of [46]. Several kinds of bifurcation are depicted and tracked with the evolution of the span-wise aspect ratio. One of them relies on a fully three-dimensional effect [15, 46] as it breaks both span-wise and top-bottom symmetries. This bifurcation is found for smaller aspect ratios than expected. Furthermore, a critical Reynolds number is found for the aspect ratio Ai=1, that was not previously reported. Finally, primary and secondary bifurcations are efficiently detected and all post-bifurcated branches are followed. It makes it possible to plot a complete bifurcation diagram for this three-dimensional case. This article is protected by copyright. All rights reserved.

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