A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics

Samtaney, Ravi

doi:10.1016/j.jcp.2009.05.042

Cited by 14 publications

(14 citation statements)

References 15 publications

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“…Numerical convergence tests of this method, performed by Gao, 24 show second order accuracy for smooth initial conditions. The method proposed here is very similar to that developed by Samtaney 18 for Cartesian slab geometry, which exhibits second order convergence for smooth flows and convergence rates between one and two for flows with shocks. In Section III E, linear simulations for m = 128, β = 16 (Fig.…”

Section: Appendix: Numerical Methodsmentioning

confidence: 92%

“…Here we extend Samtaney's numerical linear stability analysis 18 to MHD in cylindrical geometry. Linearizing the ideal MHD equations about a time dependent base state we derive a set of hyperbolic equations with source terms for the perturbed quantities.…”

Section: Introductionmentioning

confidence: 90%

“…(9), following the method originally developed by Samtaney. 18 We use the method-of-lines approach for the time discretization by rewriting Eq. (9a) as ∂Ů ∂t = R(Ů), and adopting the third order TVD Runge-kutta time discretization approach as…”

Section: Appendix: Numerical Methodsmentioning

confidence: 99%

“…Recall that in Cartesian geometry, the growth rate at the interface is suppressed by the magnetic field and it oscillates around the asymptotic value zero (see Ref. 18 for examples). We conjecture that, at the late time stage for these cases, vorticity is being continually generated at the accelerating interface, and MHD waves remove it continuously from the interface.…”

Section: Solution Details Of Mhdmentioning

confidence: 99%

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Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

et al. 2016

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Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in ideal magnetohydrodynamics (MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2pBr2) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.

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Section: Appendix: Numerical Methodsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 90%

Section: Appendix: Numerical Methodsmentioning

confidence: 99%

Section: Solution Details Of Mhdmentioning

confidence: 99%

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Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

et al. 2016

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“…In this thesis, we examine the linear stability of an azimuthally perturbed density interface accelerated by a shock wave in cylindrical geometry in both hydrodynamics and MHD. Our approach extends the numerical linear stability analysis of Samtaney [15] to MHD in cylindrical coordinates.…”

Section: Introductionmentioning

confidence: 94%

Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

Gao

Samtaney

2015

29th International Symposium on Shock Waves 2

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Linear Simulations of the Cylindrical Richtmyer-MeshkovInstability in Hydrodynamics and MHD Song GaoThe Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities.Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase.In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields. 5 ACKNOWLEDGEMENTSSincere thanks to my supervisor, Prof. Ravi Samtaney, for his profound knowledge, patience and enthusiasm.Thanks to the members of my thesis examination committee, Prof. Sigurdur Thoroddsen and Prof.Georgiy Stenchikov, for their valuable comments and precious time.Thanks to Dr. Manuel Lombardini, for the interesting discussion and invaluable help. Thanks to Mr. Wei Gao, for his great encouragement.Thanks to my parents, for raising me up, and my unmet wife.Last but not least, special thanks to Dr. Fabrizio Bisetti, for the sharp lesson he has taught me. 6

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Effects of solid circular cylinders on the dynamics of the Richtmyer–Meshkov instability

Al-Marouf

Samtaney

2020

Shock Waves

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We discuss the effect on the transient dynamics of the Richtmyer-Meshkov instability due to small-scale perturbations introduced by a set of solid circular cylinders located along the material interface. The arrangement of the cylinders mimics (in a twodimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in an experimental setup. The numerical experiments are performed by utilizing an embedded boundary-Adaptive mesh refinement method. We quantify the effect of introducing the cylinders on the mixing layer growth and the mixedness level, and qualitatively demonstrate the effect of the perturbation introduced by the cylinders on the mixing layer structure. We empirically model the effect of the solid cylinders based on their diameter, and find that the effect of the cylinders on the mixing layer growth is a linear function of the cylinder diameter. The linear model allows us to predict the change in the mixing layer growth within a ±10% range, except for very small ratios of the initial perturbation amplitude of the density interface to the cylinder diameter.

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A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics

Cited by 14 publications

References 15 publications

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

Effects of solid circular cylinders on the dynamics of the Richtmyer–Meshkov instability

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