Euler equation existence, non-uniqueness and mesh converged statistics

Glimm, James; Sharp, David H.; Lim, Hyunkyung; Kaufman, R. N.; Hu, Wenlin

doi:10.1098/rsta.2014.0282

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…Our previous work addressed convergence issues for probability density functions (PDF) and their indefinite integrals, the cumulative distribution functions (CDF) [21,22] with experimental validation in [20,23,24], relative to the hot-cold water splitter experiments [16]. We have also considered two-point statistical descriptions of RT and RM mixtures [25][26][27].…”

Section: A Transportmentioning

confidence: 99%

Mixing with applications to inertial-confinement-fusion implosions

et al. 2017

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Approximate 1D as well as 2D and 3D simulations are playing an important supporting role in the design and analysis of future experiments at NIF. This paper is mainly concerned with 1D simulations, used extensively in design and optimization. We couple a 1D buoyancy-drag mix model for the mixing zone edges with a 1D Inertial Confinement Fusion (ICF) simulation code. This analysis predicts that National Ignition Campaign designs are located close to a performance cliff, so that modeling errors, design features (fill tube and tent) and additional, unmodeled instabilities could lead to significant levels of mix. The performance cliff we identify is associated with multimode plastic ablator (CH) mix into the hot spot Deuterium and Tritium (DT). The buoyancy-drag mix model is mode number independent, and selects implicitly a range of maximum growth modes.Our main conclusion is that single effect instabilities are predicted not to lead to hot spot mix, while combined mode mixing effects are predicted to affect hot spot thermodynamics and possibly hot spot mix. Combined with the stagnation Rayleigh-Taylor instability, we find the potential for mix effects in combination with the ice to gas DT boundary, numerical effects of Eulerian species CH concentration diffusion and ablation driven instabilities.With the help of a convenient package of plasma transport parameters developed here, we give an approximate determination of these quantities in the regime relevant to the NIC experiments, while ruling out a variety of mix possibilities. Plasma transport parameters affect the 1D buoyancy-drag mix model primarily through its phenomenological drag coefficient as well as the 1D hydro model the buoyancy-drag equation is coupled to.

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Section: A Transportmentioning

confidence: 99%

Mixing with applications to inertial-confinement-fusion implosions

et al. 2017

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“…For each of these topics there is a description of the biological background and the mathematical model. J. Glimm et al in [25] review the existence and non-uniqueness for the Euler equations of fluid flow. The non-uniqueness of solutions is a fundamental obstacle to scientific predictions, preventing the success of such goals as predictive science, validation of solutions and quantification of the uncertainties on which engineers base their design conclusions.…”

Section: Applications and The Present Volumementioning

confidence: 99%

Free boundary problems: the forefront of current and future developments

Shahgholian

Vazquez

2015

Phil. Trans. R. Soc. A.

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“…Our result is a necessary condition for the admissibility of solutions of the Navier-Stokes and Euler equations of fluid dynamics. The examples of nonunique solutions of the Navier-Stokes equations [5] and the Euler equations [6,20,25,35] show the need for such an admissibility principle.…”

Section: Introductionmentioning

confidence: 99%