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 ∼35% (resp. ∼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 ∼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.
Highlights
The variational multiscale (VMS) modeling of the Navier–Stokes equations [1–5] has been widely developed for the numerical simulation of turbulent flows in several benchmarking and applicative context [6,7,8]
5 cal simulation (DNS) requires a complete representation of the whole range of spatial and temporal turbulent scales at the discrete level, the VMS introduces an a priori decomposition of the solution into coarse and fine scale components, that correspond to different scales
The relevance of the VMS for the cavity flow is established in Sec. 4 by crossanalyzing VMS and direct numerical simulation (DNS) data benchmarked at several Reynolds numbers
Summary
5] has been widely developed for the numerical simulation of turbulent flows in several benchmarking and applicative context [6,7,8]. The stabilization terms can accidentally displace its eigenvalues by a substantial amount, even though their amplitude is small [16,17,18] While this is not necessarily visible at high Reynolds numbers, where the induced variations remain small with respect to the leading 35 growth rates, the effect can be dramatic close to the instability threshold. The retained configuration is the open cavity flow documented in [21], that 45 becomes unstable at Reynolds number Re = 4140 (based on the free-stream velocity and the cavity height), exhibits a well-defined oscillatory behavior up to Re ∼ 7000 This case is especially relevant for the intended purpose, insofar as there are three concurring instabilities, whose nonlinear interactions trigger a poorly understood change in the limit cycle frequency [22]. The VMS 70 is used in Sec. 6 to tackle the sequence of bifurcation triggering the onset of the limit cycle oscillations
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