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ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

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ALE3D: An Arbitrary
Lagrangian-Eulerian
Multi-Physics Code
Charles Noble, Andrew Anderson, Nathan Barton, Jamie
Bramwell, Arlie Capps, Michael Chang, Jin Chou, David
Dawson, Emily Diana, Timothy Dunn, Douglas Faux, Aaron
Fisher, Patrick Greene, Ines Heinz, Yuliya Kanarska, Saad
Khairallah, Benjamin Liu, Jon Margraf, Albert Nichols, Robert
Nourgaliev, Michael Puso, James Reus, Peter Robinson, Alek
Shestakov, Jerome Solberg, Daniel Taller, Paul Tsuji,
Christopher White, Jeremy White
May 23, 2017
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
Lawrence Livermore National Laboratory ii
Disclaimer
This document was prepared as an account of work sponsored by an agency of the United States
government. Neither the United States government nor Lawrence Livermore National Security,
LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any
legal liability or responsibility for the accuracy, completeness, or usefulness of any information,
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name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its
endorsement, recommendation, or favoring by the United States government or Lawrence
Livermore National Security, LLC. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States government or Lawrence Livermore
National Security, LLC, and shall not be used for advertising or product endorsement purposes.
Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security,
LLC, for the U.S. Department of Energy, National Nuclear Security Administration under
Contract DE-AC52-07NA27344.
LLNL-TR-732040
Introduction
ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian-
Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and
axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid
finite element and finite volume formulation to model fluid and elastic-plastic response of
materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates
many physical phenomena.
Figure 1. ALE3D supports a wide range of applications.
ALE3D supports a wide range of simulation needs. The ALE and mesh relaxation capabilities
broaden the scope of application in comparison to tools restricted to Lagrangian-only or
Eulerian-only approaches, while maintaining accuracy and efficiency for large, multi-physics
and complex geometry simulations. For some applications ALE can deliver accuracy similar to
Eulerian techniques using as few as 1/10th the number of mesh elements and a reduction in
memory requirements.
Figure 2 provides a chart showing that ALE3D has an integrated flexible and extendable
architecture. Beyond its foundation as a hydrodynamics and structures code, ALE3D has multi-
physics capabilities that integrate various packages through an operator splitting approach.
Additional ALE3D features include heat conduction, chemical kinetics, species diffusion,
incompressible flow, a wide range of material models, chemistry models, multi-phase flow, and
magnetohydrodynamics, which can be used in numerous combinations for long (implicit) to
short (explicit) time-scale applications.
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
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Figure 2. ALE3D has an integrated flexible and extendable architecture supporting a
variety of mesh generators, and material models can be pluggable components.
The discretized domain or mesh may consist of arbitrarily connected hexahedral, shell and beam
elements. In 2D simulations, the mesh can comprise of arbitrarily connected quadrilaterals. The
mesh can be constructed from disjointed blocks of elements that interact at the boundaries via
slide surfaces or other types of boundary conditions.
Large mesh distortions can be addressed via mesh relaxation and/or the use of ALE techniques
where material is advected through the mesh. All components of the code participate in
advection and all the mature capabilities operate with slide surfaces. Advection is the process
whereby the mesh is modified to alleviate tangling or to preserve an Eulerian grid. Advection is
implemented in a Lagrange plus remap fashion. For each cycle, after a Lagrangian motion, the
state variables flow from the original mesh to the modified mesh. The mesh is allowed to cross
material boundaries and create multi-material elements. The ALE and mesh relaxation capability
broadens the scope of applications in comparison to tools restricted to Lagrangian or Eulerian
(advection) only approaches, while maintaining accuracy and efficiency for large, multi-physics
and complex geometry simulations.
Slide surfaces are boundaries between disjoint sections of the grid that may or may not be in
contact. They represent either physical contact discontinuities or a discontinuity in the zoning.
The unstructured grid is composed of 3D hexagonal elements that can be arbitrarily connected.
Triangular or prismatic elements are not allowed, but shell and beam structural elements can
couple to 3D elements.
The 2D capability includes explicit and implicit hydrodynamics, thermal diffusion, chemistry,
deflagration, shape generation, advection, and most explicit slide surface features.
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Thermal and chemistry packages are tightly coupled and have been successfully used for long
(implicit) to short (explicit) time-scale applications. The incompressible flow module has been
used in simulations of turbulent thermal convection. A multi-phase flow package (a continuum
representation of solid particulate transport in solids, liquids and gases and impulse load at
impact) is available for simulation of multi-phase fluid, structure interaction. Another package
that solves the magnetohydrodynamics equations (MHD in 3D only) can simulate a variety of
high magnetic field, high velocity, thermal applications.
ALE3D operates on a wide variety of platforms, ranging from laptops to the world’s largest
supercomputers. ALE3D has native implementations for Windows™ and Mac workstations for
smaller scale problem sets, and it is portable to virtually any Unix-based machine with C++/C
and Fortran compilers available. The code will also run in parallel on multi-processor
Windows™ and Mac machines. While most users will be interested in Linux-based versions of
the code, it has also been ported to several other lightweight kernel operating systems.
Operation on massively parallel machines has always been a core requirement for the code.
Parallelization is implemented by decomposing the mesh into computational subdomains.
Message passing is the primary mode for communication between domains. The emphasis on
message passing means that it is possible to run parallel computations on a network of
workstations, as well as utilizing multi-core processors available on most workstations.
Explicit Hydrodynamics
ALE3D’s hydrodynamics capability captures the behavior of solids and fluids and has been
successfully used for long (implicit) to short (explicit) time-scale applications. The explicit
hydrodynamics module was developed to model the behavior of objects undergoing deformation
due to the application of shocks in the kilobar regime. For such problems, the natural time step is
consistent with the Courant time scale which governs the stability of the equations.
The code explicitly conserves mass and momentum. Following DYNA3D (Hallquist, 1982), the
stress gradients and strain rates for the Lagrange step are evaluated by a lowest-order finite-
element method. A diagonal mass matrix is used. For second-order accuracy a staggered space
and time grid is also used. The stress gradient calculation has been modified so that it is
represented by an integral of the shape function over the surface of an element rather than an
integral of the gradient of the shape function over the volume. (The stress in general is
discontinuous at the surface so that the stress gradient is a delta function.) This modification
corrects a problem in which distorted elements generated forces even though the stress field was
constant. Likewise, a more accurate volume calculation is done following J. Dukowicz (JCP)
(1984). Hour-glass modes are damped using the method of Flanagan and Belytschko (1981).
The hydrodynamics is energy based rather than temperature based. Energy conservation is not
explicitly enforced but depends on the accuracy of the time integration. This averts the problem
of converting lost kinetic energy into internal energy and overheating materials. The pressure,
viscosity and strain work evaluations are fully time centered. To integrate –PdV for nonlinear
equations-of-state, a third-order Runge-Kutta method is used. Although the explicit
hydrodynamics module is isentropic except at shocks, a temperature variable exists for each
region, and the temperature Equation of State (EOS) can be evaluated either as part of a
constitutive model or from EOS tables.
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Shocks are treated with a scalar artificial viscosity. The default version simply uses
d
v/v for
compressing elements. Both linear and quadratic terms are available. R. Christensen’s monotonic
artificial viscosity (Christensen, 1990) has also been implemented. This scalar viscosity is
constructed using velocity gradients from which the linear component of the gradient has been
subtracted. The form can be derived from the linearized Riemann problem.
The most commonly used equations-of-state and constitutive models are analytic models using
the Mie-Grüneisen and Steinberg-Guinan forms, respectively (Steinberg, 1980 and 1996).
Several engineering constitutive models are available to facilitate modeling of structures.
Tabular equation-of-state models can be accessed through the Livermore equation-of-state
(LEOS) tables. The majority of the available material models are for isotropic materials and a
von Mises yield condition is applied. The deviatoric part of the stress tensor is integrated through
time, and the Jaumann stress rate is used to satisfy objectivity. A number of micro-structurally
based models have also been added to provide a more accurate representation of damage
evolution mechanisms leading to fracture and to capture anisotropy at both the single crystal and
polycrystal size scales. A few of these latter models do not have time-centered energy
evaluations or use high-order integration for the EOS. For all material models, a Navier-Stokes
viscosity is available to augment the stress tensor.
For most problems, high explosive (HE) detonation is simulated by using a programmed burn
model with a beta burn override. Several options are available for computing HE lighting times.
Reactive flow models for HE detonation are also available. These models use pressure and
volume dependent rate laws to describe the detonation process. The reactive flow models are
zoning dependent, need high resolution, and may have limited usefulness in 3D.
Implicit Mechanics
The implicit mechanics module was developed to model problems that evolve at time scales that
are orders of magnitude greater than the Courant time scale that determines the stability of the
explicit equations. The implicit hydrodynamics is a finite element displacement formulation with
single- or eight-point integration. Single-point integration requires the addition of hourglass
stabilization forces. The formulation solves the non-linear equilibrium equations using a
Newton-Raphson iteration surrounding a linearization of the equations. This linearization is
based on estimates for material properties, etc., at the end of the time step. Convergence of the
non-linear iterations is achieved when corrections to the displacements and the nodal forces are
sufficiently small. Slide surface constraints are supported. The implicit time integration can be
run using a quasi-static approximation, or the inertial terms can be included via a Hilber-Hughes-
Taylor stabilization of the standard Newmark time integration. The code can convert
automatically from implicit to explicit hydrodynamics when the time step is sufficiently small
that the explicit integration is more computationally efficient. The reverse transfer from explicit
to implicit hydrodynamics is also possible.
Slide Surfaces
The interaction between multiple material surfaces is captured with a numerical technique called
slide surfaces. As mentioned above, slide surfaces model contact discontinuities or mesh
discontinuities. Slide surfaces may be either two-sided (master / slave) or single-sided. In two-
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sided surfaces, the nodes of each side interact with the faces of the other side to conserve
momentum and enforce impenetrability. With single-sided surfaces, any node may interact with
any face, barring nearest neighbors. Single-sided slides are useful for surfaces that fold upon
themselves and surfaces consisting of many discrete segments.
There are several options for contact enforcement: the point-on-plane method for explicit or
implicit hydrodynamics, the common-plane method (available only for single-sided surfaces) for
explicit hydrodynamics, and a mortar method for implicit hydrodynamics. In addition, ALE3D
provides an automatic slide surface capability with either the point-on-plane or common-plane
approach.
For the point-on-plane method, slide surface velocities are computed with a momentum
conserving algorithm. Each side of a slide surface is independently accelerated using interpolated
physics quantities from the opposing side. First a node is accelerated as if it were on a free
surface or a surface with a pressure boundary condition. The boundary pressure is the average of
the normal stresses on each side of the surface. The acceleration of the node is decomposed into
normal and tangential components. The normal component for each side is combined with the
interpolated normal component from the opposite side to form a center-of-mass acceleration.
This acceleration is used to integrate the velocity. Unless friction is called for, the tangential
acceleration remains that of the free surface. A distinction is then made between master and slave
surfaces for the final application of continuity boundary conditions. This last step corrects for
any lack of perfect continuity in the normal direction due to truncation errors.
Techniques for ordering nodes on one side of the slide surface with respect to nodes on the other
side and for making projections normal to the slide surface are borrowed from DYNA3D. These
techniques have been modified, however, to make them more robust. The ordering algorithm has
been improved so that nodes are not prone to penetrating the slide surface and getting lost. The
normal projection algorithm uses normals that vary across a slide surface element and capture the
effects of curvature of the surface.
The opposing sides of a slide surface may be separated and come into contact during the course
of a calculation. This is called a void. When voids close, the momenta from the opposing sides
are combined to form the center-of-mass momentum. The collision is inelastic for the first layer
of nodes on each side of the slide surface. Void closing is always calculated from the perspective
of the master side. This is done to avoid miscounting momentum transferred from one side to the
other if nodes on each side of the surface close in different cycles.
By default, the tangential velocities on each side of a slide surface are decoupled. However,
coulomb friction can be applied. In this case, a tangential force is applied that opposes any
relative velocity. This force is proportional to the normal force that is inferred from the
acceleration required to change the normal velocity from its free surface value to its center-of-
mass value. For so-called tied sliding both the normal and tangential accelerations are combined
into center-of-mass accelerations. This enables one to use slide surfaces to affect a zoning
change in the middle of a region.
Special provision is made for intersecting or overlapping slide surfaces. Intersections are
assumed to be orthogonal and errors grow to the extent that this condition is violated.
The common-plane method of contact enforcement checks for contact between each pair of
faces, defined as penetration of a plane constructed midway between the two faces. If both faces
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penetrate the plane, then the intersection of their penetrations projected onto the common plane
is the area of contact, and an opposing force (penalty method) is applied to resist and reverse
penetration. This force is distributed to the nodes of the faces in contact.
The mortar method of contact is a face-on-face type of method and is implemented for use with
implicit hydrodynamics. This method considers the faces on one side of a surface that are
connected to a node, and the faces on the other side that overlap these faces, and enforces that a
weighted sum of the gap volumes of the overlap be zero.
At most one slide surface may be designated as an autocontact surface. The faces of the
autocontact surface are not explicitly specified, but typically consist of all external faces (faces
with a zone on only one side) which are not included in any other slide surface.
FEusion Embedded Mesh Coupling
The FEusion library provides an embedded mesh method that allows the coupling of two
separate, spatially overlapping meshes. The embedded mesh approach can greatly simplify the
pre-processing requirements while potentially avoiding many run-time issues related to tangling
of an ALE mesh conforming around Lagrange objects.
The approach used here, which was developed by Puso et al., uses Lagrange multipliers from a
piecewise constant space on the cut background elements to constrain the jump between
background and foreground velocities. A stabilization scheme penalizes the difference in face-
adjacent Lagrange multipliers tractions. These multipliers are solved for implicitly using a
conjugate gradient (CG) iterative method on the subset of the mesh where they are active, i.e.,
only on the cut background cells.
Advection
ALE3D uses an arbitrary Lagrangian-Eulerian (ALE) algorithm. The algorithm consists of two
distinct steps: (i) a Lagrangian step that updates nodal positions, nodal velocities, and zonal
quantities, and (ii) a remap/advection step that remaps the results of the Lagrangian step onto a
mesh determined by the relaxation method specified by the user.
In the ALE3D implementation of the ALE algorithm, the Lagrangian step is executed, a new
representation of the mesh is created, and then material variables such as mass, momentum, and
energy are advected from the old mesh to the new mesh. The advection of the material variables
is done by computing fluxes of the state variables between the Lagrangian mesh and the new
mesh. The pressure is recalculated after the remap with a call to the EOS routines. If the
materials have strength, the stress deviators, plastic strain, and other constitutive model variables
are also advected.
The advection step comprises a relaxation phase and an advection phase. An “ideal” grid is first
created using an equipotential or condition number grid relaxation algorithm. (A pure Eulerian
option is also available.) The state variables are then remapped onto the new grid by constructing
fluxes between the old grid and the new grid. The fluxes for extensive variables (mass, internal
energy, and momentum) are conservative. For pure zones, a second-order, monotonic algorithm
is used to calculate the fluxes. This technique was pioneered by van Leer (1977). Velocities are
updated by applying the results of momentum conservation. This leads to a loss of kinetic energy
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
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(which is quadratic rather than linear in the velocity), and high-order advection is required to
limit the loss. As a rule, lost kinetic energy is not added to internal energy to explicitly force total
energy conservation. However, kinetic energy lost in the vicinity of a shock can be put back into
the internal energy field. This is useful for the purpose of propagating shocks over long distances
without degradation.
For problems with several material regions, the process of advection can create mixed elements
in which more than one material region resides in an element. While material region interfaces
are currently not tracked explicitly during the advection step, they are inferred from the volume
fractions of each region in neighboring zones. This is done to determine the order in which
regions are moved from one element to another. The ordering process preserves the integrity of
region objects as they move through the mesh. When volume fractions provide no guidance,
regions are moved from one element to another in the order in which they are numbered, so it
can be very important to order regions in such a way that “more important” (i.e., non-
background) materials have lower region numbers. Separate values of the thermodynamic state
variables are maintained for each region in a mixed element, and advection is done using a first-
order upwind method. Regions in mixed elements are allowed to relax towards pressure
equilibrium. The relaxation algorithm is based on a linearized solution to the Riemann problem.
Free surfaces are not relaxed unless tangential relaxation is explicitly set up for a free surface
nodeset. Advection can take place up to, but not across, a slide surface. Ordinarily only the slave
nodes of a two-sided slide surface are relaxed, but master-side relaxation is available (similar to
tangential relaxation). If necessary, and if slide surface nodes are forced to line up across the
slide surface, the slide surface can be deleted during the course of the calculation and thereby
allow for advection after that time.
Thermal Diffusion
Thermal diffusion is the conduction of heat from a hot to a cold temperature location in a solid or
fluid. The thermal diffusion module was originally incorporated to model manufacturing
processes such as casting, forging, rolling, and extrusion. It is implemented in a manner that
allows for application to most engineering heat transfer problems. The thermal diffusion module
has also been coupled to a chemical kinetics module for the purpose of modeling thermal
ignition of high explosives. The existing capabilities include conduction with orthotropic and
temperature dependent properties, phase changes, enclosure thermal radiation, thermal contact
resistance across interfaces, and temperature, flux, thermal radiation, and convection boundary
conditions.
Two modes of coupling between the hydrodynamics and the heat transfer are supported. The first
solves the hydrodynamics and heat transfer consecutively at each step by operator splitting. The
heat transfer step changes energy without changing volume and the hydrodynamics step changes
volume without transferring heat. Cell-centered energy is made consistent with nodal
temperatures by including an adiabatic expansion source term, g (dV/V), and strain heating.
Chemical reactions also contribute a source term. The second mode solves the hydrodynamics
and heat transfer iteratively using the intermediate results of the package until they both
converge.
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The heat conduction equations are solved using a finite element approach. The solution includes
implicit time integration, direct or iterative matrix solution, hexahedral elements with second-
order Gaussian quadrature integration, nonlinear convergence by successive substitution or
Newton-Raphson methods, and variable time step control with sub-cycling of the thermal
diffusion and hydrodynamics.
Heat transfer can occur across a slide surface by perfect thermal contact or by heat conduction
using ‘virtual elements’. Virtual elements are conduction and thermal radiation resistive elements
that are inserted between the slide surfaces. The virtual elements can have zero thickness or their
resistance can be scaled with gap distance. The perfect thermal contact algorithm is formulated
as a penalty method. It maintains symmetry at boundary edges through geometrical and mass
weighting, and scales the penalty function with the magnitude of the diagonal term of the
coefficient matrix.
Chemistry and Chemical Diffusion
ALE3D’s chemistry model is capable of capturing the composition, structure and properties of
chemically reacting materials. The chemical kinetics module was developed to model
decomposition of high explosive materials in thermal environments. A chemical material is a set
of materials that can transform among each other. These materials (or species) define all the
properties of the chemical material. Several models for combining the properties of the
individual species are provided. In principle, any material model that supplies a temperature and
pressure can be used as a species in a chemical material. It is even possible to combine several
models by including a chemical material as a species in another chemical material.
The composition of a chemical material can be modified through a set of user defined chemical
reactions. ALE3D organizes the reactions into groups that act on the same set of species. Only
reactions that involve all of the species present in a chemical material are included in that
material’s full reaction scheme. The change in composition is calculated implicitly with a self-
correcting Newton-Raphson technique. The temperature derivative of the change is also
calculated for use by the thermal module.
The chemical kinetics package is normally run tightly coupled to the thermal module. However,
it can also be run during the hydrodynamics phase. When run during the hydrodynamics phase,
the chemical kinetics package can be used to emulate a variety of reactive flow detonation
propagation models. This emulation is accomplished by including the appropriate set of reaction
mechanisms with the appropriate material models for the reacting species. Both the standard
Lee-Tarver (Lee and Tarver, 1980) and PERMS (Propellant Energetic Response to Mechanical
Stimuli) (Maienschein et al., 1997) models can be implemented this way.
A chemical diffusion model is also available in ALE3D. It allows for diffusion within a chemical
material (not between chemical materials). The species diffusion equations are solved using a
finite-volume approach. The operator is explicit in time and computes fluxes of chemical species
across faces between elements based on the locally determined chemical potential gradient. Both
tracer, where the diffusing species is assumed to be only a small fraction of the total mass of the
system, and non-tracer models are available.
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Incompressible Flow
The incompressible flow package solves the incompressible Navier-Stokes equations and is
useful for simulations involving a fluid that can be approximated with a constant density, such as
low-speed aerodynamics or internal fluid mechanics. As a rule of thumb, flows with a Mach
number less than 0.3 are candidates to be considered incompressible. An obvious exception to
this rule is any flow where the density variations drive the flow, no matter how fast it is going.
The package can be coupled to the thermal package for simulations of natural convection of a
fluid with temperature gradients. The incompressible flow model may also be run simultaneously
with the standard ALE hydro package for coupled fluid-structure problems. The fluid and solid
components are coupled through their boundary conditions. The incompressible flow module
includes explicit, semi-implicit (either the advection or viscous terms implicit) and fully implicit
time integration options. An advection-diffusion solver is also available to model species
concentrations within an incompressible material.
Multiphase Flow
The ALE3D multiphase flow model was developed for simulating mixed materials with separate
velocity fields. This model reuses the species framework developed for the chemical materials.
In principle, any ALE3D material model that supplies a temperature and pressure can be used as
a species in the chemistry and multiphase packages. Often, it is desirable to create a hierarchical
chemical material for use in the multiphase model. An example of this is a multiphase flow of
particles in a fluid flow, each composed of multiple constituents that can react amongst
themselves. This hierarchy of material models enables chemical reactions to be modeled in a
unified manner with multiphase flow.
There are several models for drag and compaction in the multiphase flow package. These
include semi-analytic models where the drag terms can be integrated analytically to those which
are evaluated using backward Euler. For cases where the compaction viscosity is unknown, the
pressure relaxation module defaults to an infinite relaxation rate or pressure equilibration.
Magnetohydrodynamics
ALE3D’s magnetohydrodynamics model is capable of capturing the dynamics of electrically
conducting solids and fluids. The magnetohydrodynamics (MHD) module was developed
primarily for the modeling of coupled electro-thermal-mechanical (ETM) systems that are
inherently 3D in nature. Example applications for this capability include explosively driven
magnetic flux compression generators, induction heating / metal forming and electromagnetic
rail gun systems. The ALE3D MHD module solves the resistive magnetic induction equation
given a collection of specified current and voltage sources. The equation is solved in the
Lagrangian frame using a mixed finite element method employing H(Curl) and H(Div) finite
element basis functions which preserves the solenoidal nature of the magnetic field to machine
precision. Electromagnetic force and resistive Joule heating terms are coupled to the equations of
motion and thermal diffusion in an operator split manner. For problems that require mesh
relaxation, magnetic advection is performed using the method of algebraic constrained transport
that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection
method maintains the divergence free nature of the magnetic field and is second-order accurate
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in regions where the solution is sufficiently smooth. For regions in which the magnetic field is
discontinuous (e.g., MHD shocks), the advection step is limited using the method of algebraic
flux correction, which is local extremum diminishing and divergence preserving.
Parallelization and Scaling
ALE3D is parallelized across the problem space using domain decomposition to associate
separate pieces of physical space to individual processors. The implementation uses MPI to
communicate across processor boundaries. Several of the key characteristics of the ALE3D
software infrastructure contribute to the code’s scalability. Field data are contained in simple C
arrays, giving the compiler canonical loop iteration patterns to optimize. Ghost boundary data is
always stored contiguously, removing the need for gather / scatter operations during MPI
communication. Nearly all MPI communication is point-to-point, with only two global
reductions per time step: the duration of the next time step, and a global error status check.
The amount of point-to-point communication required is dependent on the type of calculation
being run. Problems running explicit hydrodynamics require a single communication to collect
the sum of the forces at nodes along domain boundaries, although some optional algorithms (e.g.
monotonic Q) require more communication. Problems running advection require a 20x – 30x
greater amount of communication, both in terms of the number of communication points, and the
amount of data typically sent. A rough breakdown of the steps performed in the advection are:
nodal relaxation; calculation of volume fluxes; identification of mixed elements and interface
reconstruction; advection of element centered variables; and momentum (node centered)
advection. If there are slide surfaces, additional communications are required. The approach
taken in ALE3D is to use a separate decomposition for slide surfaces. Nodes on one side of a
surface (the “master” side) are assigned statically to the various processors in a load-balanced
manner, and then nodes on the other (“slave”) side of the surface that are currently “close” to the
masters on a processor are assigned to the same processor.
The daunting task of fully characterizing the performance of ALE3D’s many packages has never
been done in a systematic way, but we present an overview of the scaling of the Lagrangian
hydrodynamics package that forms the core of ALE3D. Figure 3 shows the weak scaling
behavior of a 5695 Element / process Sedov problem from 256 to 96,000 processes.
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
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Figure 3. Weak scaling results for ALE3D’s Lagrangian mechanics package.
Conclusion
The ALE3D code continues be under active development at LLNL. In addition to new physics
and methodology improvements, the underlying computer science framework is being modified
to ensure excellent performance on the latest generation of High Performance Computing
machines. This Export Controlled and Official Use Only code is available to analysts in the
Department of Defense and associated contractors for work related to national defense. Contact
the authors for additional information.
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Lawrence Livermore National Laboratory 14
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... Many researchers have proposed various methods in this direction. For example, Lawrence Livermore National Laboratory developed a thermal-fluid solver using the arbitrary-Lagrangian Eulerian (ALE) technique [3][4][5][6]; Yan's group at National University of Singapore developed a set of volume-of-fluid (VoF) based thermal-fluid models to simulate metal AM problems, including directed energy deposition (DED) and multi-layer and multi-track laser powder bed fusion (LPBF) processes [7][8][9][10][11]; Panwisawas et al. also used a VoF approach by using OpenFOAM to analyze the inter-layer and inter-track void formation [12]; Lin et al. developed a control-volume finite element approach to simulate DED and LPBF processes [13,14]. Li et al. developed a thermal-fluid model by combining the level set method and Lagrangian particle tracking to investigate powder-gas interaction in LPBF processes [15]. ...
... denote the velocity-pressure-temperature block in , 2 = denote the Navier-Stokes block. Let , 3 , and 2 denote the preconditioning matrices for , 3 , and 2 , respectively. Here is the final preconditioning matrix, which is constructed upon the preconditioning matrix for the level set block and 3 in the following way ...
... denote the velocity-pressure-temperature block in , 2 = denote the Navier-Stokes block. Let , 3 , and 2 denote the preconditioning matrices for , 3 , and 2 , respectively. Here is the final preconditioning matrix, which is constructed upon the preconditioning matrix for the level set block and 3 in the following way ...
Preprint
Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter summarizes the recent method development at UIUC for simulating thermal multiphase flows in laser powder bed fusion (LPBF) and directed energy deposition (DED) processes. Two main method developments are discussed. The first is a mixed interface-capturing/interface-tracking computational framework aiming to explicitly treat the gas-metal interface without mesh motion/re-meshing. The second is a physics-based and non-empirical deposit geometry model for DED processes. The proposed framework's accuracy is assessed by thoroughly comparing the simulated results against experimental measurements on various quantities. We also report critical quantities that experiments can not measure to show the predictive capability of the developed methods.
... The staggered-grid discretization combined with artificial viscosity is the basis of most Lagrangian hydrodynamic schemes. [62][63][64][65][66][67][68] In 1955, at Los Alamos, Rolf Landshoff added a linear term to the artificial viscosity, 69,70 and Marshall Rosenbluth suggested turning off the artificial viscosity during expansion. 71 These additions to artificial viscosity were first publicly discussed in the 1957 edition of the book by Richtmyer and Morton. ...
... 81 The creation of shock-capturing schemes facilitated the development of two-dimensional Lagrangian shock hydrodynamics codes, 49,61,77,78,82,83 and eventually three-dimensional codes. 65,66 Modern staggered-grid Lagrangian and artificial viscosity methods have evolved from the pioneering work of the 1940s (Refs. 67 and Refs. ...
Article
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The intent of this paper is to discuss the history and origins of Lagrangian hydrodynamic methods for simulating shock-driven flows. The majority of the pioneering research occurred within the Manhattan Project. A range of Lagrangian hydrodynamic schemes were created between 1943 and 1948 by John von Neumann, Rudolf Peierls, Tony Skyrme, and Robert Richtmyer. These schemes varied significantly from each other; however, they all used a staggered grid and finite difference approximations of the derivatives in the governing equations, where the first scheme was by von Neumann. These ground-breaking schemes were principally published in Los Alamos laboratory reports that were eventually declassified many decades after authorship, which motivates us to document the work and describe the accompanying history in a paper that is accessible to the broader scientific community. Furthermore, we seek to correct historical omissions on the pivotal contributions made by Peierls and Skyrme to creating robust Lagrangian hydrodynamic methods for simulating shock-driven flows. Understanding the history of Lagrangian hydrodynamic methods can help explain the origins of many modern schemes and may inspire the pursuit of new schemes.
... Constitutive equations are implemented in finite element (FE) models within the ale3d multi-physics code [37] . Continuum balance laws of mass, momentum, and energy conservation are solved at each material point in the domain, for every time increment in a dynamic problem. ...
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Existing methods for disrupting shock waves employ low-density materials and mesostructures, which occupy significant space, are difficult to fabricate, and are often destroyed after loading. In this work we produce a gradient metamaterial with near-uniform density capable of disrupting shock waves fifty-fold in time. We utilize metastable volumetric contraction at the atomic-scale during α↔ϵ phase transformation in Fe-based alloys to disrupt shock waves. Gradient Fe-xMn alloys are fabricated and shock compressed to pressures approaching 13 GPa, with shock rise times increasing from ∼20 ns in pure Fe to ∼1000 ns in the Fe-xMn laminate. Shock-recovered microstructures indicate that the phases reversibly transform. Two-dimensional simulations, validated against planar experiments, predict geometries that can effectively focus or dissipate shock waves. To our knowledge, this work is the first to demonstrate manipulation of shock waves via alloying of phase-transforming metamaterials.
... Simulations are conducted using the arbitrary Lagrangian-Eulerian simulation code ALE3D. 51 Results of these simulations are compared to experimental results for the rear surface velocity of the target and post-mortem porosity measurements in the target. Wave propagation effects allow the central portion of material to be modeled in one dimension. ...
Article
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Spall failure is of interest due to its prevalence in high strain rate problems in which the spallation is driven by the interaction of release waves. In this article, a porosity-based damage model that includes microinertial effects is used to examine spall failure. The model is successfully calibrated to plate impact-driven experiments and then used to evaluate experimental conditions producing more extreme strain rate conditions, such as those in laser-driven experiments. The incorporation of microinertia allows us to better understand the increase in apparent macroscopic spall strength seen at high strain rates. Correspondingly, we conclude that the incorporation of microinertial effects improves the model's predictive capabilities. Microinertial effects result in more severe local tensile stresses that affect the damage evolution, and microinertia can play a significant role in the approach to the material's ideal strength at extreme loading rates. A preliminary paramet-ric study is also carried out to investigate the role of microstructural aspects such as nucleation volume fraction and initial pore radius. One counter-intuitive result from the microinertial effects is that, for a given nucleation site volume fraction, having larger initial pore nucleation sites can lead to an improved macroscopic spall strength. Published under an exclusive license by AIP Publishing. https://doi.
... Unsteady Lagrangian codes are some of the earliest hydrodynamic simulation codes developed for scientific computing [1]. Many modern Lagrangian multi-physics codes exist [2][3][4], which are able to model multi-dimensional problems with and many interacting physics processes. Such codes, though very powerful, are complex and difficult to extend to consider new physics models. ...
Article
A specialized hydrodynamic simulation code has been developed to simulate one-dimensional unsteady problems involving the detonation and deflagration of high explosives. To model all the relevant physical processes in these problems, a code is required to simulate compressible hydrodynamics, unsteady thermal conduction and chemical reactions with complex rate laws. Several verification exercises are presented which test the implementation of these capabilities. The code also requires models for physics processes such as equations of state and conductivity for pure materials and mixtures as well as rate laws for chemical reactions. Additional verification tests are required to ensure these models are implemented correctly. Though this code is limited in the types of problems it can simulate, its computationally efficient formulation allow it to be used in calibration studies for reactive burn models for high explosives.
... The initial implementation was converted to an Abaqus UMAT through a project with the High Performance Computing Modernization Program (HPCMP) Productivity Enhancement Technology Transfer and Training (PETTT) program [111]. This Abaqus UMAT based model can be used in many production codes used throughout the US Department of Defense (DoD), US Department of Energy (DOE), and Academia including Abaqus [112], Sierra/SM [113], ALEGRA [114], ALE3D [115], and EPIC [116]. The historical model has been implemented as material models in different host codes based on the published model equations by each host code developer. ...
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We describe models for the behavior of hot‐pressed boron carbide that is subjected to extreme dynamic environments such as ballistic impact. We first identify the deformation and failure mechanisms that are observed in boron carbide under such conditions, and then review physics‐based models for each of these mechanisms and the integration of these models into a single physics‐based continuum model for the material. Atomistic modeling relates the composition and stoichiometry to the amorphization threshold, while mesoscale modeling relates the processing‐induced defect distribution to the fracture threshold. The models demonstrate that the relative importance of amorphization and fracture are strongly dependent on the geometry and impact conditions, with the volume fraction of amorphized material being unlikely to be significant until very high velocities (~ 3km=s) are reached for geometries such as ball impact on plates. These connections to the physics thus provide guidelines for the design of improved boron carbide materials for impact applications.
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With dry bay fires persisting as a significant contributor to aircraft vulnerability despite chronicled developments in survivability technologies, an accurate fire prediction capability remains paramount for credible vulnerability assessments. Physics based modeling of the hydrodynamic ram (HRAM) fluid deposition process is a key component of such capability, wherein capturing the first instance of fluid spurt, referred to herein as shallow jet spurts, is a core focus. Such pre-spurts as they have been formerly identified have only been witnessed sporadically in HRAM spurt experiments. ALE3D, a first-principles multi-physics code was employed to model the shallow jet spurt phenomenon with spherical projectiles impacting water-filled tanks faced with aluminum panels, such that the underlying physics and sensitivities could be explored. Development and verification of the 2D axisymmetric model is described relative to trends observed in a prior experimental campaign. Results from the verified model suggest shallow jet spurts have at least a quadratic sensitivity to the fundamental vibrational mode of the impact plate across impact velocities 610 – 1829 m/s (2000 – 6000 ft/s). It is further explained how shallow jet spurts are arrested for impacts at the two extremes of plate rigidity. This research constitutes the first fluid-structure modeling of shallow jet spurts which future three-dimensional analyses will expound upon.
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By combining experiments and modeling from three US national laboratories, we explore compressive strength in a well-characterized material, tantalum, across pressures from zero to over 350 GPa, strain-rates from 10−3/s to 108/s and temperatures from 148 K to 3800 K. Strength values from 40+ experiments are shown to vary by nearly two orders of magnitude, from 0.15 GPa to over 10 GPa. Cross-comparison of these results allows pressure and strain-rate dependencies to be isolated, and strength increases more significantly with pressure than with strain rate over the range studied. Simulations using Preston-Tonks-Wallace, Livermore Multi-Scale, and Kink-Pair strength models test modeling capabilities and provide further insight into strength mechanics. The widely-used assumption in those models of shear-modulus scaling underpredicts strength by a factor of about two at extreme pressures in pulsed-power planar ramp-release experiments, which largely isolate pressure effects. Richtmyer-Meshkov Instability experiments, which largely isolate strain rate effects at ∼107/s, suggest that modeling assumptions about mechanisms at the highest rates need further study. Laser-driven Rayleigh-Taylor instability experiments, which simultaneously probe extreme pressures and strain rates, provide both model and cross-platform experimental validation. The large-scale collaborative nature of this study covers a wide span of experimental conditions and modeling approaches, allowing for extraordinary insight into dynamic strength.
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We study the deformation of tantalum under extreme loading conditions. Experimental velocity data are drawn from both ramp loading experiments on Sandia’s Z-machine and gas gun compression experiments. The drive conditions enable the study of materials under pressures greater than 100 GPa. We provide a detailed forward model of the experiments including a model of the magnetic drive for the Z-machine. Utilizing these experiments, we simultaneously infer several different types of physically motivated parameters describing equation of state, plasticity, and anelasticity via the computational device of Bayesian model calibration. Characteristics of the resulting calculated posterior distributions illustrate relationships among the parameters of interest via the degree of cross correlation. The calibrated velocity traces display good agreement with the experiments up to experimental uncertainty as well as improvement over previous calibrations. Examining the Z-shots and gun-shots together and separately reveals a trade-off between accuracy and transferability across different experimental conditions. Implications for model calibration, limitations from model form, and suggestions for improvements are discussed.
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Fluids at supercritical thermodynamic conditions are inherently complex due to the large variations in thermodynamic and transport properties. Multiple recent numerical and experimental investigations indicate ongoing interest for these fluids, especially supercritical CO2 and supercritical water, for a variety of applications. The potential heat transfer benefits in this regime are directly influenced by the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. Limited studies have been conducted for low-Reynolds/intermediate-Rayleigh numbers mixed-convection channel flow of supercritical water, which is the focus of this study. To investigate the thermally driven hydrodynamic instabilities in this regime, we use a high-order fully-implicit numerical method. As expected, in this channel configuration and flow regime, a competition arises between the forced and the natural convection. Buoyancy, driven by the thermal gradient at the wall, pushes the fluid upwards in the channel, while inertial forces drive the fluid from inlet to outlet. We observe significant differences in the heat transfer coefficient between the top and bottom walls of the channel flow, due to natural convection, and unstable plumes. We further quantify the buoyancy forces along the channel flow through evaluation of the Richardson number. Simulations show that with a higher negative Richardson number, there are more unstable structures along the channel, resulting in enhanced mixing. Furthermore, we demonstrate the existence of gas-like, liquid-like, and the possibility of pseudo-two-phase regimes in the supercritical fluid. The pseudo-two-phase regime occurs when the range of fluid temperatures is crossing the pseudo-critical line, also known as the Widom line. The density of the fluid varies significantly near the Widom line, and further influences the natural convection and heat transfer in the flow.
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A new approach for treating the mechanical interactions of overlapping finite element meshes is presented. Referred to as embedded mesh methods here, these overlapping mesh methods typically include a foreground solid mesh and a background Euler fluid grid or solid mesh. A number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface. Lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable. Several Lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid-structure interaction type problems. In addition, details regarding implementation in a two-step, multi-material, Arbitrary Lagrangian Eulerian (ALE) code are presented. Example problems demonstrate convergence and applicability to a range of problems. In particular, the fluid-structure interaction examples focus on blast applications.
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Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms. Care is taken to keep the scheme in conservation form. When applied to a quadratic conservation law, the scheme notably yields a monotonic shock profile, with a width of only 112 mesh.
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A classic problem in Lagrangian numerical hydrodynamics is the conservative transfer of quantities from an old,, distorted mesh to a new mesh. The same problem arises whenever the mesh is changed as, for example, in adaptive mesh techniques. This transfer of information is an interpolation process which is frequently called rezoning (or remapping). The general problem of conservative rezoning from one arbitrary mesh to another may be formulated as follows: m/sub k/ = ..integral integral integral../sub V//sub k/rho(r)dV. That is, we compute the mass m/sub k/ of each cell of the new mesh by integrating the known density distribution in the old mesh over the cell volume V/sub k/. A direct intregation is generally prohibitive. We show, however, that is is possible to convert this integral to a surface integral by the appropriate use of the divergence theorem, thus greatly reducing the complexity of the problem. For two-dimensional generall quadrilateral meshes the resulting method is exact and particularly simple.
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An ignition and growth concept is used, within the framework of a one-dimensional Lagrangian hydrodynamic code, to model the shock initiation of heterogeneous solid explosives. The leading shock wave of an initiating pulse is assumed to ignite a small fraction of the explosive at localized heated regions. These ignited regions then grow as material is consumed at their boundaries. The growth rate for a particular material is assumed to have the characteristic pressure dependence of high-pressure laminar burning experiments. Results of the model calculations are in good quantitative agreement with recent manganin pressure gage and particle velocity gage measurements of the buildup of the initiating shock front to detonation for both sustained and short duration pulses in four solid explosives: PBX−9404, TATB, cast TNT, and PETN. The predicted run distances to detonation as functions of shock pressure at various initial densities and the predicted reaction zone lengths of the fully developed detonation waves also correlate well with experimental data for these four solid explosives.
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This report provides a theoretical manual for DYNA3D, a vectorized explicit three-dimensional finite element code for analyzing the large deformation dynamic response of inelastic solids. A contact-impact algorithm that permits gaps and sliding along material interfaces is described. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 8-node solid elements, and the equations-of-motion are integrated by the central difference method. DYNA3D is operational on the CRAY-1 and CDC7600 computers.
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The treatment of zero energy modes which arise due to one-point integration of first-order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one-point integration scheme which analytically integrates the element volume and uniform strain modes is presented.
Article
A model, applicable at high‐strain rate, is presented for the shear modulus and yield strength as functions of equivalent plastic strain, pressure, and internal energy (temperature). The parameters needed to implement the model have been determined for 14 metals. Using this model, hydrodynamic computer simulations have been successful in reproducing measured stress and free‐surface‐velocity–vs–time data for a number of shock‐wave experiments.
Godunov Methods on a Staggered Mesh -An Improved Artificial Viscosity
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Equation of State and Strength Properties of Selected Materials
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Steinberg, D.J., "Equation of State and Strength Properties of Selected Materials," Lawrence Livermore National Laboratory, Report UCRL-MA-106439 (1996).