Search NASA⌕ Search

SEARCH · Search NASA

Results for “finite element Method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Bipartite mutual information in classical many-body dynamics

Information theoretic measures have helped to sharpen our understanding of many-body quantum states. As perhaps the most well-known example, the entanglement entropy (or more generally, the bipartite mutual information) has become a powerful tool for characterizing the dynamical growth of quantum correlations. By contrast, although computable, the bipartite mutual information (MI) is almost never explored in classical many particle systems; this owes in part to the fact that computing the MI requires keeping track of the evolution of the full probability distribution, a feat which is rarely done (or thought to be needed) in classical many-body simulations. Here, we utilize the MI to analyze the spreading of information in 1D elementary cellular automata (CA). Broadly speaking, we find that the behavior of the MI in these dynamical systems exhibits a few different types of scaling that roughly correspond to known CA universality classes. Of particular note is that we observe a set of automata for which the MI converges parametrically slowly to its thermodynamic value. We develop a microscopic understanding of this behavior by analyzing a two-species model of annihilating particles moving in opposite directions. Furthermore, our work suggests the possibility that information theoretic tools such as the MI might enable a more fine-grained characterization of classical many-body states and dynamics.

Cellular automata↗
DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to adequately model observed phenomena or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis, and specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference, and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modeling and algorithmic extensions which serve to show the wide applicability of nonlocal modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗
DOE OSTI2016

High-order solution methods for grey discrete ordinates thermal radiative transfer

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

CAM-SE–CSLAM: Consistent Coupling of a Conservative Semi-Lagrangian Finite-Volume Method with Spectral Element Dynamics

An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and consistent (for a constant mixing ratio, the CSLAM solution reduces to the SE solution for air mass) transport that is efficient and accurate. This is achieved by first deriving formulas for diagnosing SE airmass flux through the CSLAM control volume faces. Thereafter, the upstream Lagrangian CSLAM areas are iteratively perturbed to match the diagnosed SE airmass flux, resulting in an equivalent upstream Lagrangian grid that spans the sphere without gaps or overlaps (without using an expensive search algorithm). This new CSLAM algorithm is not specific to airmass fluxes provided by CAM-SE but applies to any airmass fluxes that satisfy the Lipshitz criterion and for which the Courant number is less than one.

Lauritzen, Peter Hjort↗
DOE OSTI2016

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.

Cross sections↗
DOE OSTI2011

The reduced basis method for the electric field integral equation

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Type IV failure in weldment of creep resistant ferritic alloys: I. Micromechanical origin of creep strain localization in the heat affected zone

Creep strength enhanced ferritic (CSEF) steels containing 9-12wt% chromium have been extensively used in fossil-fuel-fired power plants. Despite their excellent creep resistance at high temperatures, premature failures (especially Type IV cracking) are often found in the fine-grained heat affected zone (HAZ) or intercritical HAZ of the welded components. This failure mode is preceded by the strain localization in the HAZ, as measured by the Digital Image Correlation (DIC) technique. The present work aims to develop a finite-element based computational method to determine the micromechanical and microstructural origin of the strain localization phenomenon. We construct a two-dimensional digital microstructure based on the actual microstructure of ferritic steel weldments by using the Voronoi-tessellation method, to account for the effects of its large grain-size gradients. A mechanism-based finite element method is developed for modeling the high temperature deformation resulting from a synergy of thermally activated dislocation movements, diffusional flow and grain boundary sliding. The numerical results agree well with the strain measurements by our DIC technique, particularly revealing the effect of pre-welding tempering on the evolution of strain localization in HAZ of creep resistant steel weldments. It is found that the diffusional creep with dependence on grain sizes, dislocation creep with dependence on material strength, and more importantly, grain boundary sliding, contribute synergistically to the creep strain accumulation in the HAZ, and their relative degree of significance is quantified. The creep rupture life will be investigated in the companion paper.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Elastic Modulus Estimation for Copper Syntactic Foams Reinforced with Iron Hollow Spheres of Different Wall Thicknesses

The present study estimates the effect on Young’s modulus of the percentage and thickness of iron hollow spheres reinforcing copper syntactic foams. The resulting materials were modeled by inserting hollow spheres in a random arrangement, using a combination of Discrete Element Method (DEM) for generating the sphere location coordinates and Finite Element Analysis (FEA). Estimations for syntactic foams were compared to those obtained for conventional copper foams with the same porosity. Results showed that the elastic modulus of both syntactic and conventional foams drops significantly as the percentage of spheres or porosity increases. Furthermore, the increase in the wall thickness of the iron hollow spheres leads to significant rises in the Young’s modulus. Depending on the desired mechanical properties, the outcomes presented in this work could be used for selecting the kind of foam (syntactic or conventional) and predesign some characteristics such as porosity or thickness of the spheres or pores.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Leaky guided waves in generic bars: Numerical prediction and experimental validation by means of ultrasonic underwater testing

Guided Ultrasonic Waves (GUWs) are used in several industrial and civil applications for the non-destructive tests and inspection of mechanical waveguides immersed in fluids. As well known, the impedance mismatch at the fluid-structure interface causes the bulk waves traveling inside the waveguide to be partially refracted in the surrounding fluid. The leakage of bulk waves involves continuous energy radiation along the propagation direction, resulting in high attenuation rates and, consequently, reduced inspection ranges. In this work, the dispersion behaviour of leaky guided waves that propagate in immersed waveguides of general cross-section is investigated. To this end, a Semi-Analytical Finite Element (SAFE) method coupled with a 2.5D Boundary Element method (BEM) is used to extract the wave dispersion equation. The proposed formulation avoids the well known limitations of analytical methods in treating complex geometries as well as those of Finite Element-based methods in representing propagation processes in unbounded domains. Numerical and experimental results are presented, in which the dispersion curves are extracted for different bars of arbitrary shape immersed in water. The results obtained in this paper can be useful for the design of testing conditions in practical applications and to tune experimental set up.

42 ENGINEERING↗
DOE OSTI2019

Asymmetrical Magnet Shape Optimization Based on S-C Mapping for Torque Profile Mitigation in Unidirectional Application of SPMS Machine

Surface-mounted Permanent Magnet Synchronous (SPMS) machines are widely used in applications that require low torque ripple, reduced vibration and acoustic noise. For those applications of SPMSM in which only unidirectional operation is needed, asymmetric design optimization show to have significant advantages over symmetric designs. In this paper, an analytical method based on Schwarz -Christoffel mapping is presented for asymmetrical magnet shape optimization in SPMS machine. In this method, permanent magnet is divided into finite cells so that each cell can be assigned with either air (OFF) or magnet (ON). The Optimization problem is solved using Genetic Algorithms (GAs). In order to remove non-manufacturable shapes, the cluster of materials and cleaning method is used and applied into magnet cells. The analytical method can significantly reduce the computation time used by optimization process as compared with methods based on Finite Element Analysis (FEA). This method is applied to a 12-pole SPMS machine. Validation of the S-C mapping method and final results are carried out using 2D and 3D finite element analysis. Here, the results obtained demonstrate that asymmetrical magnet shape improves cogging torque and torque ripple performance of SPMS machine by a significant margin.

42 ENGINEERING↗
DOE OSTI2022

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Predicting the flow stress of Zircaloy-4 under in-reactor accident conditions - 2016-0075

During loss-of-coolant accident (LOCA) and reactivity-initiated accident (RIA), nuclear fuel rods experience high heating rates that change the microstructure and properties of zirconium cladding materials. We sought to determine how different fast heating rates affect the kinetics of transformation and whether their consequences on the material yield stresses in the dual-phase region could be predicted. Phase fraction and texture of cold-rolled Zircaloy-4 were thus measured at fast heating rates similar to those experienced during LOCA and RIA by in situ high-energy synchrotron X-ray diffraction; the yield stress was also measured at different heating rates to the same dual-phase temperature by the electrical resistance method. A crystal plasticity finite-element model was used to simulate the flow stresses with the inputs of the measured phase fraction and texture. The model was calibrated using the flow stress at the heating rate of 10 deg. C s{sup -1} and used to predict the flow stress at the heating rate of 50 deg. C s{sup -1} at the same temperature. A significant shift of the β transus temperature was identified for fast heating rates in the range of 10 to 100 deg. C s{sup -1}. There was great similarity in texture at different heating rates. In the dual-phase temperature region, the α texture was almost identical to the starting texture, and the b texture was nearly random. Yield stresses of cold-rolled Zircaloy-4 decreased at a faster heating rate at the same temperature of 920 deg. C. A good agreement was found between the experimental and predicted flow stress at different heating rates, indicating this methodology can potentially be used to predict flow behavior in a fast transient regime. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2016

Uncertainty Quantification and Comparison of Weld Residual Stress Measurements and Predictions.

In pressurized water reactors, the prevention, detection, and repair of cracks within dissimilar metal welds is essential to ensure proper plant functionality and safety. Weld residual stresses, which are difficult to model and cannot be directly measured, contribute to the formation and growth of cracks due to primary water stress corrosion cracking. Additionally, the uncertainty in weld residual stress measurements and modeling predictions is not well understood, further complicating the prediction of crack evolution. The purpose of this document is to develop methodology to quantify the uncertainty associated with weld residual stress that can be applied to modeling predictions and experimental measurements. Ultimately, the results can be used to assess the current state of uncertainty and to build confidence in both modeling and experimental procedures. The methodology consists of statistically modeling the variation in the weld residual stress profiles using functional data analysis techniques. Uncertainty is quantified using statistical bounds (e.g. confidence and tolerance bounds) constructed with a semi-parametric bootstrap procedure. Such bounds describe the range in which quantities of interest, such as means, are expected to lie as evidenced by the data. The methodology is extended to provide direct comparisons between experimental measurements and modeling predictions by constructing statistical confidence bounds for the average difference between the two quantities. The statistical bounds on the average difference can be used to assess the level of agreement between measurements and predictions. The methodology is applied to experimental measurements of residual stress obtained using two strain relief measurement methods and predictions from seven finite element models developed by different organizations during a round robin study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditioner results in faster linear solve times but the ILU preconditioner exhibits better scalability. A weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. Here, we show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Verification of the 2D Finite Element SP3 Solutions

Method(FEM) is the free geometry handling. However many of the geometries of the nuclear engineering problems are not unstructured but rather structured, such as a hexahedral, or triangular prism. Thus, the need for the use of FEM has less portion in nuclear engineering. However it is also certain that it is very hard to exclude the possibility for use of an unstructured geometry such as a PBMR core problem, fusion blanket analysis of the source problem, another design issue with an unstructured geometry. In addition, research regarding the acceleration scheme such as Coarse Mesh Finite Difference (CMFD) showed up in nuclear engineering in recent years. By considering these facts, the FEM cannot be totally exclusive. To utilize the FEM for nuclear engineering problems, several types of assistance are needed. The first is parallelization because of its slow calculation speed. The second is an acceleration scheme. With these two types of assistance the FEM can be utilized freely in the nuclear engineering field. In this research, before conducting parallelization and acceleration, the final verification for the implementation of the up-scattering treatment with an arbitrary geometry conducted through a comparison with the McCARD solution through the well-known C5G7 2D benchmark problem. Note that the earlier work for verification of the FEM for the multi-group problem without up-scattering and with a structured geometry including a mathematical formulation has already been done. The main points that will be tested here are as follows. The first is a check of the right implementation for the multi-group problem with an up-scattering cross section from the perspectives of the multiplication factor and power. The second is the transport effect for this problem by comparing the solutions from P{sub 1} and Simplified P{sub 3}(SP{sub 3}). The third is the effectiveness of the higher order basis function for the same number of unknowns. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗