2019
DOI: 10.1063/1.5083870
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Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

Abstract: The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV shows that the solution becomes unstable at very early times and eventually becomes turbulent, but a study of this transition has not been advanced so far. The computations are performed using a high accuracy compact scheme on a uniform grid, with the fourth-order Runge-Kutta time integration method. The vector pot… Show more

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Cited by 36 publications
(16 citation statements)
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“…The TGV flow is characterized by the time evolution of the volume-averaged kinetic energy Ek and viscous energy dissipation rate . While Ek decays monotonically in time, first exhibits a substantial increase until time t = tmax ≈ 9L/V0, from when a monotonic decay sets in [16,18,20,22]. The energy dissipation rate shown in Figure 2(a) compares favorably with DNS data of Dairay et al [19] at exactly the same Reynolds number.…”
Section: A Evolving Taylor-green Vortex (Tgv) Flowmentioning
confidence: 50%
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“…The TGV flow is characterized by the time evolution of the volume-averaged kinetic energy Ek and viscous energy dissipation rate . While Ek decays monotonically in time, first exhibits a substantial increase until time t = tmax ≈ 9L/V0, from when a monotonic decay sets in [16,18,20,22]. The energy dissipation rate shown in Figure 2(a) compares favorably with DNS data of Dairay et al [19] at exactly the same Reynolds number.…”
Section: A Evolving Taylor-green Vortex (Tgv) Flowmentioning
confidence: 50%
“…The initial flow field is essentially inviscid and the large-scale Taylor-Green vortices remain almost two-componential during the first stage of the flow development dominated by advection ( • ∇) and stretching ( • ∇) of vorticity [18]. Non-linear vortex stretching ⁄ (i = j) becomes increasingly important from time t ≈ 3L/V0 and the stretching of vortex lines gives rise to smaller-scale flow structures and therefore also to increasing dissipation .…”
Section: A Evolving Taylor-green Vortex (Tgv) Flowmentioning
confidence: 99%
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“…Despite the several decades that have passed since this work, the Taylor-Green vortex remains a physically interesting problem for the study of vortex dynamics and breakdown to turbulence [12,22]. The TGV case is also widely used for assessing the efficiency of numerical schemes and often acts as a validation of CFD codes [11,16,23] Reynolds, and Prandtl numbers were set to Re = 1600 and Pr = 0.71 respectively, the ratio of heat capacities was taken to be = 1.4.…”
Section: Problem Specificationmentioning
confidence: 99%
“…Despite this concern, the branching 'if-else' conditions in the TENO schemes seem to have better relative performance on the GPU than CPU. An alternative approach would be to compute the discrete TENO function (22) as the difference between the weight and threshold value, with a ceiling/floor function applied to obtain the binary stencil selection. The adaptive TENO-6A scheme has a further small increase in cost owing to the need to evaluate the shock sensor.…”
Section: Computational Cost Comparisonmentioning
confidence: 99%