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Smooth Particle Hydrodynamics(SPH) can be used to model hypervelocity impact phenomena via the additionof a strengthof materialstrealmenLSPH is the only techniquethatcan model such problemsefficientlydue to the combinationof 3-dimensionalgeometry,large translationsof material,large deformations, and large void fracYjonsfor most woblems of interesLThis makes SPH an ideal candidatefor modeling of asteroid impact, spacecraft shield modeling, and planetaryaccretion. In this paperwe describe the derivationof the strengthequationsin SPH, show several basic code tests, andpresent several impacttest cases with experimental comparisons. PHILOSOPHY OF SPH SPHis a gridless Lagrangianhydrodynamiccomputationaltechnique.With some care, it can be writtenin a fully conservative form. The form of the SPH equations is extremely simple, even in 3 dimensions. These characteristics,together with the physical "feeling" for the woblem that is embodied in a fully Lagrangiancode makes SPH an attractiveapproachfor woblems with complicatedgeometry, large void areas,fracture,or chaotic flow fields. SPH was first derivedby Lucy (1977) as a Monte-Carloapproachto solving the hydrodynanfictime evolution equations. Subsequently,Monaghanand co-workers (Monaghan 1982, 1985, 1988, Gingold and Mouaghan 1977, 1982) reformulatedthe derivationin terms of an interpolationtheory,which was shown to better estimate the errorscaling of the technique. According to the interpolationderivation,each SPH "particle"representsa mathematicalinterpolationpointat which thefluidpropertiesare known.The complete solution is obtainedat aUpoinf:;in spaceby applicationof an interpolationfunction.This functionis requiredto be continuous and dilterentiable.Gradientsthatappearin the flow equations are obtainedvia analytic differentiationof the smooth, interlx_latedfunctions. Monaghan showed that other well known lechniques, such as PIC, finite element, and finite volume methods could also be derived in this way throughappropriatechoice of interpolationtechnique. SPH is distinguishedby the simplicity of its apwoach: interpolation is done by summingover "kernels"asscgiatedwith each particle. Each kernel is a spherically symmetric function centered at the particle location and generally resembling a Gaussian in shape. The order of accuracyof the,interpolation(and thus of the difference equations) is determinedby the smoothness of the kernel. The kernelis requiredto approacha delta functionin the limit of small extent.The interpolation is accomplishedby summingeach equationor variableat any location over nearby known values at particlelocations,each weightedby its own kernelweighting function.Each kernelfunclion is requiredto integrate over aU space to exactly unity,thus normalizing the interpolation sums. By al_ly modifying the nornu_ condition, the same code can easily switch between lD, 2D,

In this paper, we present the results of high-resolution simulations of the implosion of high-convergence layered indirect-drive inertial confinement fusion capsules of the type fielded on the National Ignition Facility using the xRAGE radiation-hydrodynamics code. In order to evaluate the suitability of xRAGE to model such experiments, we benchmark simulation results against available experimental data, including shock-timing, shock-velocity, and shell trajectory data, as well as hydrodynamic instability growth rates. We discuss the code improvements that were necessary in order to achieve favorable comparisons with these data. Due to its use of adaptive mesh refinement and Eulerian hydrodynamics, xRAGE is particularly well suited for high-resolution study of multi-scale engineering features such as the capsule support tent and fill tube, which are known to impact the performance of high-convergence capsule implosions. High-resolution two-dimensional (2D) simulations including accurate and well-resolved models for the capsule fill tube, support tent, drive asymmetry, and capsule surface roughness are presented. These asymmetry seeds are isolated in order to study their relative importance and the resolution of the simulations enables the observation of details that have not been previously reported. We analyze simulation results to determine how the different asymmetries affect hotspot reactivity, confinement, and confinement time and how these combine to degrade yield. Yield degradation associated with the tent occurs largely through decreased reactivity due to the escape of hot fuel mass from the hotspot. Drive asymmetries and the fill tube, however, degrade yield primarily via burn truncation, as associated instability growth accelerates the disassembly of the hotspot. Modeling all of these asymmetries together in 2D leads to improved agreement with experiment but falls short of explaining the experimentally observed yield degradation, consistent with previous 2D simulations of such capsules.

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