Publications

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Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.

We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approach is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.

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Uncertainty quantification (UQ) deals with providing reasonable estimates of the uncertainties associated with an engineering model and propagating them to final engineering quantities of interest. We present a conceptual UQ framework for the case of shock hydrodynamics with Euler's equations where the uncertainties are assumed to lie principally in the equation of state (EOS). In this paper we consider experimental data as providing both data and an estimate of data uncertainty. We propose a specific Bayesian inference approach for characterizing EOS uncertainty in thermodynamic phase space. We show how this approach provides a natural and efficient methodology for transferring data uncertainty to engineering outputs through an EOS representation that understands and deals consistently with parameter correlations as sensed in the data.Historically, complex multiphase EOSs have been built utilizing tables as the delivery mechanism in order to amortize the cost of creation of the tables over many subsequent continuum scale runs. Once UQ enters into the picture, however, the proper operational paradigm for multiphase tables become much less clear. Using a simple single-phase Mie-Grüneisen model we experiment with several approaches and demonstrate how uncertainty can be represented. We also show how the quality of the tabular representation is of key importance. As a first step, we demonstrate a particular tabular approach for the Mie-Grüneisen model which when extended to multiphase tables should have value for designing a UQ-enabled shock hydrodynamic modeling approach that is not only theoretically sound but also robust, useful, and acceptable to the modeling community. We also propose an approach to separate data uncertainty from modeling error in the EOS. © 2012 Elsevier Ltd.

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We examine several conducting spheres moving through a magnetic field gradient. An analytical approximation is derived and an experiment is conducted to verify the analytical solution. The experiment is simulated as well to produce a numerical result. Both the low and high magnetic Reynolds number regimes are studied. Deformation of the sphere is noted in the high Reynolds number case. It is suggested that this deformation effect could be useful for designing or enhancing present protection systems against space debris.

We describe the implementation of a prototype fully implicit method for solving three-dimensional quasi-steady state magnetic advection-diffusion problems. This method allows us to solve the magnetic advection diffusion equations in an Eulerian frame with a fixed, user-prescribed velocity field. We have verified the correctness of method and implementation on two standard verification problems, the Solberg-White magnetic shear problem and the Perry-Jones-White rotating cylinder problem.

In this report we summarize research into new parallel algebraic multigrid (AMG) methods. We first provide a introduction to parallel AMG. We then discuss our research in parallel AMG algorithms for very large scale platforms. We detail significant improvements in the AMG setup phase to a matrix-matrix multiplication kernel. We present a smoothed aggregation AMG algorithm with fewer communication synchronization points, and discuss its links to domain decomposition methods. Finally, we discuss a multigrid smoothing technique that utilizes two message passing layers for use on multicore processors.

The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.

Inductive electromagnetic launchers, or coilguns, use discrete solenoidal coils to accelerate a coaxial conductive armature. To date, Sandia has been using an internally developed code, SLINGSHOT, as a point-mass lumped circuit element simulation tool for modeling coilgun behavior for design and verification purposes. This code has shortcomings in terms of accurately modeling gun performance under stressful electromagnetic propulsion environments. To correct for these limitations, it was decided to attempt to closely couple two Sandia simulation codes, Xyce and ALEGRA, to develop a more rigorous simulation capability for demanding launch applications. This report summarizes the modifications made to each respective code and the path forward to completing interfacing between them.

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Two classical verification problems from shock hydrodynamics are adapted for verification in the context of ideal magnetohydrodynamics (MHD) by introducing strong transverse magnetic fields, and simulated using the finite element Lagrange-remap MHD code ALEGRA for purposes of rigorous code verification. The concern in these verification tests is that inconsistencies related to energy advection are inherent in Lagrange-remap formulations for MHD, such that conservation of the kinetic and magnetic components of the energy may not be maintained. Hence, total energy conservation may also not be maintained. MHD shock propagation may therefore not be treated consistently in Lagrange-remap schemes, as errors in energy conservation are known to result in unphysical shock wave speeds and post-shock states. That kinetic energy is not conserved in Lagrange-remap schemes is well known, and the correction of DeBar has been shown to eliminate the resulting errors. Here, the consequences of the failure to conserve magnetic energy are revealed using order verification in the two magnetized shock-hydrodynamics problems. Further, a magnetic analog to the DeBar correction is proposed and its accuracy evaluated using this verification testbed. Results indicate that only when the total energy is conserved, by implementing both the kinetic and magnetic components of the DeBar correction, can simulations in Lagrange-remap formulation capture MHD shock propagation accurately. Additional insight is provided by the verification results, regarding the implementation of the DeBar correction and the advection scheme.

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ALEGRA is an arbitrary Lagrangian-Eulerian (multiphysics) computer code developed at Sandia National Laboratories since 1990. The code contains a variety of physics options including magnetics, radiation, and multimaterial flow. The code has been developed for nearly two decades, but recent work has dramatically improved the code's accuracy and robustness. These improvements include techniques applied to the basic Lagrangian differencing, artificial viscosity and the remap step of the method including an important improvement in the basic conservation of energy in the scheme. We will discuss the various algorithmic improvements and their impact on the results for important applications. Included in these applications are magnetic implosions, ceramic fracture modeling, and electromagnetic launch. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

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Electromagnetic induction is a classic geophysical exploration method designed for subsurface characterization--in particular, sensing the presence of geologic heterogeneities and fluids such as groundwater and hydrocarbons. Several approaches to the computational problems associated with predicting and interpreting electromagnetic phenomena in and around the earth are addressed herein. Publications resulting from the project include [31]. To obtain accurate and physically meaningful numerical simulations of natural phenomena, computational algorithms should operate in discrete settings that reflect the structure of governing mathematical models. In section 2, the extension of algebraic multigrid methods for the time domain eddy current equations to the frequency domain problem is discussed. Software was developed and is available in Trilinos ML package. In section 3 we consider finite element approximations of De Rham's complex. We describe how to develop a family of finite element spaces that forms an exact sequence on hexahedral grids. The ensuing family of non-affine finite elements is called a van Welij complex, after the work [37] of van Welij who first proposed a general method for developing tangentially and normally continuous vector fields on hexahedral elements. The use of this complex is illustrated for the eddy current equations and a conservation law problem. Software was developed and is available in the Ptenos finite element package. The more popular methods of geophysical inversion seek solutions to an unconstrained optimization problem by imposing stabilizing constraints in the form of smoothing operators on some enormous set of model parameters (i.e. ''over-parametrize and regularize''). In contrast we investigate an alternative approach whereby sharp jumps in material properties are preserved in the solution by choosing as model parameters a modest set of variables which describe an interface between adjacent regions in physical space. While still over-parametrized, this choice of model space contains far fewer parameters than before, thus easing the computational burden, in some cases, of the optimization problem. And most importantly, the associated finite element discretization is aligned with the abrupt changes in material properties associated with lithologic boundaries as well as the interface between buried cultural artifacts and the surrounding Earth. In section 4, algorithms and tools are described that associate a smooth interface surface to a given triangulation. In particular, the tools support surface refinement and coarsening. Section 5 describes some preliminary results on the application of interface identification methods to some model problems in geophysical inversion. Due to time constraints, the results described here use the GNU Triangulated Surface Library for the manipulation of surface meshes and the TetGen software library for the generation of tetrahedral meshes.

Controlled seeding of perturbations is employed to study the evolution of wire array z-pinch implosion instabilities which strongly impact x-ray production when the 3D plasma stagnates on axis. Wires modulated in radius exhibit locally enhanced magnetic field and imploding bubble formation at discontinuities in wire radius due to the perturbed current path. Wires coated with localized spectroscopic dopants are used to track turbulent material flow. Experiments and MHD modeling offer insight into the behavior of z-pinch instabilities.

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The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.

ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling resistive magnetohydrodynamics, thermal conduction, and radiation transport effects, and two material temperature physics.