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NASA NTRS1994

Hot gas in the cold dark matter scenario: X-ray clusters from a high-resolution numerical simulation

A new, three-dimensional, shock-capturing hydrodynamic code is utilized to determine the distribution of hot gas in a standard cold dark matter (CDM) model of the universe. Periodic boundary conditions are assumed: a box with size 85 h(exp -1) Mpc having cell size 0.31 h(exp -1) Mpc is followed in a simulation with 270(exp 3) = 10(exp 7.3) cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, sigma(sub 8) = 1.05, omega(sub b) = 0.06, and assuming h = 0.5, we find the X-ray-emitting clusters and compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. We find that most of the total X-ray emissivity in our box originates in a relatively small number of identifiable clusters which occupy approximately 10(exp -3) of the box volume. This standard CDM model, normalized to COBE, produces approximately 5 times too much emission from clusters having L(sub x) is greater than 10(exp 43) ergs/s, a not-unexpected result. If all other parameters were unchanged, we would expect adequate agreement for sigma(sub 8) = 0.6. This provides a new and independent argument for lower small-scale power than standard CDM at the 8 h(exp -1) Mpc scale. The background radiation field at 1 keV due to clusters in this model is approximately one-third of the observed background, which, after correction for numerical effects, again indicates approximately 5 times too much emission and the appropriateness of sigma(sub 8) = 0.6. If we have used the observed ratio of gas to total mass in clusters, rather than basing the mean density on light-element nucleosynthesis, then the computed luminosity of each cluster would have increased still further, by a factor of approximately 10. The number density of clusters increases to z approximately 1, but the luminosity per typical cluster decreases, with the result that evolution in the number density of bright clusters is moderate in this redshift range, showing a broad peak near z = 0.7, and then a rapid decline above redshift z = 3. Detailed computations of the luminosity functions in the range L(sub x) = 10(exp 40) - 10(exp 44) ergs/s in various energy bands are presented for both cluster central regions and total luminosities to be used in comparison with ROSAT and other observational data sets. The quantitative results found disagree significantly with those found by other investigators using semianalytic techniques. We find little dependence of core radius on cluster luminosity and a dependence of temperature on luminosity given by log kT(sub x) = A + B log L(sub x), which is slightly steeper (B = 0.38) than is indicated by observations. Computed temperatures are somewhat higher than observed, as expected, in that COBE-normalized CDM has too much power on the relevant scales. A modest average temperature gradient is found, with temperatures dropping to 90% of central values at 0.4 h(exp -1) Mpc and 70% of central values at 0.9 h(exp -1) Mpc. Examining the ratio of gas to total mass in the clusters normalized to Omega(sub B) h(exp 2) = 0.015, and comparing with observations, we conclude, in agreement with White (1991), that the cluster observations argue for an open universe.

Kang, Hyesung↗

NASA NTRS1998

A 3-mode, Variable Velocity Jet Model for HH 34

Variable ejection velocity jet models can qualitatively explain the appearance of successive working surfaces in Herbig-Haro (HH) jets. This paper presents an attempt to explore which features of the HH 34 jet can indeed be reproduced by such a model.

Herbig-Haro objects↗

NASA NTRS2022

Finite Difference Methods for Turbulence Simulations

The optimal finite difference discretization used in simulations of turbulent flows is influenced by both, the type of the scale resolving simulation (DNS or LES), as well as the flow-physics (hydrodynamic instabilities, shocks, acoustics, etc.) one expects to resolve. Insight into dispersion and dissipation error requirements for some common scale-resolving simulation scenarios help to highlight the issues faced in selecting a scheme.

Finite Difference Methods↗

DOE OSTI2022

Shock physics in warm dense matter: A quantum hydrodynamics perspective

Abstract Warm dense matter (WDM), an exotic, highly compressed state of matter between solid and plasma phases, is of high current interest, in particular for astrophysics and inertial confinement fusion. For the latter, in particular the propagation of compression shocks is crucial. The main unknown in the shock propagation in WDM is the behaviour of the electrons since they are governed by correlations, quantum and spin effects that need to be accounted for simultaneously. Here we describe the shock dynamics of the warm dense electron gas using a quantum hydrodynamic model. From the numerical hydrodynamic simulations, we observe that the quantum Bohm pressure induces shear force that weakens the formation and strength of the shock. In addition, the Bohm pressure induces an electron density response that takes the form of oscillations. This is confirmed by the theoretical analysis of the early stage of the shock formation. Our theoretical and numerical analyses allow us to identify characteristic dimensionless shock propagation parameters at which the effect of the Bohm force is important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗

NASA NTRS1987

The structure of the time-dependent interstellar shocks and grain destruction in the interstellar medium

A new theoretical analysis of the structure of interstellar shocks and the grain dynamics of these shocks is presented. The basic hydrodynamic equations for J-shocks in interstellar gas are given in which shock-driving pressure is allowed to be weakly time-dependent and the grains are treated as a separate two-dimensional fluid. Specific equations for the grain dynamics in the cooling postshock gas are derived. An analytic theory for the propagation of a shock driven into an interstellar cloud by the blast wave of a supernova remnant which sweeps over the cloud is developed. An improved calculation of the grain charge in postshock gas is described, giving a simple analytic approximation for the results. The consequences of including these processes in the numerical code of Seab and Shull (1983) are addressed, including the effect of realistic magnetic fields in low-density gas.

Mckee, Christopher F.↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems using MOOSE

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1993

Initiating solar system formation through stellar shock waves

Isotopic anomalies in presolar grains and other meteoritical components require nucleosynthesis in stellar interiors, condensation into dust grains in stellar envelopes, transport of the grains through the interstellar medium by stellar outflows, and finally injection of the grains into the presolar nebula. The proximity of the presolar cloud to these energetic stellar events suggests that a shock wave from a stellar outflow might have initiated the collapse of an otherwise stable presolar cloud. We have begun to study the interactions of stellar shock waves with thermally supported, dense molecular cloud cores, using a three spatial dimension (3D) radiative hydrodynamics code. Supernova shock waves have been shown by others to destroy quiescent clouds, so we are trying to determine if the much smaller shock speeds found in, e.g., asymptotic giant branch (AGB) star winds, are strong enough to initiate collapse in an otherwise stable, rotating, solar-mass cloud core, without leading to destruction of the cloud.

Boss, A. P.↗

DOE OSTI2025

Laser-driven flash x-ray radiography of a shocked metallic foil

Characterizing hydrodynamic instability evolution in millimeter-scale, high-Z foils is crucial for understanding complex phenomena in high-energy-density physics. Here, we demonstrate a proof-of-concept, laser-driven flash x-ray radiography platform tailored for two-dimensional linear density mapping in shocked high-Z foils. Using chromium (Cr) foils with internal shockwaves (∼100 μm width), our platform achieves a spatial resolution of 59.8 ± 1.4 μm by employing a broadband x-ray source extending into the hundreds of keV range. The setup combines a compound parabolic concentrator cone with a tantalum wire target, a magnetic field to deflect residual transmitted electrons, and a copper casing to shield the sides and rear of the image plate pack. By varying the delay of the short-pulse beam driving the flash x-ray source, we resolve shockwave dynamics, specifically the velocity, position, width, and density profile, within the Cr foil. Reported experimental results are consistent with the corresponding hydrodynamics and radiation transport simulations, which accurately reproduce the measured electron and x-ray source terms. These developments enable the conversion of shockwave radiographs into two-dimensional density maps, enhancing interpretability for hydrodynamic instability evolution applications and validating the simulation approach.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Quantitative x ray phase contrast imaging of oblique shock wave–interface interactions

Oblique shock wave–interface interactions of gases and liquids have been extensively studied in shock tubes using optical methods to measure equation-of-state (EOS) parameters. However, this is difficult with solids due to their opaqueness to visible light. X ray phase contrast imaging (XPCI) has the penetrative strength to probe solids while still being sensitive to mass density and enhancing the visibility of material boundaries. We investigate the accuracy and repeatability of measuring the mean value of the average mass density (areal density divided by thickness) over region S (B S ) and flow deflection angle (θ) from XPCI images of a sample. To that end, a Hough transform-based method for measuring θ is developed. To measure B S , the XPCI image intensity probability density function (PDF) is modeled accounting for the spatial distribution of x ray energy, scintillator response, and pulse-to-pulse variation in the x ray intensity. In addition, a Monte Carlo-based algorithm for computing the B S PDF is developed. Both methods are validated on an impact-generated oblique shock wave interacting at a solid polymer-to-polymer interface. Furthermore this is accomplished through a comparison to hydrodynamic simulations using well-established EOS. Under the modeling framework for the XPCI image intensity, B S is computed with an accuracy of < 0.1% and precision of 3%–5%, while θ has an uncertainty of 0.2°, respectively. This shows that the XPCI-based model that is developed here could be an invaluable tool for high-fidelity testing of hydrodynamic models in shock polar configurations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2009

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) excited in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a new 3-D relativistic particle-in-cell code, we have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. The simulation has been performed using a long simulation system in order to study the nonlinear stages of the Weibel instability, the particle acceleration mechanism, and the shock structure. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic (HD) like shock structure. In the leading shock, electron density increases by a factor of <_ 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. We discuss the possible implication of our simulation results within the AGN and GRB context. We have calculated the time evolution of the spectrum from two electrons propagating in a uniform parallel magnetic field to verify the technique. The same technique will be used to calculate radiation from accelerated electrons (positrons) in turbulent magnetic fields generated by Weibel instability.

Nishikawa, K.↗

DOE OSTI2020

Locally adaptive artificial viscosity strategies for Lagrangian hydrodynamics

To accurately model inviscid flow with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity is introduced to convert kinetic energy into internal energy, thereby providing a mechanism to generate the required entropy increase across shocks. In this paper, we propose a new method for constructing an adaptive, artificial viscosity in the context of one-dimensional, staggered-grid Lagrangian hydrodynamics. Our adaptive, artificial viscosity is defined in terms of two parameters that depend on density locally in a neighborhood around a shock, and hence, vary cell-by-cell. Our methodology is based on building a reference set of pre-computed optimal, globally constant artificial viscosity coefficients for a family of isolated shock test problems. For arbitrary flows, the evaluation of the unknown coefficients is automated by first estimating shock intensity locally, and second computing the corresponding adaptive parameter value via interpolation over the data from the pre-computed reference set of optimal, globally constant coefficient values. To illustrate the performance of our new approach, we compare our results against two existing methods. The first method is a limiter-based approach, which relies on estimating velocity gradients of the flow, and the second method is utilized in several commercial codes. Finally, we demonstrate that our new adaptive methodology produces more accurate results for a variety of tests with propagating shock waves, as well as for the aforementioned family of isolated shock problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Shocks in the Scrape-off Layer: Hydrodynamical Aspects (Summary) [Slides]

Hydrodynamical model provides a robust description of mass, momentum, and energy transfer. It can be used for benchmarking hydrodynamical modules of SOL codes. It clarifies the role of boundary conditions at the end-plates. It provides a “geometrical” model for partition of power flows between two divertor legs, both for the steady-state and pulsed flows. It indicates possible presence of shocks in the divertor legs. A framework for finding the shock location and strength has been developed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗

NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗

NASA NTRS1977

A review of the thermonuclear runaway model of a nova outburst

Kraft's (1963) model for a nova outburst caused by a thermonuclear runaway in the hydrogen-rich matter accreted onto the white dwarf in a binary system is reviewed. Hydrostatic and hydrodynamic studies of this phenomenon are summarized, analyses of shock ejection based on hydrodynamic computer codes are discussed, and one specific hydrodynamic code is outlined. Results obtained with this code are presented and evaluated for an initial model containing a white dwarf with a hydrogen-rich envelope of 0.0001 to 0.001 solar mass in hydrostatic and thermal equilibrium. It is shown that an implicit hydrodynamic computer code is required in order to study the thermonuclear-runaway phenomenon. The early evolution of three models with different intrinsic luminosities is illustrated, and enhancement of CNO nuclei at the bottom of the hydrogen-rich envelope is investigated. It is suggested that the concentration of C-13, N-15, and O-17 should be greatly enhanced in nova ejecta.

Sparks, W. M.↗