2009
DOI: 10.1017/s002211200999108x
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Topological structure of shock induced vortex breakdown

Abstract: Using a combination of critical point theory of ordinary differential equations and numerical simulation for the three-dimensional unsteady Navier–Stokes equations, we study possible flow structures of the vortical flow, especially the unsteady vortex breakdown in the interaction between a normal shock wave and a longitudinal vortex. The topological structure contains two parts. One is the sectional streamline pattern in the cross-section perpendicular to the vortex axis. The other is the sectional streamline … Show more

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Cited by 21 publications
(29 citation statements)
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References 37 publications
(76 reference statements)
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“…In the region upstream of the shock, he picks the middle slice of the computational grid and artificially sets the velocity to zero as sketched out in Figure 1. This closely corresponds to the experimental and theoretical investigations by Kalkhoran and Smart [24] and by Zhang et al [66]. It turns out that the carbuncle-like structure which comes with the Godunov-scheme is similar to the experimental results.…”
Section: Contribution By Ellingsupporting
confidence: 90%
“…In the region upstream of the shock, he picks the middle slice of the computational grid and artificially sets the velocity to zero as sketched out in Figure 1. This closely corresponds to the experimental and theoretical investigations by Kalkhoran and Smart [24] and by Zhang et al [66]. It turns out that the carbuncle-like structure which comes with the Godunov-scheme is similar to the experimental results.…”
Section: Contribution By Ellingsupporting
confidence: 90%
“…• ENO and WENO schemes were used to simulate the interactions of shocks with vortices, which involve both strong discontinuities and complicated smooth structures, especially suitable for using high-order non-oscillatory schemes. See Erlebacher, Hussaini and Shu (1997), Shu (2005, 2006b), Zhang, Jiang, Zhang and Shu (2009a), Zhang, Zhang and Shu (2009b) and Zhang et al (2013). Effects of shock waves on Rayleigh-Taylor instability were studied in Zhang, Shu and Zhou (2006c).…”
Section: Applicationsmentioning
confidence: 99%
“…WENO schemes are particularly suited for the simulation of shock-vortex interactions because of their simultaneous capability of high-order solution and non-oscillatory shock transition. Examples of such applications can be found in earlier studies [41][42][43][44][45][46][47].…”
Section: (Ii) Weighted Compact Schemesmentioning
confidence: 99%