Implicit Shock Fitting for Multimaterial Shock Dynamics using a High-Order Space-Time Discontinuous Finite-Element Method
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Implicit shock tracking for unsteady flows by the method of lines
Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the Origins of Lagrangian Hydrodynamic Methods
Not Available
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Sesame Equation of State for Kel F-800
I describe the construction of new equations of state for Kel F-800, as both linear and quadratic fits to shock data and Sesame 97200. This is the first SESAME table for Kel F-800 of which I’m aware. The SESAME table recovers shock data by construction and does reasonably well with thermal data, but differs with Brillouin scattering results for sound speed and density under static compression.
42 ENGINEERING↗
PBX9012 Tracker Gauge Data
Five shock-to-detonation transition (SDT) gas gun experiments for PBX 9012 were performed by Burns and Chiquete [2020]. The data from the experiments is available on the small-scale database. Here we focus on the tracker gauge data for the lead shock trajectory, x(t). In order to determine the shock speed U s (t) and the detonation transition point, a least squared fit to the shock trajectory is used based on a pair of ODEs with a fitting form for the shock acceleration developed by Hill and Gustavsen [2002].
42 ENGINEERING↗
The structure of cluster merger shocks: turbulent width and the electron heating time-scale
We present a new 2MsChandra observation of the cluster merger Abell 2146, which hosts two huge M ~ 2 shock fronts each ~500 kpc across. For the first time, we resolve and measure the width of cluster merger shocks. The best-fitting width for the bow shock is 17 ± 1kpc and for the upstream shock is 10.7 ± 0.3 kpc. A narrow collisionless shock will appear broader in projection if its smooth shape is warped by local gas motions. We show that both shock widths are consistent with collisionless shocks blurred by local gas motions of 290 ± 30 km s –1 . The upstream shock forms later on in the merger than the bow shock and is therefore expected to be significantly narrower. From the electron temperature profile behind the bow shock, we measure the time-scale for the electrons and ions to come back into thermal equilibrium. We rule out rapid thermal equilibration of the electrons with the shock-heated ions at the 6σ level. The observed temperature profile instead favours collisional equilibration. For these cluster merger shocks, which have low sonic Mach numbers and propagate through a high β plasma, we find no evidence for electron heating over that produced by adiabatic compression. Our findings are expected to be valid for collisionless shocks with similar parameters in other environments and support the existing picture from the solar wind and supernova remnants. Furthermore, the upstream shock is consistent with this result but has a more complex structure, including a ~2ke V increase in temperature ~50 kpc ahead of the shock.
79 ASTRONOMY AND ASTROPHYSICS↗
Vibrational response and temperature of shock-compressed Pt: In situ extended x-ray absorption fine structure measurements to 325 GPa
Single pulse (~100 ps duration) extended x-ray absorption fine structure (EXAFS) measurements were obtained in laser shocked Pt to examine atomic vibrational properties and to determine temperatures for shock pressures from 72-325 GPa. Pt x-ray absorption spectra were recorded while a planar shock wave was propagating through the Pt sample. The absorption spectrum corresponding to the shocked Pt was obtained by subtracting the ambient Pt contribution from the measured absorption spectrum. Fits to the shocked state EXAFS data provided Pt lattice parameters consistent with the known Pt Hugoniot and the mean squared relative displacements (MSRDs) for nearest neighbor Pt atoms. Pt temperatures in the shocked state, estimated from the MSRDs using the correlated Debye model and correlated Einstein models, were consistent with both the Hugoniot temperatures calculated by integration along the Hugoniot and with the Hugoniot temperatures from published first-principles calculations. However, the agreement between the Hugoniot temperatures from EXAFS measurements and the calculated Hugoniot temperatures is not as good above 200 GPa, likely due to anharmonic effects. Furthermore, the present results demonstrate that single-pulse synchrotron EXAFS measurements in laser-shocked solids are useful for quantitative temperature determination and for examination of vibrational properties, including anharmonicity, at extreme pressure-temperature conditions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Re-calibration of PBX9501 SURF model
PBX 9501 is a plastic bonded explosive composed of 95 wt % HMX and a binder; see [Gibbs and Popolato, 1980, pp. 109–119]. SURF is a reactive burn model for shock initiation and propagation of detonation waves. It has previously been calibrated for PBX 9501. Here the SURF model is recalibrated for PBX 9501; specifically, lot 730-010 at ρ = 1.837 g/cc 3 . The new calibration uses the Davis reactants and products EOS calibrated for the AWSD model [Aslam et al., 2020]. The burn rate in the shock initiation regime is fit to the Pop plot from 5 embedded gauge shock-to-detonation transition (SDT) experiments from [Gustavsen et al., 1999, see fig 12 and table 5]. In the propagation regime, the burn rate is fit to curvature effect data (detonation speed as function of front curvature); see [Aslam, 2007]. Also the burn parameters are adjusted to fit the gap-stick experiment [Hill et al., 2018]. Simulating the detonation wave speed in this experiment requires a model that is accurate for initiation with complex shock loading; in particular, a pressure decreasing gradient behind a curved lead shock. This is more difficult than calibrating to the standard SDT experiments which are 1-D and driven by a sustained shock. Simulations of the gap-stick experiment for PBX 9501 with the SURF model will be discussed in a subsequent report.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Yttrium solid phase equation of state with uncertainty quantification
We discuss the development of an equation of state (EOS) for solid yttrium up to roughly 80 GPa. The EOS makes use of different experimental datasets, including measurements of the isobaric density, isobaric specific heat, room temperature isotherm, and principal shock Hugoniot. The fitting procedure is carried out using Markov Chain Monte Carlo (MCMC), where we fit model parameters for both the cold curve and ion thermal models simultaneously. The results show close agreement with experimental data and provide meaningful uncertainty estimates on the model parameters. This work serves as a first step towards a multiphase EOS for yttrium, which will include higher pressure solid phases (> 80 GPa), as well as modeling of the liquid phase.
36 MATERIALS SCIENCE↗
Shock-induced melting of [100] lithium fluoride: Sound speed and Hugoniot measurements to 230 GPa
Although [100] lithium flouride (LiF) is the most widely used optical window material in dynamic compression experiments, its high stress (>100 GPa) shock compression response, including melting, is not well understood. To address this need, we measured wave profiles in plate impact experiments to determine the Hugoniot states and longitudinal sound speeds in [100] LiF crystals shock compressed to 231 GPa. The measured peak states are fitted well by a linear shock velocity-particle velocity relation, providing an accurate determination of the LiF Hugoniot curve to significantly higher stresses than previous experiments. The longitudinal sound speeds show a near linear increase with density compression to 182 GPa. Between 182 GPa and 195 GPa, the sound speed and the longitudinal modulus decrease abruptly, due to shock-induced melting. The increasing sound speeds and moduli at higher stresses suggest that shock compressed LiF is fully liquid at 195 GPa and above, allowing determination of the Gruneisen parameter for liquid LiF. Here, the melt stress determined here differs from that predicted by current multiphase equations of state for LiF. Our results provide important insight into the high stress solid and liquid states of shock compressed LiF and point to the need for an improved multiphase equation of state at high pressures and high temperatures.
36 MATERIALS SCIENCE↗
Tracker Fits for shot 1s1674
Gas gun shock-to-detonation experiments provide data for calibrating HE burn models. At LANL the principal diagnostic is a magnetic gauge package that provides data on the lead shock trajectory, which is used to determine the run-distance to detonation, and the lead shock speed with run distance, which together with jump-off velocity of the velocity gauges determines Hugoniot locus points for the reactants.
42 ENGINEERING↗
Probabilistic effects of porosity and chemical kinetics on the shock initiation of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) based explosive
In this work, we investigate the effects of porosity and chemical reactivity on the shock initiation of an HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)-based polymer bonded explosive due to thin flyer impact using two-dimensional mesoscale simulations. Microstructural samples are computationally generated, and the calculated shock response is compared to experiments. The sample dimensions are 0.1×1.05 mm 2 , and each sample accounts for grain scale heterogeneities, including randomized grain morphology and pore spacing. Simulations are performed using the Lawrence Livermore National Laboratory (LLNL) arbitrary Lagrangian–Eulerian multi-physics code ALE3D. Chemistry and equation of states are handled with LLNL's thermochemical code Cheetah. We employ a modified Arrhenius-based chemical kinetics model that scales the temperature exponent fitting parameter with flyer shock conditions. This new model is calibrated to the mean response of experimental shock initiation thresholds for three separate Kapton flyer thicknesses. A simplified shock initiation criterion is proposed, which classifies the macroscale initiation response based on cross-sectional temperature profiles of the shocked sample. This criterion is used to further investigate the probabilistic response of the sample to variations in the mean porosity and chemical kinetics rate, and we find an inverse correlation between the shock pressure and the confidence interval of the experimental threshold velocity. Furthermore, the methodology presented in this work for quantifying the probabilistic nature of shock initiation is material agnostic. These mesoscale studies may be used to inform continuum scale models and expedite the development of future, tailored energetic formulations.
36 MATERIALS SCIENCE↗
The equation of state and shock-driven decomposition of polymethylmethacrylate (PMMA)
We present new equations of state (EOS) for polymethylmethacrylate and its shock-driven decomposition products, generated in both tabular form and as linear U S – u p fits to all previously available shock data. Different approaches are taken for materials shocked above and below the apparent threshold for chemical reactions at pressures P ≈ 30 GPa. Both EOSs are calibrated to and compared with a broad array of experimental results, as well as new ab initio molecular dynamics simulations presented here. Comparisons are good in most cases, and we focus our particular attention on those observables that test the distinction between reactants and products.
36 MATERIALS SCIENCE↗
Electron Energy Partition across Interplanetary Shocks. III. Analysis
An analysis of model fit results of 15,210 electron velocity distribution functions (VDFs), observed within ±2 hr of 52 interplanetary (IP) shocks by the Wind spacecraft near 1 au, is presented as the third and final part on electron VDFs near IP shocks. The core electrons and protons dominate in the magnitude and change in the partialto-total thermal pressure ratio, with the core electrons often gaining as much or more than the protons. Only a moderate positive correlation is observed between the electron temperature and the kinetic energy change across the shock, while weaker, if any, correlations were found with any other macroscopic shock parameter. No VDF parameter correlated with the shock normal angle. The electron VDF evolves from a narrowly peaked core with flaring suprathermal tails in the upstream to either a slightly hotter core with steeper tails or much hotter flattop core with even steeper tails downstream of the weaker and strongest shocks, respectively. Both quasi-static and fluctuating fields are examined as possible mechanisms modifying the VDF, but neither is sufficient alone. For instance, flattop VDFs can be generated by nonlinear ion acoustic wave stochastic acceleration (i.e., inelastic collisions), while other work suggested they result from the combination of quasi-static and fluctuating fields. This three-part study shows that not only are these systems not thermodynamic in nature; even kinetic models may require modification to include things like inelastic collision operators to properly model electron VDF evolution across shocks or in the solar wind.
79 ASTRONOMY AND ASTROPHYSICS↗
Multiphase equation of state for Ta 2 O 5
A new equation of state for Ta 2 O 5 is presented. The EOS is constructed using the OpenSesame software and is referred to as SESAME 3530. The EOS uses a combination of density functional theory (DFT) calculations and experimental data. DFT calculations include cold curves and phonons of the solid phases, as well as DFT-based molecular dynamics simulations of the liquid phase. Experimental data includes isobaric, diamond anvil cell, and porous shock Hugoniot data. To fit the data, we create a multiphase EOS consisting of two solid phases and the liquid. Overall agreement with experimental data is shown, and we provide some suggestions for future experiments that could improve our knowledge of the phase diagram.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A comparison of explosively driven shock wave radius versus time scaling approaches
Abstract Explosively driven shock wave radius versus time profiles are frequently used to document energy release and relative explosive performance. Recently, two universal shock wave radius versus time profiles have been presented in the literature, which demonstrate the ability to represent explosively driven shock wave profiles for all explosive sources in any fluid environment. These two universal shock wave profiles are examined here relative to each other and relative to a commonly used nonlinear shock wave profile, which is fit to experimental data for individual explosive materials. The nonlinear profile, originally developed by Dewey, is examined here, and a universal non-dimensional form of the equation is proposed. The universal shock wave profiles are all found to be relatively similar, but with slight variations in a transition region of non-dimensional radii $$0.15\lesssim R^*\lesssim 2$$ 0.15 ≲ R ∗ ≲ 2 . The variations in this region result in different estimations of energy release or blast strength between the curve fits.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility
A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4 keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. Here, the measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.
47 OTHER INSTRUMENTATION↗
Hugoniot, sound speed, and phase transitions of single-crystal sapphire for pressures 0.2–2.1 TPa
Sapphire (Al 2 O 3 ) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. In this paper we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2–2.1 TPa and a four-segment piecewise linear shock-velocity–particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to 525 ± 13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗