Stability of spherical converging shock wave

Murakami, M.; Sanz, J.; Iwamoto, Yukiharu

doi:10.1063/1.4923437

Cited by 20 publications

(30 citation statements)

References 22 publications

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“…37 However, preliminary calculations had shown that the original SLAU2 scheme produced spurious rarefaction waves emitted from the shock front to the center. We found that this effect can be suppressed by increasing the numerical viscosities, especially in the proximity of the shock wave.…”

Section: A Simulations On a Cartesian Gridmentioning

confidence: 99%

“…Therefore it is not clear in advance whether or not it becomes unstable for certain values of gas γ and mode number l , just like the converging-shock Guderley solution is. 37 Stability analysis of the reflected-shock Guderley case, will be a natural continuation of both this work and Ref. 37, where such analysis has been done for a converging shock wave.…”

Section: Introductionmentioning

confidence: 99%

“…37 Stability analysis of the reflected-shock Guderley case, will be a natural continuation of both this work and Ref. 37, where such analysis has been done for a converging shock wave. Stability analysis of other hydrodynamic 31 and MHD 32,33 generalizations of the classic Noh solution could shed light on the stability of hot-spot formation and other cases of shock-wave stagnation in laser-fusion and Z-pinch implosions, in laboratory astrophysics experiments, 16 as well as guide verification of hydrodynamic and MHD codes.…”

Section: Introductionmentioning

confidence: 99%

“…(11)- (14). As in, 37 Substituting (12)- (15) into the fluid equations (1)- (3), in the first order in ε we obtain our linearized perturbation equations and boundary conditions. They are presented below in the form applicable to both spherical and cylindrical geometries.…”

mentioning

confidence: 99%

“…We will study the general case of 3D spherical perturbation problem, where each perturbation mode is characterized by two integer angular mode numbers, l and m , so that the corresponding displacement of the shock front is proportional to the spherical function of the polar angle θ and azimuthal angle φ , 23,37 and to obtain its explicit analytical solution. As for the cylindrical case, the general perturbation eigenmodes are characterized by two parameters, the azimuthal mode number m and the axial wavenumber k , the eigenfunctions being proportional to 23 needs to be addressed separately.…”

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confidence: 99%

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Stability of stagnation via an expanding accretion shock wave

et al. 2016

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Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy- (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a powerlaw, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydro code verification in two and three dimensions.

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Section: A Simulations On a Cartesian Gridmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Stability of stagnation via an expanding accretion shock wave

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Self-Similar Solutions of Compressible Fluids

Takabe

2024

Springer Series in Plasma Science and Technology

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Strong shock waves are used to compress and heat any matters in the laboratory. The ablation pressure by intense laser is used to compress even solid matters. In plane geometry, it is easier to design multi-shocks to compress the matters, while it is more beneficial to use the spherical compression. No simple solutions are available to know the trajectories of shocks in one-dimensional spherical symmetry. Here we see several analytical solutions with the self-similar method. The method is to find new governing solution of ordinary differential equation from partial differential fluid equations. The self-similar method is known before the birth of computer.The blast wave is the most famous one. Here, we review the basic method to derive several self-similar solutions allowing the spherical implosion, useful to laser driven implosion. The isobaric solution provides uniform pressure and spark-main fuel structure, and isochoric solution gives us uniform density profile at the maximum compression. It is shown that even including thermal conduction, it is possible to find a solution of ablation structure. This is an extended solution more appropriate compared to the steady state solutions shown in the previous chapter.The blast waves are widely used from laser experiments to supernova remnants (SNRs). SNRs are blast waves driven by the matters exploding by supernova explosion. A self-similar solution with forward and reverse shock waves is found to explain many observation data of SNRs. A numerical simulation shows that the solution of ejecta-driven shock changes from Chevalier’s self-similar solution to the other Sedov-Taylor one. The self-similarity is one of the key physics controlling nonlinear hydrodynamic equations.

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Self-similar solutions to the compressible Euler equations and their instabilities

Biasi

2021

Communications in Nonlinear Science and Numerical Simulation

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Stability of spherical converging shock wave

Cited by 20 publications

References 22 publications

Stability of stagnation via an expanding accretion shock wave

Stability of stagnation via an expanding accretion shock wave

Self-Similar Solutions of Compressible Fluids

Self-similar solutions to the compressible Euler equations and their instabilities

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