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DOE OSTI2024

Recent developments in mathematical aspects of relativistic fluids

Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

Disconzi, Marcelo (ORCID:0000000234497778)↗

DOE OSTI2022

Aero-Optics of Hypersonic Turbulent Boundary Layers

Aero-optics refers to optical distortions due to index-of-refraction gradients that are induced by aerodynamic density gradients. At hypersonic flow conditions, the bulk velocity is many times the speed of sound and density gradients may originate from shock waves, compressible turbulent structures, acoustic waves, thermal variations, etc. Due to the combination of these factors, aero-optic distortions are expected to differ from those common to sub-sonic and lower super-sonic speeds. This report summarizes the results from a 2019-2022 Laboratory Directed Research and Development (LDRD) project led by Sandia National Laboratories in collaboration with the University of Notre Dame, New Mexico State University, and the Georgia Institute of Technology. Efforts extended experimental and simulation methodologies for the study of turbulent hypersonic boundary layers. Notable experimental advancements include development of spectral de-aliasing techniques for highspeed wavefront measurements, a Spatially Selective Wavefront Sensor (SSWFS) technique, new experimental data at Mach 8 and 14, a Quadrature Fringe Imaging Interferometer (QFII) technique for time-resolved index-of-refraction measures, and application of QFII to shock-heated air. At the same time, model advancements include aero-optic analysis of several Direct Numerical Simulation (DNS) datasets from Mach 0.5 to 14 and development of wall-modeled Large Eddy Simulation (LES) techniques for aero-optic predictions. At Mach 8 measured and predicted root mean square Optical Path Differences agree within confidence bounds but are higher than semi-empirical trends extrapolated from lower Mach conditions. Overall, results show that aero-optic effects in the hypersonic flow regime are not simple extensions from prior knowledge at lower speeds and instead reflect the added complexity of compressible hypersonic flow physics.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Collaborative Research: Vlasov–Maxwell Simulations to resolve electron heating and dissipation, in quasiperpendicular shocks (Final Technical Report)

The project is to study electron heating at quasi-perpendicular shocks. We have analyzed measurements from the Magnetosphere Multiscale (MMS) spacecraft and particle-in-cell simulations to address the question. One key discovery is that waves and are excited in the shock transition region, which further develop into complicated structures and thin current layers, which contribute to accelerate and heat electrons. We further investigated the excitation and evolution of these waves and structures, and their association with ion and electron dynamics. In addition, the analysis technique of Vlasov equation terms is further applied to study electron dynamics at the dayside magnetopause, to understand the effect of density, velocity and temperature variations on electron distributions and kinetics.

58 GEOSCIENCES↗

DOE OSTI2021

Experiments at TA-55 have used optical pyrometry to measure temperatures of shocked plutonium on the 40mm gun

Researchers at LANL, along with collaborators from MSTS, have worked for more than a decade to develop and implement an optical pyrometry method to measure the temperature of metals shocked to the high pressures and temperatures. Because traditional shock wave measurements only provide information on the mechanical state of the material, temperature measurements are required to validate and improve equation-of-state (EOS) models for materials. The conditions sampled are complex; commenserate with those found in planetary impacts, and accressed by conventional and nuclear weapons. Optical pyrometry is currently the best available method for inferring the temperature of shocked metals, by careful measurement of the calibrated radiance emitted by a surface at finite temperature. These measurements are difficult often complicated by the short time scales associated with shock wave experiments (<1 µs) coupled with the many sources of non-thermal light (impact flash, fracture light, etc.) that pollutes the radiant light measured from the sample.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Shock Hugoniot of Forged and Additively Manufactured 304L Stainless Steel

The purpose of this research was to measure the equation of state for additively manufactured (AM) and forged 304L stainless steel using a novel experimental technique. An understanding of the dynamic behavior of AM metals is integral to their timely adoption into various applications. The Hugoniot of the AM 304L was compared to that of the forged 304L at particle velocities where the material retains a two-wave structure. This comparison enabled us to determine the sensitivity of the equation of state to microstructure as varied due to processing. Our results showed that there was a measurable difference in the measured shock velocity between the AM and forged 304L. The shock wave velocities for the AM 304L were found to be ~3% slower than those for the forged 304L at similar particle velocities. To understand these differences, properties such as densities, sound speeds, and texture were measured and compared between the forged and AM materials. Our results showed that no measurable difference was found in these properties. Additionally, it is possible that differing elastic wave amplitudes may influence shock velocity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Shock Hugoniot of forged and additively manufactured 304L stainless steel

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Curated Dataset of Regional Meteor Events with Simultaneous Optical and Infrasound Observations (2006–2011)

We present a curated, openly accessible dataset of 71 regional meteor events simultaneously recorded by optical and infrasound instrumentation between 2006 and 2011. These events were captured during an observational campaign using the all-sky cameras of the Southern Ontario Meteor Network and the co-located Elginfield Infrasound Array. Each entry provides optical trajectory measurements, infrasound waveforms, and atmospheric specification profiles. The integration of optical and acoustic data enables robust linkage between observed acoustic signals and specific points along meteor trajectories, offering new opportunities to examine shock wave generation, propagation, and energy deposition processes. This release fills a critical observational gap by providing the first validated, openly accessible archive of simultaneous optical–infrasound meteor observations that supports trajectory reconstruction, acoustic propagation modeling, and energy deposition analyses. By making these data openly available in a structured format, this work establishes a durable reference resource that advances reproducibility, fosters cross-disciplinary research, and underpins future developments in meteor physics, atmospheric acoustics, and planetary defense.

astrometry↗

DOE OSTI2023

Imaging velocity interferometer system for any reflector (VISAR) diagnostics for high energy density sciences

Two variants of optical imaging velocimetry, specifically the one-dimensional streaked line-imaging and the two-dimensional time-resolved area-imaging versions of the Velocity Interferometer System for Any Reflector (VISAR), have become important diagnostics in high energy density sciences, including inertial confinement fusion and dynamic compression of condensed matter. Here, we give a brief review of the historical development of these techniques, then describe the current implementations at major high energy density (HED) facilities worldwide, including the OMEGA Laser Facility and the National Ignition Facility. We illustrate the versatility and power of these techniques by reviewing diverse applications of imaging VISARs for gas-gun and laser-driven dynamic compression experiments for materials science, shock physics, condensed matter physics, chemical physics, plasma physics, planetary science and astronomy, as well as a broad range of HED experiments and laser-driven inertial confinement fusion research.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Wave steepening and shock formation in ultracold neutral plasmas

We present observations of wave steepening and signatures of shock formation during expansion of ultracold neutral plasmas formed with an initial density distribution that is centrally peaked and decays exponentially with distance. The plasma acceleration and velocity decrease at large distance from the plasma center, leading to central ions overtaking ions in the outer regions and the development of a steepening front that is narrow compared to the size of the plasma. The density and velocity change dramatically across the front, and significant heating of the ions is observed in the region of steepest gradients. For a reasonable estimate of electron temperature, the relative velocity of ions on either side of the front modestly exceeds the local sound speed (Mach number M≳1). This indicates that by sculpting steep density gradients, it is possible to create the conditions for shock formation, or very close to it, opening a new avenue of research for ultracold neutral plasmas.

Computational fluid dynamics↗

DOE OSTI2022

Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG. First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize viscosity for a 1D propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.

42 ENGINEERING↗

DOE OSTI2023

Shock-induced transformation of nitinol shape memory alloy: Effect of stress state on transformation

Due to its numerous practical applications and intriguing phase transformation behavior, shape memory alloys (SMAs) have garnered significant research and development interests. In the past, most studies on the mechanical behavior of SMAs have been conducted under uniaxial stress loadings. Limited research on SMAs under shock loading has not provided conclusive results regarding their transformation behavior and transformation stress under such loading. Additionally, there is a lack of comprehensive understanding regarding the effects of different stress states on transformation behavior. The main objectives of this study are to address these issues. To achieve these objectives, a series of shock wave experiments were designed and conducted. Additionally, quasi-static and dynamic uniaxial stress experiments were carried out to establish a baseline for comparison. The results revealed that the transformation stress under dynamic uniaxial strain shock loading was approximately 1.92 GPa in contrast to 0.5 GPa (quasi-static) to 0.8 GPa (dynamic) observed in uniaxial stress loading. The transformation behavior exhibited noticeable rate sensitivity for both types of loading. There appeared to be a critical strain rate above which the austenite phase was driven to a metastable state. This estimated critical axial strain rate along the loading direction was approximately 2 × 10 3 /s–4 × 10 3 /s for uniaxial stress loading and approximately 2 × 10 6 /s for uniaxial strain loading. The apparent high transformation stress for uniaxial strain loading can likely be attributed to a combination of high-pressure confinement and high strain rate. Furthermore, determining their relative contributions remains an open issue.

36 MATERIALS SCIENCE↗

DOE OSTI2025

HARD: A performance portable radiation hydrodynamics code based on FleCSI framework

Hydrodynamics And Radiation Diffusion (HARD) is an open-source application for high-performance simulations of compressible hydrodynamics with radiation-diffusion coupling. Built on the FleCSI (Bergen et al., 2021 [1]) (Flexible Computational Science Infrastructure) framework, HARD expresses its computational units as tasks whose execution can be orchestrated by multiple back-end runtimes, including Legion (Bauer et al., 2012 [2]), MPI (Forum, 1994 [3]), and HPX (Kaiser et al., 2020 [4]). Node-level parallelism is handled through Kokkos (Edwards et al., 2014 [5]), providing a single-source, portable code base that runs efficiently on laptops, small homogeneous clusters, and the largest heterogeneous supercomputers currently available. To ensure scientific reliability, HARD includes a regression test suite that automatically reproduces canonical verification problems such as the Sod and LeBlanc shock tubes, and the Sedov blast wave, comparing numerical solutions against known analytical results. The project is distributed under an OSI-approved license, hosted on GitHub, and accompanied by reproducible build scripts and continuous integration workflows. This combination of performance portability, verification infrastructure, and community-focused development makes HARD a sustainable platform for advancing radiation hydrodynamics research across multiple domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Microscopic changes governing melting anisotropy: Real-time nanosecond x-ray diffraction

To understand the microscopic origins governing melting anisotropy, in-situ x-ray diffraction (XRD) measurements were obtained in aluminum single crystals shocked along $\langle$100$\rangle$ and $\langle$110$\rangle$ to stresses below and above the melting threshold for each orientation. XRD results and analysis for the two orientations showed significant differences in the microstructure prior to the melting threshold stresses, demonstrating the key role of deformation induced microstructure – in addition to temperature and pressure – on the melting transition. As a result, our findings make a strong case for reconsidering theoretical approaches to melting, specifically for dislocation mediated melting, in shock compressed solids.

crystal melting↗

DOE OSTI2020

Spall and subsequent recompaction of copper under shock loading

Research was undertaken to study spall and subsequent recompaction of oxygen-free high-thermal-conductivity copper using a single-stage large-bore light gas gun capable of planar impacts. Gun experiments were conducted that produced an initial spall in the target with a subsequent recompaction of the spall damage/layer by the use of layered impactors. Symmetric spall experiments at similar conditions were also conducted as a control to the recompaction experiments. Photonic Doppler velocimetry was used to obtain the velocity history of the target’s back surface; these velocity histories were analyzed, and the results were compared to numerical simulations. After recovery of selected samples, the microstructure was analyzed using optical imaging microscopy and electron backscatter diffraction. Recompaction waves were clearly observed in the time-resolved data obtained at the back surface of the targets. Two different series of experiments were performed to understand the effect of damage morphology on the stress required for spall recompaction. In the initial series, the peak pressure of the first shock was systematically increased to alter the amount of damage in the material. While in the second series, the peak pressure of the second shock was increased, keeping the magnitude of the first shock relatively constant to understand the effect of peak stress on the recompaction process. Findings clearly show that recompaction results in a perturbed band of the microstructure at the location of the expected spall plane in all cases except where the peak stress of the second shock is lower than the critical value.

, recompaction↗

DOE OSTI2022

Peculiarities of planar shockwave interaction with air–water interface and solid target

We present the results of the research on underwater electrical explosion of planar copper wire arrays, accompanied by the generation of a planar shock, using the synchrotron-based phase-contrast radiography imaging capabilities of the ID19 beamline at the European Synchrotron Radiation Facility. It is shown that the interaction of a strong shock with an air–water interface leads to additional acceleration of the wire expansion due to a rarefaction wave along with the emergence of micro-jets. In the case of a target placed above the array, we observed the formation of a cavity between the array and the target due to the interaction of two rarefaction waves. Furthermore, the results of two-dimensional hydrodynamic simulations of the wire explosion and the interaction of the generated shock with the water–air and water-target interfaces showed good agreement with experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗

DOE OSTI2025

Modeling detonation with CartaBlanca simulations

The accurate modeling of high explosive (HE) detonation and the con- sequent large solid deformation, failure, plastic flow, porosity growth, and shock wave propagation is important because simulations can capture spatial and temporal features that experimental diagnostics cannot capture. However, the simulation of the explosive event poses challenges to a computational scientist. These include the accurate modeling of ductile damage, crack formation, plastic deformation, as well as physical and nu- merical instabilities. The material response can be history-dependent and subject to large material deformation. Our research simulates the impact of a high explosive (Detasheet) onto a tantulum metal plate. We performed the simulations using CartaBlanca at different mesh resolutions. We decided the study would be impactful if we perform the simulations with the Material Point Method. Differences were observed at the different mesh resolutions in velocity and nodal stress magnitude, so increased mesh resolutions may be required. In addition, the Discontinuous Galerkin method would be needed to account for the large gas expansion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Collaborative Research: Vlasov-Maxwell Simulations to Resolve Electron Heating and Dissipation, in Quasi-Perpendicular Shocks

The major goals of the project are to study three fundamental questions related to collisionless, non-relativistic, quasi-perpendicular shocks by combining continuum Vlasov-Maxwell simulations (the Gkeyll framework) and high resolution, in situ heliospheric observations from the MMS spacecraft. The specific questions are: 1. How and where are electrons energized and heated in a quasi-perpendicular shock, including the ultimate source of entropy production? 2. What role do waves, turbulence, and secondary instabilities play in the conversion of directed flow energy to electron energy? 3. How do the parameters of the shock determine the energization of electrons?

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗