Simulation Of Shock Waves Research Articles

Euler–Lagrange simulation of high pressure shock waves

This paper presents the numerical simulation of overdriven detonation (or O.D.D.) that occurs when a high velocity object impacts an explosive. The pressure and the velocity at this state are higher than those of the Chapman–Jouguet (C–J) state. First, before the simulation of this event, a study of PBX air blast by using multi-material Eulerian method is presented. Pressure peaks are computed for several distances from the explosive. Second, the O.D.D. phenomenon is modeled by the Euler–Lagrange penalty coupling, which permits to couple a Lagrangian mesh of the flyer plate to multi-material Eulerian mesh of explosives and air. This coupling gives us the high detonation velocities in the acceptor explosive and demonstrates that it is able to handle shock–structure interaction problems.

Source parameters for the numerical simulation of lightning as a nonlinear acoustic source

Researchers have proposed using acoustic data to obtain additional insight into aspects of lightning physics. However, it is unclear how much information is retained in the nonlinear acoustic waveform as it propagates and evolves away from the lightning channel. Prior research in tortuous lightning has used simple N-waves as the initial acoustic emission. It is not clear if more complex properties of the lightning channel physics are also transmitted in the far-field acoustic signal, or if simple N-waves are a sufficient source term to predict far-field propagation. To investigate this, the authors have conducted a numerical study of acoustic emissions from a linear lightning channel. Using a hybrid strong-shock/weak-shock code, the authors compare the propagation of a simple N-wave and emissions from a source derived from simulated strong shock waves from the lightning channel. The implications of these results on the measurement of sound from nearby lightning sources will be discussed.

Simulations of focused shear shock waves in soft solids and the brain

Because of a very small speed, shear waves in soft solids are extremely nonlinear, with nonlinearities four orders of magnitude larger than in classical solids. Consequently, these nonlinear shear waves can transition from a smooth to a shock profile in less than one wavelength. We hypothesize that traumatic brain injuries (TBI) could be caused by the sharp gradients resulting from shear shock waves. However, shear shock waves are not currently modeled by simulations of TBI. The objective of this paper is to describe shear shock wave propagation in soft solids within the brain, with source geometry determined by the skull. A 2D nonlinear paraxial equation with cubic nonlinearities is used as a starting point. We present a numerical scheme based on a second order operator splitting which allows the application of optimized numerical methods for each terms. We then validate the scheme with Guiraud's nonlinear self-similarity law applied to cusped caustics. Once validated, the numerical scheme is then applied to a blast wave problem. A CT measurement of the human skull is used to determine the initial conditions and shear shock wave simulations are presented to demonstrate the focusing effects of the skull geometry.

Modeling blast waves, gas and particles dispersion in urban and hilly ground areas

The numerical simulation of shock and blast waves as well as particles dispersion in highly heterogeneous media such as cities, urban places, industrial plants and part of countries is addressed. Examples of phenomena under study are chemical gas products dispersion from damaged vessels, gas dispersion in urban places under explosion conditions, shock wave propagation in urban environment. A three-dimensional simulation multiphase flow code (HI2LO) is developed in this aim. To simplify the consideration of complex geometries, a heterogeneous discrete formulation is developed. When dealing with large scale domains, such as countries, the topography is considered with the help of elevation data. Meteorological conditions are also considered, in particular regarding complex temperature and wind profiles. Heat and mass transfers on sub-scale objects, such as buildings, trees and other obstacles are considered as well. Particles motion is addressed through a new turbulence model involving a single parameter to describe accurately plumes. Validations against experiments in basic situations are presented as well as examples of industrial and environmental computations.

Multiphase dynamic flash simulations using entropy maximization and application to compressible flow with phase change

A isochoric‐isoenergetic flash solver using a direct entropy maximization principle for phase splitting and Gibbs free energy minimization for phase stability is developed. The solver searches for the global stable state in a rigorous and thermodynamically consistent way. The solver is demonstrated to be robust and efficient to handle multiphase flash, even in the vicinity of phase boundaries. Dynamic flash computations and gas dynamics simulations of shock waves are considered for pure ethylene and for binary ethylene‐nitrogen mixtures. The simulations show significantly different shock wave characteristics when phase separation is considered due to intensive energy exchange, compared to the frozen flow limiting single‐phase solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3013–3024, 2014

A Pseudo Arc-Length Method for Numerical Simulation of Shock Waves

A pseudo arc-length method is proposed for the numerical simulation of shock wave propagations. This method passes the discontinuities and establishes adaptive moving meshes in the physical space by introducing the arc-length parameter and transforming the computational domain. Numerical experiments of the Sod problem, double Mach reflection problem and explosion problem demonstrate that this approach is more efficient than traditional numerical methods in capturing and tracking discontinuous solutions of singular or nearly singular problems.

Shock-induced plasticity and the Hugoniot elastic limit in copper nano films and rods

Shock deformation of copper nano-films and nano-rods is examined with Molecular Dynamics (MD) simulations. The influence of the small system size on the onset of plasticity, its origin resulting from the nucleation of dislocation loops, and its reversible nature are determined. While simulations of large systems with periodic boundary conditions indicate that tremendous axial stresses are needed to induce plastic deformation in perfect copper crystals, the present results suggest that the stress levels needed to initiate irreversible plasticity in nano-rods are more than one order of magnitude smaller than what has been reported for bulk single crystals. MD studies of nano-films show that shock waves are purely elastic up until the Hugoniot elastic limit of PHEL ≈ 30–40 GPa, at which point Shockley partial dislocations are internally nucleated at the shock front. However, our recent experiments on shocked nano-rods show that plasticity is evident at much lower axial stress levels, on the order of 1–2 GPa. The present MD simulations of shocked nano-rods show that Shockley partial dislocations prefer to nucleate at lower stresses from the rod surface, at PHEL ≈ 1–2 GPa, consistent with our concurrent experimental observations, leading to surface step formation and mechanical damage. Nucleated dislocations are found to be Shockley partials in the [100] and [111] oriented nano-rods, with the additional presence of perfect dislocations in the latter. MD simulations of rarefaction shock waves in nano-films indicate that they can be spalled via a mechanism of nano-void nucleation, growth and coalescence at the spall plane. The origin of these nano-voids is shown to be at the intersection of stacking faults on conjugate slip {111} planes. Spallation by void nucleation and coalescence is found not to be achievable in nano-rods. Rarefaction shocks with high stresses were found to either severely deform or melt the nano-rod before it can be spalled.

Molecular dynamics simulations of shock waves in hydroxyl-terminated polybutadiene melts: Mechanical and structural responses

The mechanical and structural responses of hydroxyl-terminated cis-1,4-polybutadiene melts to shock waves were investigated by means of all-atom non-reactive molecular dynamics simulations. The simulations were performed using the OPLS-AA force field but with the standard 12-6 Lennard-Jones potential replaced by the Buckingham exponential-6 potential to better represent the interactions at high compression. Monodisperse systems containing 64, 128, and 256 backbone carbon atoms were studied. Supported shock waves were generated by impacting the samples onto stationary pistons at impact velocities of 1.0, 1.5, 2.0, and 2.5 km s(-1), yielding shock pressures between approximately 2.8 GPa and 12.5 GPa. Single-molecule structural properties (squared radii of gyration, asphericity parameters, and orientational order parameters) and mechanical properties (density, shock pressure, shock temperature, and shear stress) were analyzed using a geometric binning scheme to obtain spatio-temporal resolution in the reference frame centered on the shock front. Our results indicate that while shear stress behind the shock front is relieved on a ∼0.5 ps time scale, a shock-induced transition to a glass-like state occurs with a concomitant increase of structural relaxation times by several orders of magnitude.

Numerical Simulation of Shock Wave in Air Based on FCT Method

Blast wave is numerical simulated based on FCT method. According to the comparative analysis, taking Henrych empirical formula as a standard, FCT method is more accuracy than Godunov method. Moreover, it has been found that the numerical accuracy is insufficient when the distance is small, it is necessary to develop and modify the numerical method continuously.

Building a Hydrodynamics Code with Kinetic Theory

We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the Point-of-Closest-Approach methods to solve the collision integral of the Boltzmann equation. With that, we achieve a high spatial accuracy in simulations while maintaining computational feasibility when applying a large number of test-particles. The hybrid setup of our approach allows us to study systems which move in and out of the hydrodynamic regime, with low and high particle densities. To demonstrate our code's ability to reproduce hydrodynamic behavior we perform shock wave simulations and focus here on the Sedov blast wave test. The blast wave problem describes the evolution of a spherical expanding shock front and is an important verification problem for codes which are applied in astrophysical simulation, especially for approaches which aim to study core-collapse supernovae.

Pressure Measurements and Numerical Simulation of Underwater Shock Wave for Food Processing

This study attempts to clarify underwater shock waves using a food container designed for food processing. The underwater shock wave is driven by a spark or wire explosion from a high-capacity condenser bank. Since the applied pressure must be known to control the experimental conditions, a numerical simulation was conducted and the results were compared with measurements using an elastic bar placed in the water.

Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme

High-resolution morphological modeling of fluvial processes with complex, rapidly varying flows has been limited so far by model accuracy or computational efficiency. One of the most widely used numerical algorithms is based on the total variation diminishing method, solved by either upwind or centered approaches. An upwind scheme preserves high accuracy but is complex and computationally demanding, whereas the simplicity and efficiency of a centered approach compromise the accuracy. The present paper extends a recent upwind-biased centered scheme originally developed for clear water and scalar transport over a rigid bed, to sediment-laden flows over an erodible bed. It does so by developing a fully coupled 2-D mathematical model using a finite volume method for structured grids. The complete set of noncapacity-based governing equations, involving the effects of bed deformation and sediment density variation, as well as the influences of turbulence and sediment diffusion, and the temporal and spatial scales needed for sediment adaptation, is solved at one time to obtain synchronous solutions for the entire computational domain. For stability, a two-stage splitting approach together with a second-order Runge-Kutta method is employed for the source terms. The model is verified in a number of tests covering a wide range of complex (sediment-laden) flows. The model is demonstrated to accurately simulate shock waves and reflection waves, but also rapid bed deformations at high sediment transport rates. The combination of high numerical accuracy and computational efficiency makes the model an important tool to forecast flood events in morphologically complex areas.

Lattice Boltzmann model for ultrarelativistic flows

We develop a relativistic lattice Boltzmann model capable of describing relativistic fluid dynamics at ultra-high velocities, with Lorentz factors up to $\ensuremath{\gamma}\ensuremath{\sim}10$. To this purpose, we first build a new lattice kinetic scheme by expanding the Maxwell-J\"uttner distribution function in an orthogonal basis of polynomials and applying an appropriate quadrature, providing the discrete versions of the relativistic Boltzmann equation and the equilibrium distribution. To achieve ultra-high velocities, we include a flux limiter scheme, and introduce the bulk viscosity by a suitable extension of the discrete relativistic Boltzmann equation. The model is validated by performing simulations of shock waves in viscous quark-gluon plasmas and comparing with existing models, finding very good agreement. To the best of our knowledge, we for the first time successfully simulate viscous shock waves in the highly relativistic regime. Moreover, we show that our model can also be used for near-inviscid flows even at very high velocities. Finally, as an astrophysical application, we simulate a relativistic shock wave, generated by, say, a supernova explosion, colliding with a massive interstellar cloud, e.g., molecular gas.

Comment on “Species separation in inertial confinement fusion fuels” [Phys. Plasmas 20, 012701 (2013)

A recent paper presents numerical simulations of shock waves in a two-ion-component plasma, investigating how species separation occurring in the latter can affect the nuclear fusion yield of inertial confinement fusion targets. Here, it is shown that an important physical mechanism has obviously been omitted in those calculations, which thus lead to significantly overestimated results.

Molecular Dynamics Simulations of Shock Waves in Mixtures of Noble Gases

We study the structure of a normal shock wave in noble gas mixtures (Xe-He and Ar-He) of various compositions using molecular dynamics and direct simulation Monte Carlo. The molecular dynamics simulations are first validated against experimental data. Good agreement is found between the molecular dynamics solutions and the experimental measurements, with the exception of the parallel temperature profile in the 24.7% Ar-He mixture, despite the satisfactory agreement between the parallel velocity profiles. Secondly, a validation against direct simulation Monte Carlo solutions obtained with the accurate generalized hard sphere model is presented. As expected, the generalized hard sphere direct simulation Monte Carlo and molecular dynamics solutions are in near-perfect agreement. Finally, molecular dynamics results are compared to those obtained with the lower fidelity variable hard sphere model, which, if inappropriately parametrized, fails to describe the shock wave structure. This work exemplifies how full molecular dynamics solutions could be used to precisely discern differences between phenomenological models of various accuracy.

Ultrashort shock waves in nickel induced by femtosecond laser pulses

The structure and evolution of ultrashort shock waves generated by femtosecond laser pulses in single-crystal nickel films are investigated by molecular dynamics simulations. Ultrafast laser heating is isochoric, leading to pressurization of a 100-nm-thick layer below the irradiated surface. For low-intensity laser pulses, the highly pressurized subsurface layer breaks into a single elastic shock wave having a combined loading and unloading time $\ensuremath{\approx}$10--20 ps. Owing to the time-dependent nature of elastic-plastic transformations, an elastic response is maintained for shock amplitudes exceeding the Hugoniot elastic limit determined from simulations of steady shock waves. However, for high-intensity laser pulses (absorbed laser fluence $>$$0.6\phantom{\rule{0.28em}{0ex}}\mathrm{J}/{\mathrm{cm}}^{2}),$ both elastic and plastic shock waves are formed independently from the initial high-pressure state. Acoustic pulses emitted by the plastic front support the motion of the elastic precursor resulting in a fluence-independent elastic amplitude; whereas the unsupported plastic front undergoes significant attenuation during propagation and may fully decay within the metal film.

Chondrules born in plasma? Simulation of gas–grain interaction using plasma arcs with applications to chondrule and cosmic spherule formation

Abstract–We are investigating chondrule formation by nebular shock waves, using hot plasma as an analog of the heated gas produced by a shock wave as it passes through the protoplanetary environment. Precursor material (mainly silicates, plus metal, and sulfide) was dropped through the plasma in a basic experimental set‐up designed to simulate gas–grain collisions in an unconstrained spatial environment (i.e., no interaction with furnace walls during formation). These experiments were undertaken in air (at atmospheric pressure), to act as a “proof‐of‐principle”—could chondrules, or chondrule‐analog objects (CAO), be formed by gas–grain interaction initiated by shock fronts? Our results showed that if accelerating material through a fixed plasma field is a valid simulation of a supersonic shock wave traveling through a cloud of gas and dust, then CAO certainly could be formed by this process. Melting of and mixing between starting materials occurred, indicating temperatures of at least 1266 °C (the olivine‐feldspar eutectic). The production of CAO with mixed mineralogy from monomineralic starting materials also shows that collisions between particles are an important mechanism within the chondrule formation process, such that dust aggregates are not necessarily required as chondrule precursors. Not surprisingly, there were significant differences between the synthetic CAO and natural chondrules, presumably mainly because of the oxidizing conditions of the experiment. Results also show similarity to features of micrometeorites like cosmic spherules, particularly the dendritic pattern of iron oxide crystallites produced on micrometeorites by oxidation during atmospheric entry and the formation of vesicles by evaporation of sulfides.

THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics

We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a variety of different reconstruction algorithms, such as the popular weighted essentially non oscillatory and monotonicity-preserving schemes, or the more specialised bandwidth-optimised WENO scheme that has been specifically designed for the study of compressible turbulence. We show the first systematic comparison of these schemes in Newtonian physics as well as for special-relativistic flows. In particular we will present the results obtained in simulations of grid-aligned and oblique shock waves and nonlinear, large-amplitude, smooth adiabatic waves. We will also discuss the results obtained in classical benchmarks such as the double-Mach shock reflection test in Newtonian physics or the linear and nonlinear development of the relativistic Kelvin-Helmholtz instability in two and three dimensions. Finally, we study the turbulent flow induced by the Kelvin-Helmholtz instability and we show that our code is able to obtain well-converged velocity spectra, from which we benchmark the effective resolution of the different schemes.

Mesoscale simulation of shock wave propagation in discrete Ni/Al powder mixtures

A numerical model is developed to simulate shock wave propagation in discrete Ni/Al powder mixtures. The model is used to investigate the particle-level deformation, heating, and mixing of two distinct Ni/Al powders, as mixing intensity dictates whether or not shock ignition is achieved in these reactive material systems. The main innovations of this work are (1) use of a rate-dependent, dislocation-based model of particle flow stress in the shock simulations and (2) quantitative analysis of the Ni/Al interfaces that are formed during wave propagation. An experimental powder, which is composed of micron-scale spherical Ni and Al particles, is simulated to validate the numerical model. An additional powder, composed of smaller particles, is simulated to investigate the effects of particle size on constituent deformation and mixing under shock wave loading. The simulations indicate that a reduction in particle size leads to increased Ni/Al interface temperature and dislocation density, as well as increased stress-sensitivity of Ni/Al interface formation. Finally, it is shown that accounting for the rate-dependence of particle flow stress likely yields improved accuracy in predicted flow morphologies, especially at intermediate stress wave amplitudes.

Shock propagation in liquids containing bubbly clusters: a continuum approach

AbstractThe present work investigates the influence of bubble clustering on the propagation of shock waves in bubbly liquids. A continuum model is developed to describe the macroscopic response of a bubbly liquid with a cluster structure, using a two-step homogenization technique. The proposed methodology allows us to simulate shock wave propagation over long distances with a small computation time and to study the effect of bubble clustering on the shock structure. It is shown that the typical length of the shock profile is related to the global response of the clusters instead of the single-bubble dynamics, as in homogeneous bubbly flows. The accuracy of the proposed modelling is assessed through comparisons with axisymmetric simulations, in which clusters are directly specified, with given positions and sizes, and with experimental data.