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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Advancements in ion diode and triode design

Selfconsistent laminar flow models, which enable to predict the optimal cathode and anode geometry in simple diodes, must be modified to account for the anode aperture and the effect of other electrodes. An equation for charge coupled to arbitrary laminar flows is here first presented and its numerical solutions are obtained with a new method, based on mesh transformations. It is found that a close match to theoretical flows requires an increase of the simple diode voltage v{sub 0} by an amount v{sub δ}, which, for a typical case designed for zero exit angle condition, are v{sub 0} = 0.7465 and v{sub δ} = 0.0294 in adimensional units. States “in” and “out” for the anode lens are also shown, where “out” is a new and nonlinear solution for the beam expansion in a drift tube.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2012

Methods for Detector Placement and Analysis of Criticality Accident Alarm Systems

Determining the optimum placement to minimize the number of detectors for a criticality accident alarm system (CAAS) in a large manufacturing facility is a complex problem. There is typically a target for the number of detectors that can be used over a given zone of the facility. A study to optimize detector placement typically begins with some initial guess at the placement of the detectors and is followed by either predictive calculations of accidents at specific locations or adjoint calculations based on preferred detector locations. Within an area of a facility, there may be a large number of potential criticality accident sites. For any given placement of the detectors, the list of accident sites can be reduced to a smaller number of locations at which accidents may be difficult for detectors to detect. Developing the initial detector placement and determining the list of difficult accident locations are both based on the practitioner's experience. Simulations following fission particles released from an accident location are called 'forward calculations.' These calculations can be used to answer the question 'where would an alarm be triggered?' by an accident at a specified location. Conversely, 'adjoint calculations' start at a detector site using the detector response function as a source and essentially run in reverse. These calculations can be used to answer the question 'where would an accident be detected?' by a specified detector location. If the number of accidents, P, is much less than the number of detectors, Q, then forward simulations may be more convenient and less time-consuming. If Q is large or the detectors are not placed yet, then a mesh tally of dose observed by a detector at any location must be computed over the entire zone. If Q is much less than P, then adjoint calculations may be more efficient. Adjoint calculations employing a mesh tally can be even more advantageous because they do not rely on a list of specific difficult-to-detect accident sites, which may not have included every possible accident location. Analog calculations (no biasing) simply follow particles naturally. For sparse buildings and line-of-sight calculations, analog Monte Carlo (MC) may be adequate. For buildings with internal walls or large amounts of heavy equipment (dense geometry), variance reduction may be required. Calculations employing the CADIS method use a deterministic calculation to create an importance map and a matching biased source distribution that optimize the final MC to quickly calculate one specific tally. Calculations employing the FW-CADIS method use two deterministic calculations (one forward and one adjoint) to create an importance map and a matching biased source distribution that are designed to make the MC calculate a mesh tally with more uniform uncertainties in both high-dose and low-dose areas. Depending on the geometry of the problem, the number of detectors, and the number of accident sites, different approaches to CAAS placement studies can be taken. These are summarized in Table I. SCALE 6.1 contains the MAVRIC sequence, which can be used to perform any of the forward-based approaches outlined in Table I. For analog calculations, MAVRIC simply calls the Monaco MC code. For CADIS and FW-CADIS, MAVRIC uses the Denovo discrete ordinates (SN) deterministic code to generate the importance map and biased source used by Monaco. An adjoint capability is currently being added to Monaco and should be available in the next release of SCALE. An adjoint-based approach could be performed with Denovo alone - although fine meshes, large amounts of memory, and long computation times may be required to obtain accurate solutions. Coarse-mesh SN simulations could be employed for adjoint-based scoping studies until the adjoint capability in Monaco is complete. CAAS placement studies, especially those dealing with mesh tallies, require some extra utilities to aid in the analysis. Detectors must receive a minimum dose rate in order to alarm; therefore, a simple yes/no plot could be more useful to the analyst than a standard dose rate contour plot. Alarm systems that require several detectors to alarm simultaneously for a given accident would need to combine several yes/no plots in order to show accident sites where multiple detectors would be triggered. This could require a plot of 'areas of coverage' that is mapped over the building geometry. Several new utilities (which will be part of SCALE 6.2) were created to help with CAAS analysis.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2012

Three-dimensional plastic response in polycrystalline copper via near-field high-energy X-ray diffraction microscopy

The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Here, using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ~2 µm length scale with ~0.1° orientation precision. Lattice rotations within grains are tracked between states with ~1° precision. Detailed analysis is presented for a sample cross section before and after ~6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.

Baek, Jonghyuk↗
DOE OSTI2015

Predictive Engineering Tools for Injection-Molded Long-Carbon-Fiber Thermoplastic Composites - Second FY 2015 Quarterly Report

During the second quarter of FY 2015, the following technical progress has been made toward project milestones: 1) Autodesk reviewed 3D fiber orientation distribution (FOD) comparisons and provided support on improving accuracy. 2) Autodesk reviewed fiber length distribution (FLD) data comparisons and provided suggestions, assisted PNNL in FOD and FLD parameter settings optimization, and advised PNNL on appropriate through thickness thermal conductivity for improved frozen layer effect on FOD predictions. Autodesk also participated in project review meetings including preparations and discussions towards passing the go/no-go decision point. 3) Autodesk implemented an improved FOD inlet profile specification method through the part thickness for 3D meshes and provided an updated ASMI research version to PNNL. 4) The University of Illinois (Prof. C.L. Tucker) provided Autodesk with ideas to improve fiber orientation modeling 5) Purdue University re-measured fiber orientation for the fast-fill 50wt% LCF/PA66 edge-gated plaque, and delivered the fiber orientation data for this plaque at the selected locations (named A, B, and C, Figure 1) to PNNL. Purdue also re-measured fiber orientation for locations A on the fast-fill 30wt% LCF/PP and 50wt% LCF/PA66 center-gated plaques, which exhibited anomalous fiber orientation behavior. 6) Purdue University conducted fiber length measurements and delivered the length data to PNNL for the purge materials (slow-fill 30wt% LCF/PP and 30wt% LCF/PA66 purge materials) and PlastiComp plaques selected on the go/no-go list for fiber length model validation (i.e., slow-fill edge-gated 30wt% LCF/PP and 30wt% LCF/PA66 plaques, Locations A, B, and C). 7) PNNL developed a method to recover intact carbon fibers from LCF/PA66 materials. Isolated fibers were shipped to Purdue for length distribution analysis. 8) PNNL completed ASMI mid-plane analyses for all the PlastiComp plaques defined on the go/no-go list for fiber orientation (FO) model validation and compared the predicted fiber orientations with the measured data provided by Purdue at Locations A, B, and C on these plaques. The 15% accuracy criterion based on evaluation of tensile and bending stiffness was used to assess the accuracy in fiber orientation predictions. 9) PNNL completed ASMI mid-plane analyses for all the PlastiComp plaques defined on the go/no-go list for fiber length distribution (FLD) model validation and compared the predicted length distributions with the measured data provided by Purdue at Locations A, B, and C on these plaques. The 15% accuracy criterion based on evaluation of tensile and bending stiffness was used to assess the accuracy in fiber orientation predictions. 10) PNNL tested the new ASMI version received from Autodesk in March 2015, examined and discussed 3D fiber orientation predictions for PlastiComp plaques. 11) PlastiComp, Inc. (PlastiComp), Toyota Research Institute North America (Toyota) and Magna Exteriors and Interiors Corporation (Magna) participated in discussions with team members on the go/no-go plan. Toyota continued the discussion with Magna on tool modification for molding the complex part in order to achieve the target fiber length in the part.

42 ENGINEERING↗
DOE OSTI2025

Evaluating pulse-shaping capabilities of next-generation pulsed power architectures

This project evaluated the pulse shaping capabilities of next-generation pulsed power (NGPP) architectures. NGPP architectures share several common attributes including multiple independent pulse-generation lines, a radial water-insulated impedance transformer, and a central vacuum insulated load region. A multi-module circuit model was developed, incorporating independent pulse-generation lines and a 2-D transmission line mesh of the radial impedance transformer to assess the effects of azimuthal asymmetry in pulse-shaped experiments. Circuit model simulations demonstrated that NGPP architectures are able to produce the the desired current pulse shapes for exemplar NGPP experiments. Additionally, the project explored automated methods for experiment design, including derivative -ree optimization and machine learning. Pulse-shaped experiments require designers to determine machine parameters that reliably produce the desired current pulse at the load, a process that typically relies on expert knowledge and iterative adjustments using the Z circuit model. Given the increased complexity of NGPP systems, this manual approach may be impractical. While the evaluated methods do not eliminate the need for manual iteration, they can reduce the time required for experiment design. Derivative-free optimization automates much of the trial-and-error process, providing a close starting point for manual adjustments or making small modifications to near-final designs. Meanwhile, deep neural network methods can generate a good qualitative match to the desired current pulse in under one second without requiring circuit model simulations.

42 ENGINEERING↗
DOE OSTI2021

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. Here, a completely new approach, termed TEMO (truncation error matching and optimization), is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles directly allow for the construction of stable 8th To the best of the authors' knowledge, these are the highest orders ever achieved for a cut-cell discretization by a significant margin. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

The Simulation of Precipitation Evolutions and Mechanical Properties in Friction Stir Welding with Post-Weld Heat Treatments

A finite element model of friction stir welding capable of re-meshing is used to simulate the temperature variations. Re-meshing of the finite element model is used to maintain a fine mesh resolving the gradients of the solution. The Kampmann–Wagner numerical model for precipitation is then used to study the relation between friction stir welds with post-weld heat treatment (PWHT) and the changes in mechanical properties. Results indicate that the PWHT holding time and PWHT holding temperature need to be optimally designed to obtain FSW with better mechanical properties. Higher precipitate number with lower precipitate sizes gives higher strength in the stirring zone after PWHT. The coarsening of precipitates in HAZ are the main reason to hinder the improvement of mechanical property when PWHT is used.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Physical Model for Understanding the Activation of MoS 2 Basal-plane Sulfur Atoms for the Hydrogen Evolution Reaction

All the DFT calculations are done with the Vienna Ab Initio Simulation Package (VASP) using the projector augmented wave method. The Bayesian error estimation exchange-correlation functionals (BEEF) with van der Waals interactions are employed. A plane-wave cutoff energy of 400 eV is used together with PAW-PBE potentials where semi core p states are treated as valence. All the calculations allow for spin-polarization. The structures are relaxed until the force is converged to < 0.01 eV/Å. The lattice parameter of MoS 2 unit cell, optimized with this functional, is 3.19 Å. A (4×4) supercell is used to model all the transition metal doped MoS 2 systems studied here, including those with S vacancies. For calculations in the initial dopant structure exploration, the Brillouin zone is sampled with a 3x3x1 Monkhorst-Pack k-point mesh. A 6×6×1 Monkhorst-Pack k-point mesh is used for the H binding energy and density of states calculations. In all calculations, the vacuum layer is set as 15 Å to eliminate periodic interaction perpendicular to the basal plane.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗
DOE OSTI2023

Rate of Para-Orthohydrogen Conversion in Cryogenic Vortex Tube

Raising efficiency of the cooling process for cryogenic hydrogen and minimizing hydrogen boil-off during storage and transportation of liquid hydrogen are critically important factors for widening implementation of hydrogen-based clean energy systems. One novel approach involves utilization of relatively simple catalyzed vortex tubes, where hydrogen in the primarily para- nuclear spin isomer form is converted into the ortho- form while consuming a significant amount of heat. To design such systems effectively, better understanding is required about catalyst-assisted para-orthohydrogen conversion rates in high-speed vortical flows. In this study, a computational fluid dynamics simulation has been set up to model an experimental system with cryogenic hydrogen vortex tubes. Mesh-verification and a validation study has been conducted first for a non-catalyzed tube. Then, the rate coefficient of the para-orthohydrogen conversion of cryogenic hydrogen has been determined by matching numerical results with experimental data available for a catalyzed vortex tube. Furthermore, the presented information can help design and optimize cryogenic hydrogen cooling within vortex tubes.

08 HYDROGEN↗
DOE OSTI2016

Comparison between Flownex and Corona thermal-hydraulic models for a single HTR prismatic fuel assembly - 18544

Computational tools and methodologies that can perform thermal-hydraulic analyses to reasonably predict the temperature distribution for the whole core of HTRs are useful for operational and safety analyses. In this paper, Flownex (a system code based on a one-dimensional thermal-fluid network methodology) and CORONA (Core Reliable Optimization and thermo-fluid Network Analysis) thermal-hydraulic models and results for a vertically stacked single fuel assembly will be compared. In Flownex, a basic unit cell containing part of the graphite and the associated fuel elements and coolant channels was developed. CORONA uses a basic unit cell concept for generating computational grids using several types of basic unit cells to model the heat transfer through the hexagonal blocks and a 1-D formulation to model the flow through the coolant channels. In CORONA, computational grids are generated using a combination of pre-generated mesh cells. The coolant channels and fuel rods are modelled explicitly. Flownex in contrast, models fuel and coolant channels implicitly by defining representative coolant channels, fuel rods and coated particle layers associated with each unit cell. Flownex can therefore model temperatures at coated particle level and also through each graphite block. The computational mesh employed by Flownex is much coarser than the mesh employed by CORONA. In both models, the helium gap between the fuel compact and the graphite block is modelled as stagnant. Flownex results were found to be of the same order of magnitude as those obtained using CORONA. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

h5bench: A unified benchmark suite for evaluating HDF5 I/O performance on pre‐exascale platforms

Summary Parallel I/O is a critical technique for moving data between compute and storage subsystems of supercomputers. With massive amounts of data produced or consumed by compute nodes, high‐performant parallel I/O is essential. I/O benchmarks play an important role in this process; however, there is a scarcity of I/O benchmarks representative of current workloads on HPC systems. Toward creating representative I/O kernels from real‐world applications, we have created h5bench , a set of I/O kernels that exercise hierarchical data format version 5 (HDF5) I/O on parallel file systems in numerous dimensions. Our focus on HDF5 is due to the parallel I/O library's heavy usage in various scientific applications running on supercomputing systems. The various tests benchmarked in the h5bench suite include I/O operations (read and write), data locality (arrays of basic data types and arrays of structures), array dimensionality (one‐dimensional arrays, two‐dimensional meshes, three‐dimensional cubes), I/O modes (synchronous and asynchronous). In this paper, we present the observed performance of h5bench executed along several of these dimensions on existing supercomputers (Cori and Summit) and pre‐exascale platforms (Perlmutter, Theta, and Polaris). h5bench measurements can be used to identify performance bottlenecks and their root causes and evaluate I/O optimizations. As the I/O patterns of h5bench are diverse and capture the I/O behaviors of various HPC applications, this study will be helpful to the broader supercomputing and I/O community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Iteration-based Linearized Distribution-level Locational Marginal Price for Three-phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Choosing Transport Events for Initiating Splitting and Rouletting

A study was performed to determine which transport events should be used to initiate a weight window lookup to achieve the best variance reduction performance. A weight window lookup potentially triggers particle splitting (in important regions of phase space) or rouletting (in unimportant regions), thereby optimizing computational effort. Potential initiating transport events include collisions (both pre- and post-collision), geometry surface crossings, traversing a mean-free path, and streaming across a weight window boundary. Permutations of these initiating events were tested on an urban model with background radiation sources and a spent fuel cask with a neutron dose mesh tally. Generally, all methods perform better with finer weight window meshes. Tracking on weight windows performs well for coarse weight window meshes, while a combination of splitting each mean-free path, geometric surface crossing, and before collisions performs well for fine weight window meshes.

42 ENGINEERING↗
DOE OSTI2021

Method and apparatus for shape-based energy analysis of solids

A computer-readable medium stores instructions including storing a model of a physical structure and defining a mesh for the model. The mesh includes finite elements, each defined by a respective set of edges. The instructions include, for each finite element, identifying a governing differential equation and a set of complementary functions that exactly satisfy the governing differential equation. The instructions include determining an applied physical stimulus for the physical structure. The instructions include generating an energy optimization model that minimizes a difference between internal energy and external energy of the finite elements in response to the applied physical stimulus. The model includes a matrix of respective scalar multipliers for the complementary functions for each finite element. The instructions include transforming the matrix and calculating a physical parameter of interest. The instructions include, in response to the physical parameter not satisfying a design parameter, updating the model of the physical structure.

Spears, Robert E.↗