A multiphase Lagrangian discontinuous Galerkin hydrodynamic method for high-explosive detonation physics
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Results for “Lagrangian hydrodynamics”
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Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method
Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.
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Some techniques for transport in radiation hydrodynamics [Slides]
Summary: Non-relativistic IMC/SN with Lagrangian hydrodynamics; IMC-DDMC momentum deposition; Post-ALE IMC particle remap and SN remap; collapse of multi-material state per zone.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
CNO abundances and hydrodynamic models of the nova outburst.
We have used a fully implicit, Lagrangian, hydrodynamic computer code incorporating a nuclear reaction network to follow thermonuclear runaways in the hydrogen-rich envelopes of white dwarfs in order to produce a nova outburst. Because of the short time-scales and the high nuclear burning rates produced in our models, the nuclear reactions are far out of equilibrium and the beta-plus unstable nuclei become the most abundant nuclei in the envelope except for hydrogen and helium. Our models have ejected 1.00017 solar mass with kinetic energies of 8 times 10 to the 44-th power ergs, a value that agrees quite closely with the observed values for novae.
Starrfield, S.↗
Gas distribution and starbursts in shell galaxies
Detailed maps of most elliptical galaxies reveal that, whereas the greatest part of their luminous mass originates from a smooth distribution with a surface brightness approximated by a de Vaucouleurs law, a small percentage of their light is contributed by low surface brightness distortions termed 'fine structures'. The sharp-edged features called 'shells' are successfully reproduced by merger and infall models involving accretion from less massive companions. In this context, dwarf spheroidal and compact disk galaxies are likely progenitors of these stellar phenomena. However, it is probable that the sources of shell-forming material also contain significant amounts of gas. This component may play an important role in constraining the formation and evolution of shell galaxies. To investigate the effects of the gaseous component, numerical simulations were performed to study the tidal disruption of dwarf galaxies containing both gas and stars by more massive primaries, and the evolution of the ensuing debris. The calculations were performed with a hybrid N-body/hydrodynamics code. Collisionless matter is evolved using a conventional N-body technique and gas is treated using smoothed particle hydrodynamics in which self-gravitating fluid elements are represented as particles evolving according to Lagrangian hydrodynamic equations. An isothermal equation of state is employed so the gas remains at a temperature 104 K. Owing to the large mass ratio between the primary and companion, the primary is modeled as a rigid potential and the self-gravity of both galaxies is neglected.
Weil, Melinda L.↗
REYNO: A Reactive Hydrodynamics Modeling Suite
REYNO is a Python library that is primarily designed as a platform for the agile development and testing of novel reactive flow models. Equations of state and multi-step rate laws can be implemented using the provided class hierarchy with different thermodynamic closure conditions. The library includes a one-dimensional Lagrangian hydrodynamic solver to simulate multi-material reactive or inert problems in planar, cylindrical, or spherical coordinates. Custom time-dependent boundary conditions are also available for problems such as ramp compression. This document describes the different numerical methods and algorithms that are included in REYNO.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems
Projection based dimensionality reduction is used to approximate the full discretiza tion of a PDE problem in order to reduce the cost of its numerical simulation while staying faithful to the full dynamics. For nonlinear problems, hyperreduction methods are additionally needed to remove the dependence of the nonlinear terms on the full problem’s size. In this project, we develop an energy conserving hyperreduction method and apply it to Eulerian-Lagrangian hydrodynamics problems, demonstrating that the reduced model successfully accelerates the numerical simulations while conserving the problem’s total energy with high accuracy.
97 MATHEMATICS AND COMPUTING↗
A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics
The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.
97 MATHEMATICS AND COMPUTING↗
Taylor wave solution for a general equation of state
This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.
97 MATHEMATICS AND COMPUTING↗
High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries
We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.
97 MATHEMATICS AND COMPUTING↗
Using deep machine learning to interpret proton radiography data from a pulsed power experiment
Deep machine learning is used to analyze a proton radiograph from a tin pulsed power experiment and determine density values for each pixel in the image. Two promising convolutional neural network architectures that have proven to be effective for image analysis in other applications are applied to analyze a proton radiograph and find density values. The process of creating a suitable training dataset is described, involving the Lagrangian hydrodynamic model used for simulations of the experiment, the proton radiography forward model to make synthetic images for training, and the manner in which data augmentation is used to expand the resulting image dataset. It is shown that machine learning not only produces a reasonable density field but is also able to predict features in the density field that are suggested by the proton radiograph but not captured by simulations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.
97 MATHEMATICS AND COMPUTING↗
Modeling soot growth in Comp-B using a detonation history
A chemical kinetics procedure for soot formation calculation is summarized. By importing Lagrangian hydrodynamic calculations, species history is consistently accounted for. Detonation product composition is assumed in region with the burnt high explosive (HE). Soot formation is calculated using the density and energy obtained in the hydrodynamics calculation of HE detonation. Ideal gas equation-of-state (EOS) with temperature-dependent specific heat is used in the HE product region. Sample calculations show reasonably-expected temperature and soot formation.
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Preconditioning for Hyper-reduction in Reduced Order Models
Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.
97 MATHEMATICS AND COMPUTING↗
Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models
To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG. First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize viscosity for a 1D propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.
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Spark Channel Dynamics of Electrostatic Discharges (Rev. 1) [Slides]
To model spark discharges, this work implemented, verified, and validated: 1-D radial conservative Lagrangian hydrodynamic scheme (with heat conduction); Eddington/P1 radiative transfer approximation, time-implicit scheme; RLC circuit solver, time-implicit scheme (adaptable to other circuit types). Novel analytics EOS fit for air up to temperatures of ~150,000 K. Novel "seed" electron concept to initialize finite conductivity in spark without pre-heating the air in the channel, as typically used in spark modeling literature. Reasonable, if conservative (from an engineering viewpoint), agreement with experimental data for indirect (circuit) and direct (interferometry) measurements of spark. Many potential avenues of future work: Two-temperature dryodynamics (requires two-temperature EOS development); 2-D axisymmetric geometry for axial (z) variation, modeling delectric electrodes; Kinetic equations for time-dependent charged species populations.
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Dependence of Dust Formation on the Supernova Explosion
We investigate the properties, composition, and dynamics of dust formation and growth for a diverse set of core-collapse supernovae (CCSNe), with 15, 20, and 25 M ⊙ progenitor masses, explosion energies ranging from 0.5 to 120 foe, and varied engine type. These explosions are evolved with a 1D Lagrangian hydrodynamics code out to a minimum of 1157 days to model the ejecta as it expands and cools. A multigrain dust nucleation and growth model is applied to these results. We find that higher explosion energies lead to an earlier onset of dust formation, smaller grain sizes, and larger silicate abundances. Further, we see that nuclear burning during the explosion leads to enhanced formation of silicate dust. Finally, we build composite models from our suite to predict the efficiency of CCSN dust production as a function of metallicity.
79 ASTRONOMY AND ASTROPHYSICS↗
On the mass of the Cepheid X Cygni
Using a new non-Lagrangian hydrodynamic radiation transport code, models of the Cepheid X Cygni have been calculated and compared with new observations. Adopting an effective temperature of 5300 K, the luminosity was varied for stellar masses of 6, 8, and 9 solar masses in order to obtain a period of 16.4d. The results indicate that in order to find reasonable agreement between the light curves as calculated and observed, the mass used in the models must be nearly the evolutionary mass, not some 60% less as found in earlier work for Cepheids with periods from 7d to 10d. In addition, the new observations support the physical reality of the so-called 'artificial viscosity dip'.
Davis, C. G.↗