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Time-accurate calculation and bifurcation analysis of the incompressible flow over a square cavity using variational multiscale modeling

Abstract : A thorough variational multiscale (VMS) modeling of the Navier-Stokes equations is used to compute numerical solutions of the incompressible flow over an open cavity. This case features several competing instabilities, and is highly challenging for VMS methods with regard to frequency and pattern selection, because of the non-normality of the linearized Navier-Stokes operator. The relevance of the approach is thus carefully assessed by comparing to direct numerical simulation (DNS) data benchmarked at several Reynolds numbers, and highly accurate time advancing methods are shown to predict relevant evolutions of the transient and saturated solutions. The VMS reduces substantially the computational cost, by similar to 35% (resp. similar to 60%) in terms of CPU time using a semi-implicit discretization scheme based on backward differentiation formula (resp. the implicit Crank-Nicholson scheme), and by similar to 80% in terms of memory requirement. Eventually, the highly efficient semi-implicit VMS numerical framework is used to unravel the onset of the flow oscillations and the selection of the limit cycle frequency, that happens to involve a subcritical Neimark-Sacker bifurcation.
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Philippe Meliga, Elie Hachem. Time-accurate calculation and bifurcation analysis of the incompressible flow over a square cavity using variational multiscale modeling. Journal of Computational Physics, Elsevier, 2019, 376, pp.952-972. ⟨10.1016/j.jcp.2018.09.036⟩. ⟨hal-01946893⟩

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