Lagrangian Code Research Articles

THREE-DIMENSIONAL MODELING OF LONG-WAVE RUNUP: SIMULATION OF TSUNAMI INUNDATION WITH GPU-SPHYSICS

Tsunamis need to be studied more carefully and quantitatively to fully understand their destructive impact on coastal areas. Numerical modeling provides an accurate and useful method to model tsunami inundations on a coastline. However, models must undergo a detailed verification and validation process to be used as an accurate hazard assessment tool. Using standards and procedures given by NOAA, a new code in hydrodynamic modeling called GPU-SPHysics can be verified and validated for use as a tsunami inundation model. GPU-SPHysics is a meshless, Lagrangian code that utilizes the computing power of the Graphics Processing Unit (GPU) to calculate high resolution hydrodynamic simulations using the equations given by Smooth Particle Hydrodynamics (SPH). GPU-SPHysics has proven to be an accurate tool in modeling complex tsunami inundations, such as the inundation on a conical island, when tested against extensive laboratory data.

Alfvén wave phase-mixing and damping in the ion cyclotron range of frequencies

Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k^2di^2 where k is wavenumber and di is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k^2di^2>>1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.

Isochoric heating with laser-accelerated proton beams

Numerical simulations are used to study acceleration of protons by intense laser pulses and the induced heating of a secondary target using this proton beam. Laser-plasma interaction and ion acceleration are modeled with a multidimensional, relativistic particle-in-cell code. Proton slowing-down and secondary target heating are computed with a two-dimensional Monte Carlo and a one-dimensional Lagrangian hydrodynamics codes. Strategies for optimization of heating uniformity include tailoring the accelerated proton spectrum with specific target geometries or laser pulse parameters. A trade-off must then be found between heating uniformity and efficiency. The parameters (temperature, depth and radius of heated zone, characteristic heating and hydrodynamics times) that could be obtained on current short pulse laser facilities, using a typical 50 fs Gaussian pulse with an intensity of several 1019 W/cm2, are explored.

Modelling and numerical simulation of plasma flows with two-fluid mixing

For the modelling of plasma flows at very high temperature such as the ones produced by laser beams, one must account for a bi-temperature compressible Euler system coupled to electron thermal conduction and radiative conduction. Moreover, mixing of two different fluids can occur, the two fluids occupying the same volume. For modelling such a phenomenon, instead of dealing with the conservation of mass, momentum and energy for each fluid, we propose here a simplified model which will be easier to implement in a multi-physics Lagrangian 2D code. The principle is to use a closure for expressing the relative velocity between the two fluids with the help of the gradient of the concentration. So, besides the classical system, the final model consists in a nonlinear diffusion equation for the concentration and an equation for the mixing kinetic energy (analogous to the one used in turbulence models). We present also first numerical 2D simulations using this model.

Nonlocal effects in gyrokinetic turbulence simulations using GENE

Modeling of anomalous transport, typically based on gyrokinetic theory, is an essential tool for better understanding and possibly improving the confinement of magnetic fusion plasmas. A well-benchmarked and established implementation of the gyrokinetic Vlasov-Maxwell system of equations can, for instance, be found in the software package GENE. This Eulerian code has recently been enhanced to optionally consider full radial temperature, density, and geometry variations allowing for investigations of nonlocal effects instead of using the radially local flux-tube approximation. First investigations on the importance of finite-size effects are presented and compared with results from the gyrokinetic Lagrangian PIC code ORB5 [S. Jolliet et al. 2007 Comput. Phys. Commun. 177 409, B.F. McMillan et al. 2008 Phys. Plasmas 15 052308]. Special attention is drawn to a specific nonlocal effect, namely heat flux avalanches.

Ignition studies in support of the European High Power Laser Energy Research Facility project

The European High Power Laser Energy Research Facility (HiPER) project is one of a number of large-scale scientific infrastructure projects supported by the European Commission’s Seventh Framework Programme (FP7). Part of this project involves the development of a target area for the exploration of inertial fusion energy. This paper describes some of the research that is being carried out by the author in support of this aspect of the program. The effects of different regions of the fusion target mixing prior to thermonuclear ignition have been investigated using the 1D Lagrangian radiation hydrodynamics simulation code HYADES. Results suggest that even low (few parts per million) levels of contamination of fuel by high-Z ion species may inhibit ignition due to radiative cooling of the ignition spot.

A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence

We compare the statistics of driven, supersonic turbulence at high Mach number using FLASH a widely used Eulerian grid-based code and PHANTOM, a Lagrangian SPH code at resolutions of up to 512^3 in both grid cells and SPH particles. We find excellent agreement between codes on the basic statistical properties: a slope of k^-1.95 in the velocity power spectrum for hydrodynamic, Mach 10 turbulence, evidence in both codes for a Kolmogorov-like slope of k^-5/3 in the variable rho^1/3 v as suggested by Kritsuk et al. and a log-normal PDF with a width that scales with Mach number and proportionality constant b=0.33-0.5 in the density variance-Mach number relation. The measured structure function slopes are not converged in either code at 512^3 elements. We find that, for measuring volumetric statistics such as the power spectrum slope and structure function scaling, SPH and grid codes give roughly comparable results when the number of SPH particles is approximately equal to the number of grid cells. In particular, to accurately measure the power spectrum slope in the inertial range, in the absence of subgrid models, requires at least 512^3 computational elements in either code. On the other hand the SPH code was found to be better at resolving dense structures, giving max. densities at a resolution of 128^3 particles that were similar those resolved in the grid code at 512^3 cells, reflected also in the high density tail of the PDF. We find SPH to be more dissipative at comparable numbers of computational elements in statistics of the velocity field, but correspondingly less dissipative than the grid code in the statistics of density weighted quantities such as rho^1/3 v. For SPH simulations of high Mach number turbulence we find it important to use sufficient non-linear beta-viscosity to prevent particle interpenetration in shocks (we require beta=4 instead of the default beta=2).

Neutrino oscillation and expected event rate of supernova neutrinos in the adiabatic explosion model

We study how the influence of the shock wave appears in neutrino oscillations and the neutrino spectrum using density profile of adiabatic explosion model of a core-collapse supernova which is calculated in an implicit Lagrangian code for general relativistic spherical hydrodynamics. We calculate expected event rates of neutrino detection at SK and SNO for various theta_{13} values and both normal and inverted hierarchies. The predicted event rates of bar{nu}_e and nu_e depend on the mixing angle theta_{13} for the inverted and normal hierarchies, respectively, and the influence of the shock appears for about 2 - 8 s when sin^2 2 theta_{13} is larger than 10^{-3}. These neutrino signals for the shock propagation is decreased by < 30 % for bar{nu}_e in inverted (SK) or by < 15 % for nu_e in normal hierarchy (SNO) compared with the case without shock. The obtained ratio of the total event for high-energy neutrinos (20 MeV < E_{nu} < 60 MeV) to low-energy neutrinos (5 MeV < E_{nu} < 20 MeV) is consistent with the previous studies in schematic semi-analytic or other hydrodynamic models of the shock propagation. The time dependence of the calculated ratio of the event rates of high-energy to low-energy neutrinos is a very useful observable which is sensitive to theta_{13} and hierarchies. Namely, time-dependent ratio shows clearer signal of the shock propagation that exhibits remarkable decrease by at most factor \sim 2 for bar{nu}_e in inverted (SK), whereas it exhibits smaller change by \sim 10 % for nu_e in normal hierarchy (SNO). Observing time-dependent high-energy to low-energy ratio of the neutrino events thus would provide a piece of very useful information to constrain theta_{13} and mass hierarchy, and eventually help understanding the propagation how the shock wave propagates inside the star.

Numerical simulation of friction stir spot welding process for aluminum alloys

Thermo-mechanical simulations of the Friction Stir Spot Welding (FSSW) processes were performed for AA5083-H18 and AA6022-T4, utilizing commercial Finite Element Method (FEM) and Finite Volume Method (FVM) codes, which are based on Lagrangian and Eulerian formulations, respectively. The Lagrangian explicit dynamic FEM code, PAM-CRASH, and the Eulerian Computational Fluid Dynamics (CFD) FVM code, STAR-CD, were utilized to understand the effect of pin geometry on weld strength and material flow under the unsteady state condition. Using FVM code, material flow patterns near the tool boundary were analyzed to explain weld strength difference between welds by a cylindrical pin and welds by a triangular pin, whereas the frictional energy concept using the FEM code had a limited capacity to explain the weld strength difference.

EvoL: the new Padova Tree-SPH parallel code for cosmological simulations

<i>Context. <i/>We present the new release of the Padova <i>N<i/>-body code for cosmological simulations of galaxy formation and evolution, EvoL. The basic Tree + SPH code is presented and analysed, together with an overview of the software architectures.<i>Aims. <i/>EvoL is a flexible parallel Fortran95 code, specifically designed for simulations of cosmological structure formations on cluster, galactic and sub-galactic scales.<i>Methods. <i/>EvoL is a fully Lagrangian self-adaptive code, based on the classical oct-tree by Barnes & Hut (1986, Nature, 324, 446) and on the smoothed particle hydrodynamics algorithm (SPH, Lucy 1977, AJ, 82, 1013). It includes special features like adaptive softening lengths with correcting extra-terms, and modern formulations of SPH and artificial viscosity. It is designed to be run in parallel on multiple CPUs to optimise the performance and save computational time.<i>Results. <i/>We describe the code in detail, and present the results of a number of standard hydrodynamical tests.

Computational investigation of the magneto-Rayleigh–Taylor instability in Z-pinch implosions

The instability evolvement induced by single mode and random density seeds have been investigated by using the Magnetics Atom Radiation Electron Dynamics (MARED) code, which is a two dimensional, three temperature, radiation magnetohydrodynamic Lagrangian code developed for the Z-pinch implosion simulation. The instability development during each stage (linear, weak nonlinear, and nonlinear) and its corresponding characteristics are studied with single-mode seeds. The evolvement of the dominant mode and its final wavelength are revealed through the development of seeds composed of modes covering the “whole” spectrum or just a “band-type” range of it. In addition, the relationship between the initial perturbation amplitude and the final x-ray output are also discussed. Through these discussions, the MARED code is found able to reproduce the primary dynamic characteristics of the Z-pinch implosions and the development of the instability qualitatively agrees with the theoretical analyses and experimental observations, which shows us a modest expectation of the broad coverage of the future application.

激光驱动飞片过程中激光烧蚀深度的计算

A one-dimensional bulk absorption model to simulate the accelerating process of laser-driven flyer plate is presented, in which the laser energy deposition, the laser absorption in plasma and acceleration of flyer plates are included. In the laser intensity range of GW/cm2, the gasdynamical behavior of the ablated foil plasma is described with a modified one-dimensional Lagrangian hydrodynamic code. The histories of the flyer velocity and the density profiles are given by this model. The calculated results of the ablated thickness of films in the launch of laser-driven flyer plates are in good agreement with the experimental results.

Simplified one-dimensional calculation of 13.5 nm emission in a tin plasma including radiation transport

Many next generation lithography schemes for the semiconductor industry are based on a 13.5 nm tin plasma light source, where hundreds of thousands of 4d-4f, 4p-4d, and 4d-5p transitions from Sn5+–Sn13+ ions overlap to form an unresolved transition array. To aid computation, transition arrays are treated statistically, and Hartree–Fock results are used to calculate radiation transport in the optically thick regime with a one-dimensional Lagrangian plasma hydrodynamics code. Time-dependent spectra and conversion efficiencies of 2% in-band 13.5 nm emission to laser energy are predicted for a Nd:YAG (yttrium aluminum garnet) laser incident on a pure tin slab target as a function of laser power density and pulse duration at normal incidence. Calculated results showed a maximum conversion efficiency of 2.3% for a 10 ns pulse duration at 8.0×1010 W/cm2 and are compared to experimental data where available. Evidence for the need to include lateral expansion is presented.

Numerical tests and properties of waves in radiating fluids

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare the solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.

A lagrangian approach to analyse the tropospheric ozone climatology in the tropics: Climatology of stratosphere–troposphere exchange at Reunion Island

Sixteen years of ozone measurements (1992–2006) at Reunion Island (21°S, 55.5°E) have been processed to detect stratospheric signatures on each single ozone profile. The characterisation method consists in the advection of the potential vorticity (PV) over two to ten days of backtrajectory with the lagrangian trajectory code LACYTRAJ. LACYTRAJ is a Trajectory-Reverse Domain Filling code using the ERA40 ECMWF database and allowing the reconstruction of high resolution advected PV profiles. Correlation between high values of ozone mixing ratio and high PV is interpreted as a stratospheric signature. A climatology of STE events at Reunion has been derived and reveals that STE events occur more frequently during spring (SON) and summer (DJF). The method is tested for a set of PV threshold values (i.e. 1 PVU, 1.5 PVU and 2 PVU) and for a set of duration of backtrajectories (i.e. 2 days, 5 days and 10 days). The number of detected STE is sensitive to PV threshold values and duration criterions. For instance, the number of stratospheric intrusions detected in October with a 1.5 PVU criterion ranges between 25% (2 days of backtrajectories) and 56% (10 days of backtrajectories). The vertical distributions of STE show intrusions covering the whole free troposphere (between 7 and 15 km) and mainly located in the upper troposphere. Finally, results show that an important number of stratospheric intrusions are detected during spring and in the upper troposphere what points at the contribution of the stratospheric source to the tropospheric ozone spring maximum which is strongly influenced by the biomass burning emissions from South Africa and Madagascar.

Simulation of magmatic and metamorphic fluid production coupled with deformation, fluid flow and heat transport

A methodology for simulating magmatic and metamorphic fluid production coupled with mechanical deformation, fluid flow and heat transport is presented. The methodology is implemented in FLAC3D, a lagrangian finite difference code designed for simulation of coupled deformation, fluid flow and heat transport in porous media. The rate of metamorphic fluid production is governed by the rate of temperature change and an approximation of the variation in bound water content of appropriate lithologies with temperature. Magmatic fluid production is governed by the rate of cooling and the variation in free water content of a mafic granitic magma with temperature. Changes in porosity and fluid pressure due to fluid production, deformation, and thermal expansion are taken into account. Dilation associated with thermal expansion and fluid production leads to rotation of the principal stresses around fluid source regions. Fluid properties are calculated using an equation of state for pure water. The methodology has been applied to examples representing aspects of Archaean gold mineralisation in Western Australia, providing insight into the role of magmatic and metamorphic fluids in mineralisation, and effects arising from interactions between deformation, heat transport and fluid production.

High-speed frictional slip at metal-on-metal interfaces

In this study plate-impact pressure-shear friction experiments are employed to investigate dynamic slip resistance and time-resolved growth of molten metal films during dry metal-on-metal slip under extreme interfacial conditions. By employing a tribo-pair comprising of a hard tool-steel against a relatively low melt-point metal (7075-T6 Al alloy), interfacial normal stress of up to 5 GPa and slip speeds of approximately 250 m/s have been achieved. These extreme interfacial conditions are conducive to the development of molten metal film at the tribo-pair interface. A Lagrangian finite element code is developed to understand the evolution of the thermo-mechanical fields and their relationship to the observed slip response. The code accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below the melting point of the tribo-pair materials are described as isotropic, thermally softening, elastic–viscoplastic solids. For material elements with temperatures in excess of the melt temperature a purely Newtonian fluid constitutive model is employed. The results of this hybrid experimental–computational approach provide new insights into the thermo-plastic interactions during the high-speed metal-on-metal slip. During the early part of frictional slip the coefficient of kinetic friction is observed to decrease with increasing slip velocity. During the later part, transition in interfacial slip occurs from dry metal-on-metal sliding to the formation of molten Al film at the slip interface. During this slip phase, the interfacial resistance approaches the shear strength of the molten Al alloy under normal pressures of approximately 1–4.5 GPa and shear-strain rates of ∼10 7 s −1. The results of the study indicate that under such extreme interfacial conditions molten aluminum films maintain a shearing resistance as high as 50–100 MPa. Scanning electron microscopy of the slip surfaces reveal molten aluminum to be smeared on the tribo-pair interface at high impact velocities. Also, the extent of the molten area, as observed from the SEM micrographs, increases with increasing impact velocities.

Semi-Infinite Target Penetration by Ogive-Nose Penetrators: ALEGRA/SHISM Code Predictions for Ideal and Nonideal Impacts

The physics of ballistic penetration mechanics is of great interest in penetrator and countermeasure design. The phenomenology associated with these events can be quite complex, and a significant number of studies have been conducted ranging from purely experimental to “engineering” models based on empirical and/or analytical descriptions to fully coupled penetrator/target, thermomechanical numerical simulations. Until recently, however, there appears to be a paucity of numerical studies considering “nonideal” impacts (Goldsmith, 1999, “Non-Ideal Projectile Impact on Targets,” Int. J. Impact Eng., 22, pp. 95–395). The goal of this work is to demonstrate the SHISM algorithm implemented in the ALEGRA multimaterial arbitrary Lagrangian Eulerian code (Boucheron, et al., 2002, ALEGRA: User Input and Physics Descriptions, Version 4.2, SAND2002-2775, Sandia National Laboratories, Albuquerque, NM). The SHISM algorithm models the three-dimensional continuum solid mechanics response of the target and penetrator in a fully coupled manner. This capability allows for the study of nonideal impacts (e.g., pitch, yaw, and/or obliquity of the target/penetrator pair). In this work predictions using the SHISM algorithm are compared with previously published experimental results for selected ideal and nonideal impacts of metal penetrator-target pairs. These results show good agreement between predicted and measured maximum depths-of-penetration (DOPs), for ogive-nose penetrators with striking velocities in the 0.5–1.5 km/s range. Ideal impact simulations demonstrate convergence in predicted DOP for the velocity range considered. A theory is advanced to explain disagreement between predicted and measured DOPs at higher striking velocities. This theory postulates uncertainties in angle-of-attack for the observed discrepancies. It is noted that material models and associated parameters used here were unmodified from those in literature. Hence, no tuning of models was performed to match experimental data.

Influence of a preplasma on electron heating and proton acceleration in ultraintense laser-foil interaction

Two-dimensional particle-in-cell simulations are performed to study laser-induced proton acceleration from solid-density targets in the presence of laser-generated preformed plasma. The preplasma generation and hydrodynamics are described using a one-dimensional Lagrangian code. The electron acceleration mechanism is shown to depend on the plasma scale length, exhibiting a transition from j⃗×B⃗ heating to standing wave heating as smoother and smoother profiles are considered. Accordingly, the relativistic electron temperature and the cutoff proton energy are found to increase with the preplasma characteristic length.

Two dimensional mesoscale simulations of projectile instability during penetration in dry sand

To gain insight into the instability and trajectory change in projectiles penetrating dry sand at high velocities, two dimensional plane strain mesoscale simulations were carried out using representative models of a particulate system and of a small projectile. A program, ISP-SAND, was developed and used to generate the representative particulate system with mean grain sizes of 60 and 120 μm as well as ±30% uniform size distribution from the mean. Target porosities ranged from 30% to 40%. The penetration of ogive nose steel projectiles with caliber radius head of 3.5 and length-to-diameter (l/d) ratio of 3.85 was simulated using the updated Lagrangian explicit parallel finite element code ISP-TROTP. Deformation of the projectile and individual sand grains was analyzed using a nonlinear elastic-inelastic model for these materials. Grain-grain and grain-projectile interactions were analyzed using a contact algorithm with and without friction. Projectile instability was quantified and compared using the lateral displacement of the center of mass, lateral force acting on the projectile, and its rotational momentum about the center of mass. The main source of projectile instability and the ensuing trajectory change in the penetration simulations was found to be the inhomogeneous loading of the projectile due to the heterogeneities and randomness inherent in a particulate media like sand. The granularity of the media has not been considered explicitly in previous work. Projectile instability increased with impact velocity, as expected. However, it also increased for the case of elastic impactor that preserved the nose shape, with an increase in grain size, and for uniform grain sizes. Moreover, friction, inherently present in geologic materials, was found to be a major contributor to instability. Conclusions derived from one projectile depth simulations were confirmed by two deeper penetration simulations considering up to three full lengths of penetration (requiring a larger sand target). The deep penetration simulation predicted considerable instability with a trajectory change of approximately 45° when friction was considered in the dry sand medium. An overall conclusion of this work is that projectile penetration studies in geologic materials need to explicitly consider the heterogeneous or particulate nature of these materials.