Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Sohn, Sung-Ik

doi:10.1103/physreve.69.036703

Cited by 47 publications

(93 citation statements)

References 32 publications

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“…This equation and the vortex method (Krasny 1987;Kotelnikov et al 2000;Sohn 2004;Matsuoka & Nishihara 2006a) enable us to calculate the roll-up of the interface. The velocity of the interface (x, y) = (X (b, t), Y (b, t)) is given as (Baker et al 1982;Matsuoka & Nishihara 2006a)…”

Section: (C) Arbitrary Amplitude Theory In Planar Geometrymentioning

confidence: 99%

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

129

128

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A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

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Section: (C) Arbitrary Amplitude Theory In Planar Geometrymentioning

confidence: 99%

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

129

128

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“…Numerical results showed the convergence of the curvature to ζ 1 ≈ k/4, at late times [20]. We have also presented the multi-harmonic model in the cylindrical geometry and have obtained a new type of asymptotic solution of the axisymmetric bubble.…”

Section: Discussionmentioning

confidence: 92%

Multi-Harmonic Models for Bubble Evolution in the Rayleigh-Taylor Instability

Choi¹,

Sohn²

2017

Journal of the Korean Mathematical Society

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Abstract. We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.

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“…For numerical integrations, we employ the standard fourth-order Runge-Kutta method. On the In Figure 2, we compare the solutions for the bubble velocity and curvature of the RT instability for A = 0.3 from the low-and high-order source-flow model, and the low-order Layzer model [7] with the numerical result taken from Sohn [13]. The units in Fig.…”

Section: Comparisons Of the Modelsmentioning

confidence: 99%

“…The dimensionless velocity, curvature and time are defined by U √ k/g, ζ 1 /k and t √ kg, respectively. The numerical simulations in [13] are performed by the point vortex method based on the vortex sheet model. Note that the point vortex method has a regularization parameter for the finite density jump cases, which yields smoothing effects on the solution.…”

Section: Comparisons Of the Modelsmentioning

confidence: 99%

High-Order Potential Flow Models for Hydrodynamic Unstable Interface

Sohn¹

2012

Journal of the Korea Society for Industrial and Applied Mathema

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ABSTRACT. We present two high-order potential flow models for the evolution of the interface in the Rayleigh-Taylor instability in two dimensions. One is the source-flow model and the other is the Layzer-type model which is based on an analytic potential. The late-time asymptotic solution of the source-flow model for arbitrary density jump is obtained. The asymptotic bubble curvature is found to be independent to the density jump of the fluids. We also give the timeevolution solutions of the two models by integrating equations numerically. We show that the two high-order models give more accurate solutions for the bubble evolution than their loworder models, but the solution of the source-flow model agrees much better with the numerical solution than the Layzer model.

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Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Cited by 47 publications

References 32 publications

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Multi-Harmonic Models for Bubble Evolution in the Rayleigh-Taylor Instability

High-Order Potential Flow Models for Hydrodynamic Unstable Interface

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