Results for “Discrete Element Method” — Page 22

DOE OSTI2025

A stable potential-based time-domain method for wideband elec- tromagnetic analysis

In previous research, the frequency-domain A-ϕ formulation has been validated using the finite element method for electromagnetic simulations of low-frequency and multi- scale problems, demonstrating excellent numerical accuracy, good matrix condition, and high computational efficiency. Time- domain simulations provide significant advantages for modeling wideband problems and are crucial for multiphysics applications. In this paper, the frequency-domain A-ϕ formulation is extended to the time domain. The central difference scheme is employed for temporal discretization to ensure both accuracy and stability. A numerical example is presented to demonstrate the capability of the proposed time-domain method in wideband electromagnetic analysis.

Mekonnen, Minyichil↗

DOE OSTI2022

Modeling gas breakthrough and flow phenomena through engineered barrier systems using a discrete fracture approach

Compacted clays are being considered to build engineered barrier systems (EBS) intended for the safe isolation of high-level nuclear waste (HLW) and spent nuclear fuel (SNF). The corrosion of the metallic canister containing the HLW/SNF will lead to the generation and buildup of the gas pressure in the more internal part of the clay buffer. This phenomenon would eventually trigger the formation and propagation of fractures in the clay barrier, jeopardizing its safety functions. Here, in this work, we propose to use the fragmentation technique (MFT) to model evolving fractures in clays triggered by gas pressurization. The MFT has been successfully used to model the formation of fractures in concrete, drying cracks in soil, hydraulic and thermo-fractures in rocks. In this work, we extend the MFT to deal with multiphase fluid flow in deformable porous media, and we upgraded a fully coupled computer finite element code using the extended technique. The proposed approach is first verified against analytical solutions and is then applied to model gas breakthrough experiments in clays. A very satisfactory performance of the method is observed in all the analyses, showing the potential of the MFT to tackle multiphase flow problems in deformable porous media with evolving discontinuities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Local element operations for curved simplex meshes

Summary Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post‐processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In order to perform high‐order mesh optimization, these ingredients must also be extended to high‐order (curved) meshes. In this work, we present a method to perform local element operations on curved meshes. The mesh operations discussed in this work are edge/face swaps, edge collapses, and edge splitting (more generally refinement) for triangular and tetrahedral meshes. These local operations are performed by first identifying the patch of elements which contain the edge/face being acted on, performing the operation as a “straight‐sided one" by placing the high‐order nodes via an isoparametric mapping from the master element, and smoothing the high‐order nodes on the elements in the patch by minimizing a Jacobian‐based high‐order mesh distortion measure. Since the initial “straight‐sided guess” from the placement of the nodes via the isoparametric mapping frequently results in invalid elements, the distortion measure must be regularized which allows for mesh untangling for the optimization to succeed. We present several examples in 2D and 3D to demonstrate these local operations and how they can be combined with a high‐order node smoothing procedure to maintain mesh quality when faced with severe deformations.

Shi, A.↗

DOE OSTI2020

Radioactive Source Localization via Bayesian Particle Filter

In the event of a misplaced radioactive source or other emergency situation, measuring a radiation field, mapping its distribution, and determining a source location are essential tasks to ameliorating the situation. However, radiation fields may be extremely hazardous to human surveyors and minimizing received radiation doses is just as essential. Robots appear to be a potential solution to these problems. Beyond simply measuring radiation, the robot's computer processing capabilities offer a way to apply complex data analysis methods to radiation measurements in real-time. Methods which predict likely source locations can then feed this information into other processes, potentially improving path planning and enabling more efficient measurements. Given a robot mounted with a gamma-ray detector, can we: develop a methodology to account for detector performance across a wide range of source angles, distances, and photon energies? operate an autonomously navigating robot to effectively survey and characterize an area of interest? implement a data analysis method, conventionally used in measurements of motion, for source localization purposes? An open-source TurtleBot 3 robot, running Robot Operating System (ROS) on Ubuntu 16.04 LTS, was fitted with a Kromek GR1{sup R} Cadmium Zinc Telluride (CZT) solid-state gamma-ray detector. As a part of ROS, the packages OpenSlam, gmapping, and amcl were used to perform Simultaneous Localization and Mapping (SLAM), determining the robot's position and mapping the surrounding area. Data was acquired via Lidar mounted on top the TurtleBot 3. Detector Calibration Fit: The equation was fit to 365 counts of various energies, distances, and angles. A MATLAB{sup R} program was written to simulate measurements taken a robot on a random walk, with count data and positions discretized into finite element pixels. Using this program, a sample of 100 runs was performed on a map with a simulated source at the center, with a total of 200 of 2 pixels each. Similarly, multiple runs of the filter were performed on recorded robot measurement data. In both simulation and real tests, when corrected for errors (particles placed outside of bounds or on the robot, and simulation-specific errors), corresponding t-tests of predicted x and y-coordinates were within a 95% confidence interval of the actual position. For the real trial, these positions are slightly skewed right in the x-axis as the robot remained mainly to the left side of the source within the sample area. These simulations demonstrate potential validity for the usage of a particle filter as method of radioactive source localization. In the future, true real-time implementation and data fusion may further augment the performance of the robot to localize lost sources. Additionally, identification of multiple sources, determination of source types, and usage of a collimator are areas to potentially be explored.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

High-Order Hybrid RANS-LES Study of NACA0012 Wing Sections

We develop hybrid RANS-LES strategies within Nek5000 for application to airfoil sections at small flight configurations. We present a validation and verification study of $k \space – \space \tau$ SST applied to a NACA 0012 wing section in a pure RANS and in a hybrid RANS-LES setup. The study shows good corroboration with existing experimental and numerical datasets. We also analyze some of the observed discrepancies with the experiments by evaluating the side wall “blocking” effect. We demonstrate that for the hybrid turbulence modeling approach a high-order spectral- element discretization converges faster (i.e., with less resolution) than a representative low-order finite-volume-based approach.

42 ENGINEERING↗

DOE OSTI2019

Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations.

Abstract not provided.

Lim, Hojun↗

DOE OSTI2019

Electromagnetic wave propagation based upon spectral-element methodology in dispersive and attenuating media

SUMMARY We build on mathematical equivalences between Maxwell’s wave equations for an electromagnetic medium and elastic seismic wave equations. This allows us to readily model Maxwell’s wave propagation in the spectral-element codes SPECFEM2D and SPECFEM3D, written for acoustic, viscoelastic and poroelastic seismic wave propagation, providing the ability to handle complex geometries, inherent to finite-element methods and retaining the strength of exponential convergence and accuracy due to the use of high-degree polynomials to interpolate field functions on the elements, characteristic to spectral-element methods (SEMs). Attenuation and dispersion processes related to the frequency dependence of dielectric permittivity and conductivity are also included using a Zener model, similar to shear attenuation in viscoelastic media or viscous diffusion in poroelastic media, and a Kelvin–Voigt model, respectively. Ability to account for anisotropic media is also discussed. Here, we limit ourselves to certain dielectric permittivity tensor geometries, in order to conserve a diagonal mass matrix after discretization of the system of equations. Doing so, simulation of Maxwell’s wave equations in the radar frequency range based on SEM can be solved using explicit time integration schemes well suited for parallel computation. We validate our formulation with analytical solutions. In 2-D, our implementation allows for the modelling of both a transverse magnetic (TM) mode, suitable for surface based reflection ground penetration radar type of applications, and a transverse electric (TE) mode more suitable for crosshole and vertical radar profiling setups. Two 2-D examples are designed to demonstrated the use of the TM and TE modes. A 3-D example is also presented, which allows for the full TEM solution, different antenna orientations, and out-of-plane variations in material properties.

58 GEOSCIENCES↗

DOE OSTI2022

The DPG Method for the Convection-Reaction Problem, Revisited

In this work, we study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis – construction of a local Fortin operator – is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Electrodes, lithium-ion batteries, and methods of making and using same

Described herein are improved composite anodes and lithium-ion batteries made therefrom. Further described are methods of making and using the improved anodes and batteries. In general, the anodes include a porous composite having a plurality of agglomerated nanocomposites. At least one of the plurality of agglomerated nanocomposites is formed from a dendritic particle, which is a three-dimensional, randomly-ordered assembly of nanoparticles of an electrically conducting material and a plurality of discrete non-porous nanoparticles of a non-carbon Group 4A element or mixture thereof disposed on a surface of the dendritic particle. At least one nanocomposite of the plurality of agglomerated nanocomposites has at least a portion of its dendritic particle in electrical communication with at least a portion of a dendritic particle of an adjacent nanocomposite in the plurality of agglomerated nanocomposites.

Yushin, Gleb↗

DOE OSTI2022

Electrodes, lithium-ion batteries, and methods of making and using same

Described herein are improved composite anodes and lithium-ion batteries made therefrom. Further described are methods of making and using the improved anodes and batteries. In general, the anodes include a porous composite having a plurality of agglomerated nanocomposites. At least one of the plurality of agglomerated nanocomposites is formed from a dendritic particle, which is a three-dimensional, randomly-ordered assembly of nanoparticles of an electrically conducting material and a plurality of discrete non-porous nanoparticles of a non-carbon Group 4A element or mixture thereof disposed on a surface of the dendritic particle. At least one nanocomposite of the plurality of agglomerated nanocomposites has at least a portion of its dendritic particle in electrical communication with at least a portion of a dendritic particle of an adjacent nanocomposite in the plurality of agglomerated nanocomposites.

Yushin, Gleb↗

DOE OSTI2023

Electrodes, lithium-ion batteries, and methods of making and using same

Described herein are improved composite anodes and lithium-ion batteries made therefrom. Further described are methods of making and using the improved anodes and batteries. In general, the anodes include a porous composite having a plurality of agglomerated nanocomposites. At least one of the plurality of agglomerated nanocomposites is formed from a dendritic particle, which is a three-dimensional, randomly-ordered assembly of nanoparticles of an electrically conducting material and a plurality of discrete non-porous nanoparticles of a non-carbon Group 4A element or mixture thereof disposed on a surface of the dendritic particle. At least one nanocomposite of the plurality of agglomerated nanocomposites has at least a portion of its dendritic particle in electrical communication with at least a portion of a dendritic particle of an adjacent nanocomposite in the plurality of agglomerated nanocomposites.

Yushin, Gleb↗

DOE OSTI2023

Electrodes, lithium-ion batteries, and methods of making and using same

Described herein are improved composite anodes and lithium-ion batteries made therefrom. Further described are methods of making and using the improved anodes and batteries. In general, the anodes include a porous composite having a plurality of agglomerated nanocomposites. At least one of the plurality of agglomerated nanocomposites is formed from a dendritic particle, which is a three-dimensional, randomly-ordered assembly of nanoparticles of an electrically conducting material and a plurality of discrete non-porous nanoparticles of a non-carbon Group 4A element or mixture thereof disposed on a surface of the dendritic particle. At least one nanocomposite of the plurality of agglomerated nanocomposites has at least a portion of its dendritic particle in electrical communication with at least a portion of a dendritic particle of an adjacent nanocomposite in the plurality of agglomerated nanocomposites.

Yushin, Gleb↗

DOE OSTI2022

An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗

DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗

DOE OSTI2021

Fermionic Partial Tomography via Classical Shadows

Here we propose a tomographic protocol for estimating any k-body reduced density matrix (k-RDM) of an n-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits. We prove that estimating all k-RDM elements to additive precision ϵ requires on the order of ($^{n}_{k}$)k 3/2 log(n)/ϵ 2 repeated state preparations, which is optimal up to the logarithmic factor. Furthermore, numerical calculations show that our protocol offers a substantial improvement in constant overheads for k ≥ 2, as compared to prior deterministic strategies. We also adapt our method to particle-number symmetry, wherein the additional circuit depth may be halved at the cost of roughly 2–5 times more repetitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗