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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Understanding the evolution of liquid and solid microjets from grooved Sn and Cu samples using radiography

Experiments were performed on grooved Sn and Cu samples to study the temporal evolution of microjets. Jets were generated by the impact of gun-launched flyer plates against the back of grooved targets made from either Cu or Sn (groove depth of ~250 μm). The Hugoniot states in the various Sn targets encompassed conditions where solid phases are maintained throughout (7 and 16 GPa) and also conditions where melting occurs upon the release of compression (25 and 34 GPa); the transition occurs near a Hugoniot pressure of 23 GPa. Cu targets at 27 and 56 GPa provide comparisons in which the jets move at similar speeds but remain solid. In all cases, the spatial distribution of mass within the microjets was measured using high-speed synchrotron radiography. The result is a time history of the jet thickness profile from which quantities like total jet mass and jet velocity can be derived. In both the solid and liquid states, we generally observe that an increase in the shock strength leads to an increase in jet mass. However, this trend breaks down for Hugoniot states near the transition from continuously solid to melted-on-release. This is evidenced by the observation that there was no difference in the rate of mass flow in Sn jets at 16 and 25 GPa, while similar pressure jumps on either side of this range caused substantial changes in the jet mass. This contrasts with the behavior of smaller polishing defects that were present on the same samples (~1 μm deep). From these, no ejecta mass was detected below the melt boundary, but obvious microjets were generated once melting occurred. This indicates that crossing the bulk melt-on-release threshold can alternately promote or inhibit the flow of mass into microjets based on the amplitude of the initial perturbation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Mesoscale simulations of pressure-shear loading of granular tungsten carbide

Numerical simulations of pressure-shear loading of a granular material are performed using the shock physics code CTH. A simple mesoscale model for the granular material is used that consists of a randomly packed arrangement of solid circular or spherical grains of uniform size separated by vacuum. The grain material is described by a simple shock equation of state, elastic perfectly plastic strength model, and fracture model with baseline parameters for WC taken from previous mesoscale modeling work. Simulations using the baseline material parameters are performed at the same initial conditions of pressure-shear experiments on dry WC powders. Except for some localized flow regions appearing in simulations with an approximate treatment of sliding interfaces among grains, the samples respond elastically during shear, which is in contrast to experimental observations. By extending the simulations to higher shear wave amplitudes, macroscopic shear failure of the simulated samples is observed with the shear strength increasing with increasing stress confinement. The shear strength is also found to be strongly dependent on the grain interface treatment and on the fracture stress of the grains, though the variation in shear strength due to fracture stress decreases with increasing stress confinement. At partial compactions, the transverse velocity histories show strain-hardening behavior followed by formation of a shear interface that extends through the transverse dimensions of the sample. Near full compaction, no strain hardening is observed and, instead, the sample transitions sharply from an elastic response to formation of an internal shear interface. Agreement with experiment is shown to worsen with increasing confinement stress with simulations overpredicting the shear strengths measured in experiment. The source of the disagreement can be ultimately attributed to the Eulerian nature of the simulations, which do not treat contact and fracture realistically.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The LISE package: solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density ap- proximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and take advantage of graphic processing units (GPU) for accelerating execution. The dynamic codes have checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. The code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vor- tices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence.

Jin, Shi↗
DOE OSTI2021

Implosion dynamics of triple-nozzle gas-puff z pinches on COBRA

Experiments on the 1-MA, 220-ns COBRA generator at Cornell University were conducted to provide detailed measurements of structured cylindrical gas-puff z pinches. In the experiments, a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet initialize the z-pinch load with various working gases, radial density profiles, and externally applied axial magnetic fields. Planar laser-induced fluorescence provides a measure of the initial neutral gas density of the load, while three-frame laser shearing interferometry and multi-frame extreme ultraviolet (XUV) cameras reveal the formation and propagation of a magneto-Rayleigh–Taylor (MRT) unstable shock layer. Implosion trajectories are compared to simple, experimentally informed models and found to be in good agreement. Differences in the structure of the accelerating plasma sheath and evolution of the MRT instability are observed for different gas species and axial magnetic field strengths, correlating with differences in pinch uniformity and x-ray emission. Here, the average instability growth is compared to linear MRT theory predictions using the instantaneous acceleration of the best-fit implosion models and characteristic instability wavelength, with the effective Atwood number and seed perturbation size as fit parameters. For high density argon center jets, ionization prior to the arrival of the imploding plasma sheath suggests a heating mechanism consistent with photoionization by XUV self-emission.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Pressure Response Optimization of an Eddy Current-Driven Flyer Plate Valve for the ITER Shattered Pellet Injection System

One technique for mitigating disruptions in a tokamak is shattered pellet injection (SPI). SPI is a process in which a large solid pellet consisting of deuterium, neon, or argon is desublimated in a pipe gun barsrel and launched downstream. Pellets are shattered just before entering the plasma by an impact with an angled tube. Injection of these materials into the plasma radiates stored thermal energy, limits current decay rates, suppresses the generation of runaway electrons, and dissipates runaway electrons if necessary. A critical element of the SPI system is a fast-acting valve that releases high-pressure gas to dislodge and accelerate pellets directly, or indirectly via a mechanical punch. A prototype valve sized for the ITER SPI system has been designed and fabricated. A pulsed high-voltage power supply energizes the valve’s internal magnetic coil, which induces eddy currents in the adjacent flyer plate resulting in a repulsive force between the flyer plate and the coil. The flyer plate action lifts a valve seat, allowing high-pressure gas to flow from the valve plenum to the downstream (breech) location of the pellet or mechanical punch. All of the valve’s internal components are designed to operate in ITER-level static background magnetic fields. Here, a study was conducted to optimize the downstream pressure response for a range of valve sizes and operating pressures. In particular, the study analyzes the breech pressure response associated with varying plenum pressures as well as varying breech volumes. A computational fluid dynamics simulation was built in STAR-CCM+ and validated against data from laboratory experiments. The resulting simulation outputs, in the form of downstream responses for a variety of initial plenum pressures and breech volumes, will be used as a complement to experimental data to ensure the pressure pulse is suitable for pellet survivability. These data, combined with studies on pellet shear strength and shock response, will be applied to optimization of overall operating parameters of the ITER SPI system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Solid-to-plasma transition of polystyrene induced by a nanosecond laser pulse within the context of inertial confinement fusion

Laser Direct Drive (LDD) Inertial Confinement Fusion (ICF) involves irradiating a spherical target of thermonuclear fuel coated with an ablator, usually made of polystyrene. Laser energy absorption near the target surface leads to matter ablation, hydrodynamic shocks, and ultimately capsule implosion. The conservation of spherical symmetry is crucial for implosion efficiency, yet spatial modulations in laser intensity can induce nonuniformities, causing the laser imprint phenomenon. Understanding laser imprint, especially considering the initial solid state, is essential for advancing LDD ICF. A first microscopic model of solid-to-plasma transition was built in 2019, accounting for laser absorption in the solid state with a band structure based ionization model. This model has been improved to include chemical fragmentation and a more accurate description of electron collision frequency in various matter states. The latest development involves assessing the model reliability by comparing theoretical predictions with experimental observations. Despite the success of this approach, questions remain, leading to further investigations and observations under different irradiation conditions. This work presents an experiment with a nanosecond pulse, taking into account hydrodynamic effects, and measures transmission dynamics over the entire laser beam area to observe two-dimensional effects. As a result, the objective is to adapt the theoretical model, couple it with a hydrodynamic code, and observe additional effects related to the initial solid state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗
DOE OSTI2024

Simulations of three-layer Richtmyer–Meshkov mixing in a shock tube

Here, the Richtmyer–Meshkov instability causes perturbations to grow after a shock traverses a fluid density interface. This increases the mixing rate between fluid from either side of the interface. We use the Flash Eulerian hydrodynamic code to investigate alterations when a thin third layer of intermediate density is placed along the interface, effectively creating two adjacent unstable interfaces. This is a common occurrence in engineering applications where a thin barrier initially separates two materials. We find that the width of the mixing layer is similar or slightly reduced; however, the total mass of mixed material can actually increase. The mixing layer becomes more compact and efficient. However, the normalized mixed mass decreases, meaning that finger entrainment becomes more important than in the simple two-layer case. The effect of adding the central layer appears to decrease when the Atwood number is decreased. The Flash results are also benchmarked against two-layer experimental data from a shock tube at the University of Arizona.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Shock compression of silver to 300 GPa: Wave profile measurements and melting transition

Recent in-situ x-ray diffraction (XRD) measurements on laser-shock compressed Ag foils demonstrated a face-centered-cubic to body-centered-cubic transformation at ~150 GPa and melting between 172 and 197 GPa [Phys. Rev. Lett. 124, 235701 (2020)]. As a complement to the XRD work, we conducted plate impact experiments to obtain shock velocity and wave profile measurements on thicker Ag samples shock-compressed to peak stresses between 30 and 300 GPa. The shock velocity–particle velocity results were fitted very well by a linear relation over the entire stress range, providing an accurate determination of the Ag Hugoniot (locus of the stress-volume states achieved under shock compression). For peak stresses below 187 GPa and above 210 GPa—corresponding to the solid and liquid phases, respectively—the wave profiles show clean single waves. No wave profile features related to the fcc-bcc transformation at ~150 GPa were observed, implying minimal volume change for the transformation. For stresses between 187 and 210 GPa, an initial jump was followed by a time-dependent increase in the particle velocity (20–80 ns risetime) to the peak state—corresponding to the solid-liquid mixed phase response. Unlike the solid and liquid response, the mixed-phase response cannot be readily analyzed analytically. Instead, numerical simulations incorporating an accurate multiphase equation of state for Ag—not currently available—are required to analyze the wave profiles measured at 187–210 GPa stresses. Furthermore, the present work shows the potential for using wave profile measurements to examine the melting transition under shock compression.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Experimental platforms for investigating feature-driven jets for HED mix model validation

High-energy-density (HED) systems, such as inertial confinement fusion (ICF), are susceptible to hydrodynamic instabilities that can significantly affect both experimental results and modeling predictions. Isolated features, such as fill tubes or divots in the capsule, can cause material to jet as a result of the compressive shock exciting the Richtmyer–Meshkov instability, and serve as one of the primary degradation mechanisms in ICF yield. Simulations of feature-driven jets and how they mix require extensive experimental validation, particularly for understanding to what degree the initial size and shape of a feature influence jet dynamics, and how much instability feeds through downstream layers. A better understanding of feature-driven jetting can improve our mix modeling capabilities and increase hydrodynamic simulation accuracy. This manuscript describes a series of experimental platforms fielded by Los Alamos National Laboratory as a part of the Mshock Omega 60 and ModCons Omega EP campaigns to explore feature-driven jetting. These platforms are designed to benchmark jet evolution and growth as a function of initial feature size and shape, investigate jet-layer interactions leading to instability feedthrough, and will be used to characterize jet-jet interactions resulting from clusters of features. In conclusion, preliminary results for both platforms are shown. The ModCons experiments are on-going, and a discussion of future work directions is included.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Space weather observations, modeling, and alerts in support of human exploration of Mars

Space weather observations and modeling at Mars have begun but they must be significantly increased to support the future of Human Exploration on the Red Planet. A comprehensive space weather understanding of a planet without a global magnetosphere and a thin atmosphere is very different from our situation at Earth so there is substantial fundamental research remaining. It is expected that the development of suitable models will lead to a comprehensive operational Mars space weather alert (MSWA) system that would provide rapid dissemination of information to Earth controllers, astronauts in transit, and those in the exploration zone (EZ) on the surface by producing alerts that are delivered rapidly and are actionable. To illustrate the importance of such a system, we use a magnetohydrodynamic code to model an extreme Carrington-type coronal mass ejection (CME) event at Mars. The results show a significant induced surface field of nearly 3,000 nT on the dayside that could radically affect unprotected electrical systems that would dramatically impact human survival on Mars. Other associated problems include coronal mass ejection (CME) shock-driven acceleration of solar energetic particles producing large doses of ionizing radiation at the Martian surface. In summary, along with working more closely with international partners, the next Heliophysics Decadal Survey must include a new initiative to meet expected demands for space weather forecasting in support of humans living and working on the surface of Mars. It will require significant effort to coordinate NASA and the international community contributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Preshot Report for the NIF DDCyl Campaign: H_Hyd_DDCyl_DRT_AAA/BBB/CCC

The first two cylinder shot days on the National Ignition Facility, allocated through the Discovery Science program, provided a successful demonstration of the cylinder platform on the NIF. Both of these shot days used cylinders that were nominally 3 times larger in radial dimension than cylinders fielded at the OMEGA laser facility, here referred to as scale-3 targets. In the first Discovery Science shot day, we demonstrated that Rayleigh-Taylor instability growth during the deceleration phase is scale-invariant between the scale-1 OMEGA experiments and similarly tailored scale-3 NIF experiments at the same convergence ratio of CR=initial radius/final radius=2.25. In the second Discovery Science shot day, we increased the convergence ratio by lowering the density of the central foam from 300 mg/cm 3 to roughly 40 mg/cm 3 with the same laser drive, resulting in a higher CR=5 at the time when the rebounding shock strikes the aluminum marker. We also greatly improved the imaging setup for the second shot day, resulting in much higher quality (greater signal-to-noise) radiographs of the implosion. This current shot day was awarded through the High Energy Density (HED) Council, following this demonstration of platform viability. It was originally scheduled for June 2020, but it was postponed several times due to the COVID-19 pandemic. It is currently scheduled for January 6, 2021. For this shot day, we will increase the radial dimension of the cylinder to four times the OMEGA-scale targets, and these will be referred to as scale-4 cylinders. Increasing the radial dimension of the target is advantageous as we push these targets to higher convergence ratio. By starting with an initially larger target, the target can push to a higher CR while maintaining the same final viewing area. Other than the larger radial dimension, the targets are very similar in design to the previous ones, consisting of an epoxy ablator, an embedded aluminum marker layer, and a low density central CH foam. These will also use a 40 mg/cm3 CH foam, reaching a CR~4.5 with the same laser energy (the added target mass reduces the final CR slightly). Note that this is NOT designed to be scale-invariant with the previous scale-1 OMEGA and scale-3 NIF shots. It was determined that the laser energy required to achieve a scale-invariant implosion was above the allowable optics damage limits (though achievable on the NIF) for these scale-4 targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

High-energy neutrino emission from magnetized jets of rapidly rotating protomagnetars

ABSTRACT Relativistic jets originating from protomagnetar central engines can lead to long duration gamma-ray bursts (GRBs) and are considered potential sources of ultra-high-energy cosmic rays and secondary neutrinos. We explore the propagation of such jets through a broad range of progenitors, from stars which have shed their envelopes to supergiants which have not. We use a semi-analytical spin-down model for the strongly magnetized and rapidly rotating protoneutron star (PNS) to investigate the role of central engine properties such as the surface dipole field strength, initial rotation period, and jet opening angle on the interactions and dynamical evolution of the jet-cocoon system. With this model, we determine the properties of the relativistic jet, the mildly relativistic cocoon, and the collimation shock in terms of system parameters such as the time-dependent jet luminosity, injection angle, and density profile of the stellar medium. We also analyse the criteria for a successful jet breakout, the maximum energy that can be deposited into the cocoon by the relativistic jet, and structural stability of the magnetized outflow relative to local instabilities. Lastly, we compute the high-energy neutrino emission as these magnetized outflows burrow through their progenitors. Precursor neutrinos from successful GRB jets are unlikely to be detected by IceCube, which is consistent with the results of previous works. On the other hand, we find that high-energy neutrinos may be produced for extended progenitors like blue and red supergiants, and we estimate the detectability of neutrinos with next generation detectors such as IceCube-Gen2.

Astronomy & Astrophysics↗
DOE OSTI2023

Intergranular Hotspots: A Molecular Dynamics Study on the Influence of Compressive and Shear Work

Numerous crystal- and microstructural-level mechanisms are at play in the formation of hotspots, which are known to govern high explosives initiation behavior. Most of these mechanisms, including pore collapse, interfacial friction, and shear banding, involve both compressive and shear work done within the material and have thus far remained difficult to separate. Here, we assess hotspots formed at shocked crystal–crystal interfaces using quasi-1D molecular dynamics simulations that isolate effects due to compression and shear. Two high explosive materials are considered (TATB and PETN) that exhibit distinctly different levels of molecular conformational flexibility and crystal packing anisotropy. Temperature and intramolecular strain energy localization in the hotspot are assessed through parametric variation of the crystal orientation and two velocity components that respectively modulate compression and shear work. The resulting hotspots are found to be highly localized to a region within 5–20 nm of the crystal–crystal interface. Compressive work plays a considerably larger role in localizing temperature and intramolecular strain energy for both materials and all crystal orientations considered. Shear induces a moderate increase in energy localization relative to unsheared cases only for relatively weak compressive shock pressures of approximately 10 GPa. These results help isolate and rank the relative importance of hotspot generation mechanisms and are anticipated to guide the treatment of crystal–crystal interfaces in coarse-grained models of polycrystalline high-explosive materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Integrated TBC/EBC for SiC Fiber Reinforced SiC Matrix Composites for Next Generation Gas Turbines (Final Report)

In this ambitious project, a significant challenge preventing widespread use of ceramic matrix composites in hot section components of gas power generating turbines was addressed. Hot section components made from SiC fiber reinforced SiC matrix composites (SiC/SiC composites), have the potential to achieve a combined cycle energy efficiency of above 65%. To achieve this efficiency, the temperature of the combustion gases on the turbine component surface is expected to reach as high as ~1700ºC (3100ºF). However, SiC/SiC composites suffer from volatilization at high temperature under high velocity steam environment – typical in a turbine hot chamber. This integrated collaborative project, between two research groups at Clemson University and a team of engineers and scientists at GE Gas Power, focused on design, fabrication and evaluation of a new graded environmental barrier coating. Using the excellent compositional tailorability of polymer derived ceramics (PDCs), we developed an integrated EBC/BC that smoothly transitions from bottom SiC/SiC bond interface to hermetic sesquioxide (Y 2 O 3 ) top surface. This smooth compositional transition avoided the sharp CTE mismatch at interfaces to greatly reduce the thermal stress. The developed EBC is compatible with and bonds well with the bond coat that GE uses. The top hermetic oxide surface ensures low oxygen transportation and volatilization rates under the high velocity steam environment. The graded microstructure with increasing sesquioxide concentration also decreases the amount of Si and C elements near the top hermetic sesquioxide layer. Coatings made using a process suitable for manufacturing – atmospheric plasma spraying was demonstrated. The microstructure of coatings made using this process were fully characterized. Finally, the performance of these coatings was investigated under the most demanding conditions for this application. Specifically, high temperature, high velocity steam exposure; thermal shock test; and thermal cycling tests. The graded coatings performed exceptionally well in all these tests. Specific suggestions for future development in this area have also been identified. In addition to the excellent technical progress, this project helped initiate a robust collaboration between the research groups at Clemson and GE Gas Power. It also provided a high-quality learning and mentoring opportunity for the three post-doctoral research associates and two UG students at Clemson University who worked on this project. All proposed tasks, sub-tasks were completed, and all milestones achieved.

03 NATURAL GAS↗
DOE OSTI2022

Characterization of a new ultra-high pressure shock tube facility for combustion and propulsion studies

A new shock tube facility has been designed, constructed, and characterized at the University of Central Florida. This facility is capable of withstanding pressures of up to 1000 atm, allowing for combustion diagnostics of extreme conditions, such as in rocket combustion chambers or in novel power conversion cycles. For studies with toxic gas impurities, the high initial pressures required the development of a gas delivery system to ensure the longevity of the facility and the safety of the personnel. Data acquisition and experimental propagation were implemented with remote access to ensure safety, paired with a LabVIEW- and Python-based user interface. Thus far, test pressures of 270 atm, blast pressures of 730 atm, and temperatures approaching 10 000 K have been achieved. The extreme limitations of this facility allow for emission spectroscopy to be performed during the oxidation of fuel mixtures, e.g., alkanes diluted in argon and carbon dioxide. Ignition delay times were determined and compared to simulations using chemical kinetic mechanisms. The design, experimental procedures, processes of analysis, and uncertainty determination are outlined, and typical pressure profiles are compared with a new gas dynamics solver and empirical correlations developed across multiple shock tube facilities. Preliminary reactive mixture analyses are included with further investigation of the mixtures outlined.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Soliton Generation in Negative Thermal Expansion Materials

Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Differentiable programming for online training of a neural artificial viscosity function within a staggered grid Lagrangian hydrodynamics scheme

Lagrangian methods to solve the inviscid Euler equations produce numerical oscillations near shock waves. A common approach to reducing these oscillations is to add artificial viscosity (AV) to the discrete equations. The AV term acts as a dissipative mechanism that attenuates oscillations by smearing the shock across a finite number of computational cells. However, AV introduces several control parameters that are not determined by the underlying physical model, and hence, in practice are tuned to the characteristics of a given problem. We seek to improve the standard quadratic-linear AV form by replacing it with a learned neural function that reduces oscillations relative to exact solutions of the Euler equations, resulting in a hybrid numerical-neural hydrodynamic solver. Because AV is an artificial construct that exists solely to improve the numerical properties of a hydrodynamic code, there is no offline ‘viscosity data’ against which a neural network can be trained before inserting into a numerical simulation, thus requiring online training. We achieve this via differentiable programming, i.e. end-to-end backpropagation or adjoint solution through both the neural and differential equation code, using automatic differentiation of the hybrid code in the Julia programming language to calculate the necessary loss function gradients. A novel offline pre-training step accelerates training by initializing the neural network to the default numerical AV scheme, which can be learned rapidly by space-filling sampling over the AV input space. We find that online training over early time steps of simulation is sufficient to learn a neural AV function that reduces numerical oscillations in long-term hydrodynamic shock simulations. These results offer an early proof-of-principle that online differentiable training of hybrid numerical schemes with novel neural network components can improve certain performance aspects existing in purely numerical schemes.

97 MATHEMATICS AND COMPUTING↗