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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods

In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗
DOE OSTI2022

A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces

Here we present a new method for coupled linear elasticity problems whose finite element discretization may lead to spatially non-coincident discretized interfaces. Our approach combines the classical Dirichlet–Neumann coupling formulation with a new set of discretized interface conditions obtained through Taylor series expansions. We show that these conditions ensure linear consistency of the coupled finite element solution. We then formulate an iterative solution method for the coupled discrete system and apply the new coupling approach to two representative settings for which we also provide several numerical illustrations. The first setting is a mesh-tying problem in which both coupled structures have the same Lamé parameters whereas the second setting is an interface problem for which the Lamé parameters in the two coupled structures are different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. Furthermore, this work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

42 ENGINEERING↗
DOE OSTI2020

Simulation of the Fast Reactor Fuel Assembly Duct-Bowing Reactivity Effect Using Monte Carlo Neutron Transport and Finite Element Analysis

This paper discusses a new method of simulating the fuel assembly duct-bowing reactivity coefficient for EBR-II run 138B. Quantification of the fuel assembly duct-bowing reactivity effect in liquid metal–cooled fast reactors has been a persistent problem since they were first designed and operated. Simulation of the duct-bowing reactivity effect is difficult because the level of detail required to simulate the effect has exceeded most modeling capabilities. The new method outlined in this paper utilizes the finite element analysis code ANSYS to analyze the thermal and structural components. Here, the displacement of the fuel assembly duct due to thermal expansion and mechanical interaction was calculated by ANSYS using recorded EBR-II run 138B temperature and power boundary value data. The displacement values were incorporated into to a Monte Carlo model of EBR-II run 138B and keff was calculated. Multiple Monte Carlo calculations were performed with duct displacement values corresponding to different reactor temperatures. Using the calculated keff values associated with the different duct displacement results allowed calculation of the duct-bowing reactivity coefficient. The duct-bowing reactivity coefficient was calculated to be –14.5 × 10 –4 $/°C/ ± 4.4%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enabling topography-resolving structural dynamic contact simulation

Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces may have a strong effect, especially in the partial slip/liftoff regime. We recently proposed a multi-scale method, which couples finite element and boundary element modeling. The primary benefit of this approach is that it permits to analyze the effect of the actual contact topography on the dynamics of jointed structures. While this multi-scale modeling method was initially developed for quasi-static analysis, we demonstrate herein how it can be used for time step integration and Harmonic Balance analysis. We cross-verify those fully dynamic analysis methods against each other and quasi-static results, for the S4 Beam benchmark. We compare the multi-scale method against state-of-the-art full-FE analysis, in terms of numerical damping and computational performance. Some discrepancy is found to be of physical origin. Depending on the load history, it is shown that the system settles to a slightly different equilibrium. Finally, transient multi-scale simulations enable the prediction of this interesting phenomenon, for the first time, for a structure with bolted joints.

Frictional-unilateral contact↗
DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Solving differential equations using deep neural networks

Recent work on solving partial differential equations (PDEs) with deep neural networks (DNNs) is presented. The paper reviews and extends some of these methods while carefully analyzing a fundamental feature in numerical PDEs and nonlinear analysis: irregular solutions. First, the Sod shock tube solution to the compressible Euler equations is discussed and analyzed. This analysis includes a comparison of a DNN-based approach with conventional finite element and finite volume methods, and demonstrates that the DNN is competitive in terms of degrees of freedom required for a given accuracy. Further, the DNN-based approach is extended to consider performance improvements and simultaneous parameter space exploration. Next, a shock solution to compressible magnetohydrodynamics (MHD) is solved for, and used in a scenario where experimental data is utilized to enhance a PDE system that is a priori insufficient to validate against the observed/experimental data. This is accomplished by enriching the model PDE system with source terms that are then inferred via supervised training with synthetic experimental data. The resulting DNN framework for PDEs enables straightforward system prototyping and natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of an entire parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

IC reports (2021)

We requested HPC support to continue research on the seismic waves generated by impacts. We used the following codes: (1) the Hybrid Optimization Software Suite (HOSS), developed at LANL. HOSS is based on a combined Finite and Discrete Element Method (FDEM). New material models are developed for the sedimentary rocks. HOSS has been recently benchmarked to iSale and FLAG codes. SPECFEM3D is an open-source code developed since the last 90s. It won the Gordon Bell award for best performance in 2003, was finalist again in 2008 for a run at 0.16 petaflops on 149,784 cores on the ‘Jaguar’ Cray system at Oak Ridge National Laboratory. It also won the BULL Joseph Fourier supercomputing award in 2010.; SW4 is a 4th-order finite difference code developed at LLNL which is currently actively developed to handle complex 3D models and to be ported on future exascale platforms. We assessed our need to a total of 3.9M CPU-hrs for year 1 and and 3.1 M for year 2.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Multiscale and multiphysics FEA simulation and materials optimization for laser ultrasound transducers

In this study, the relationship between the nanocomposite design and the laser ultrasound transducer (LUT) characteristics was investigated through simulations in multiple scale levels for material behavior, device response, and acoustic wave propagation in media. First, the effects of the nanoparticle size and concentration on the effective properties of composites were quantitatively investigated with the finite element analysis (FEA) method. Second, the effective properties of the nanocomposite were assigned to the layer, which is modeled as a homogeneous material, in the FEA for the LUT simulating the energy conversion from the incident laser to the acoustic wave. Finally, the ultrasound propagation in the water was calculated by a theoretical wave propagation model. The FEA-based prediction was compared with the experimental data in the literature and a theoretical analysis for LUT based on Thermal-Acoustic coupling. As a result, the ultrasound waves on the transducer surface and at a distance in the water could be predicted. Based on the hierarchically integrated prediction procedure, the optimal conditions of the photoacoustic nanocomposites were investigated through the parametric study with the particle size and concentration as variables. The results guide the material designs optimized for different device characteristics, such as high pressure and broad bandwidth.

36 MATERIALS SCIENCE↗
DOE OSTI2026

X-ray tomography of damage dynamics in advanced materials using a laser wakefield accelerator

Additively manufactured (AM) metals offer the potential for customizable, cost-effective components, but qualification and certification are crucial. Key to this process is understanding pore dynamics under stress, typically analyzed using micro-computed tomography. This study introduces laboratory-scale “betatron” x-rays from laser wakefield acceleration as a high-throughput alternative for x-ray tomography of advanced materials, such as AM AlSi10Mg alloys. Coupled with 3D finite element modeling, this method provides detailed insights into stress-porosity interactions. The approach delivers high-resolution scans, revealing that pore shape and local triaxiality significantly influence fracture dynamics, supporting advanced material characterization. This work also demonstrates the potential and versatility of laser-betatron x-ray μCT for generating large datasets to accelerate our understanding of the stochastic, process-specific nature of pore formation in AM alloys.

Senthilkumaran, Vigneshvar↗
DOE OSTI2022

A Structural Design Approach Tailored for the Rapid Preliminary Design of Microreactor Components

High-temperature microreactors can play a role in developing reliable, portable energy sources for off-grid remote locations, microgrid concepts, and industrial process heat. Portability and passive safety criteria tend to skew microreactor structural component designs toward complex geometries, high thermal stresses, and design bases with large numbers of startup/shutdown cycles. Current design rules, as typified by Section III of the American Society of Mechanical Engineers (ASME) Boiler & Pressure Vessel Code, are less than optimal for these conditions, particularly for preliminary component designs where developers need to rapidly consider a large number of potential component configurations. This paper presents a design method targeted toward rapid, efficient evaluation of preliminary component designs using modern finite element analysis. The new method retains key connections with the ASME Code rules and design data while streamlining the design approach. This paper presents the design method, several verification examples illustrating the similarities and differences between the new method and the current ASME rules, and the application of the new approach to the evaluation of a test article mimicking key features of a heat pipe–cooled microreactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

mgsflib

Code for my PhD thesis that creates meshes using gmsh and code I wrote to create high-order hybrid meshes to use for testing a hybrid method between spectral element method and generalized finite differences. It also uses a tetrahedral mesh improvement method called "stellar" to improve mesh quality near a curved boundary.

Jones, Jacob↗
DOE OSTI2022

Unstructured mesh-based multi-physics reactor transient simulation with iMC code

In this study, we present a time-dependent Monte Carlo simulation result about a complex fuel-loaded light water reactor system with thermal-hydraulic feedback using the KAIST iMC code. The intra-pin temperature distribution is calculated based on Monte Carlo-tallied detailed power distribution and the finite element heat transfer method. The temperature effect of fuel, absorber, and coolant are adequately reflected into the dynamic response by the on-the-fly Doppler broadened cross-section correction. For the time-dependent Monte Carlo transport simulation, the predictor-corrector quasi-static Monte Carlo method is used for this study. We tested the coupled analysis framework with a 17-by-17 fuel assembly loaded with the centrally-shielded burnable absorber (CSBA) fuel element. The temperature feedback effect on the material cross-section and the moderator density incurred negative reactivity in response to the external positive reactivity insertion, showing the inherent stability of the reactor system. The pin-wise power and temperature change during the system transient are presented and discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Recent Progress in U-10Mo Mechanical and Thermophysical Property Characterization

Results are presented on the mechanical and thermophysical property characterization of U-10Mo as part of the MP-1 qualification campaign. The thermal diffusivity, specific heat and thermal conductivity of as fabricated U-10Mo fuel foils and plates were measured using the thermal conductivity microscope (TCM), differential scanning calorimeter (DSC) and laser flash analyzer (LFA) all of which located in a shielded glove box – thermal property cell (TPC). A novel inverse method based on finite element analysis was developed to evaluate the thermal diffusivity of composite/layered materials via the LFA technique such as the 5-lyered U-10Mo monolithic fuel mini-plates.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗