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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An Immersed Finite Element Lagrangian-Eulerian Code-Coupling Framework

This report presents an assessment of immersed Eulerian-Lagrangian code-coupling techniques suitable for use in a broad range of mechanics applications. The coupling algorithm is based on an immersed finite element method that considers the Lagrangian and Eulerian overlap regions in the overall variational formulation. In this report the basic formulation details are presented followed by various aspects of the code-coupling algorithm using OpenIFEM as the Lagrangian/coupling framework. A series of representative test cases that illustrate the code-coupling algorithm are discussed. The current work provides an in-depth investigation into the immersed finite element method for the purposes of providing a rigorous coupling technique that is minimally invasive in the respective Eulerian and Lagrangian codes. A number of extensions to the base immersed finite element method have been examined. These extension include nodal and quadrature-based indicator functions, a Lagrangian volume-fraction calculation in regions of overlap, and the use of penalty constraints between the Lagrangian and Eulerian domains. A unique MPI-based coupling strategy that retains the independent MPI structure of each code has been demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via h and p-Geometric Refinement [Slides]

Spectral element methods (SEM) are extensions of finite element methods (FEM) that employ Gauss-Lobatto or similar nodes instead of equidistant nodes for high-order elements. SEM can deliver superior accuracy compared to equidistant FEM due to potential superconvergence. However, significant challenges remain for domains with curved boundaries, which have limited the advantages of SEM for real-world applications. In this work, we propose a novel approach to bolster the overall accuracy and preserve the superconvergence of SEM over curved domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Unified cohesive zone model (UCZM) for fracturing and fragmenting solids

Here, a Unified Cohesive Zone Model (UCZM), which inherits most of the advantages while overcoming the shortcomings of existing Cohesive Zone Models (CZMs), is proposed. Similar to the traditional extrinsic CZM approach, UCZM dynamically inserts the cohesive elements into the system based on local material states (e.g., stress, strain). However, the transition from continua to discontinua is smoothly achieved, thereby eliminating the “time-discontinuous” issue seen in the extrinsic CZM. Moreover, within the novel UCZM framework, the point of transition from continua to discontinua is controllable through the introduction of crack initialization criteria. As a result, the UCZM allows any material models (e.g., elastic, plastic, damage models) for continuum solids and for discrete fracture behavior to work together. In essence, both an enhanced extrinsic cohesive zone model and an intrinsic cohesive zone model can be represented by the proposed unified model. The proposed UCZM has been verified through different numerical examples. The work demonstrates that the UCZM is a highly effective approach for modeling fracture and fragmentation processes in solids.

42 ENGINEERING↗
DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A novel peridynamics-based approach to predict pharmaceutical tablet robustness

The pharmaceutical drug product development process can be greatly accelerated through the use of modeling and simulation techniques to predict the manufacturability and performance of a given formulation. The anticipation and possible mitigation of tablet damage due to manufacturing stresses represents a specific area of interest in the pharmaceutical industry for predicting formulation and tableting performance. While the finite element method (FEM) has been extensively used for predicting the mechanical behavior of powder material in the compaction processes, a shortcoming of the approach is the inherent difficulty to predict discontinuities (e.g., damage or cracking) within a tablet as FEM is a continuum-based approach. In this work, we propose a novel method utilizing peridynamics (PD), a numerical method that can capture discontinuities such as tablet fracture, to predict the evolution of damage and breakage in pharmaceutical tablets. The approach links (1) the finite element method – to elucidate the behavior of powders during die compaction – with (2) the peridynamics modeling technique – to model the discontinuous nature of damage and predict tablet breakage during the critical stages of unloading and ejection from the compression die. This short communication presents a proof of concept including a workflow to calibrate the linked FEM-PD simulation models. Further, it demonstrates promising results from a preliminary experimental validation of the approach. Following further development, this approach could be used to guide the optimization of compression processes through targeted changes to formulation material properties, compression process conditions, and/or tooling geometries to deliver improved process efficiency and tablet robustness.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Transformer Leakage Inductance Design Methodology

The leakage inductance exhibited by a transformer depends on its winding geometry, which generally involves the selection of several key design parameters in addition to the winding structure and the interleaving configuration. With few resources explaining the effects of these design choices on the observed leakage inductance, numerous trial-and-error iterations become necessary to realize the desired leakage inductance. This paper explores more than a hundred winding geometries feasible in a 2-winding transformer comprising the same magnetic core, number of turns, and wire gauge, and finds the leakage inductance for each unique design using 2-D finite element method (FEM) simulations in association with the semi-analytical double- 2-D model. These leakage inductances are plotted and further analyzed to understand the effects of different design parameters on the effective leakage inductance. The results presented herein and the conclusions drawn from this research can serve as a valuable resource for future design practitioners from both industry and academia.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

NEAMS TH CRAB

The MOOSE framework is a library designed to make it straightforward for physicists and engineers to model partial differential equations using finite element and finite volume methods. Finite elements have been a part of the framework library since MOOSE's inception over a decade ago. Initial finite volume capability, however, was added only as recently as May of 2020. Since that time, significant work has been conducted to develop fluid modeling capability based on the finite volume method. Much of this work has taken place in MOOSE's navier_stokes module and in the NEAMS program's coarse mesh CFD code Pronghorn. We report here on development in MOOSE and Pronghorn of incompressible, porous incompressible, and weakly compressible finite volume simulation capabilities and their application to modeling of MSR and FHR advanced reactor concepts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗
DOE OSTI2025

Advanced System Thermal Fluids Solver Development for SAM

This work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key is the implementation of a high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. Leveraging the existing capabilities of the SAM code, significant code coverages were established in the finite volume method code. This in turn allows for a suite of test problems with different problem sizes and levels of complexity to be used to quantify the performance improvement of the finite volume method code. As evidently shown in this study, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE for the wide range of selected problems. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. In addition, for a complex reactor model, transient simulation was performed using the finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development. In this work, short-term priority development and testing items were identified, and long-term code adoption and integration plans were made for the eventual deployment of the finite volume method in the SAM code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

NRC Multiphysics Analysis Capability Deployment FY2020: Part 3

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Sup- port for Advanced Non-Light Water Reactors.” The tasks completed for this report are: Task2c: Explicit modeling of pebble transient temperature response. In this simulation, the 400 MWth Pebble-Bed Modular Reactor (PBMR) design, PBMR- 400, experiences a 20-second power ramp from 100% to 150% power. This is followed by a similar reduction in the power back to 100%. Several multiscale pebble coupling approaches are tested with one pebble per mesh element in the active core region. The results show good conservation behavior and the stability of the coupling.; Extended scope part 1: An assessment of the computational efficiency of the Discontinuous Finite Element Method (DFEM) heat transfer solver shows good scalability. The DFEM solver is a factor of 4 more expensive in solution time than the Finite Element Method (FEM) solver for heat transfer problems due to the increased number of degrees of freedom. Nonetheless, the DFEM approach provides the user with the flexibility to model gap heat transfer problems.; Extended scope part 2: The GapHeatTransferInterfaceMaterial was improved to give the user increased flexibility with the modeling of heat transfer through gaps with the DFEM solver. A number of gap parameters can now be coupled both through functions and variables.; Extended scope part 3: Demonstration of how the gap width between hexagonal fuel cells can be calculated during a heat-up transient and used in the GapHeatTransferInterface model. A full-domain DFEM model with gap expansion is coupled to a SubApp that models the thermal expansion of the base plate. The results show the expected physical behavior, although have not been fully bench-marked at this point in time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Deep Learning-Assisted Real-Time Forward Modeling of Electromagnetic Logging in Complex Formations

Higher dimensional (i.e., 2-D and 3-D) modeling is indispensable to correctly evaluate the responses of electromagnetic logging tools in complex formation environments. However, limited by the high computational cost of rigorous modeling such as finite difference method and the finite element method, the real-time applications in the well logging industry primarily rely on the 1-D forward solver, which would result in erroneous formation evaluation for complex scenarios. As a result, aiming at realizing fast modeling for electromagnetic logging tools in complex formations, this paper proposes a general framework assisted by deep neural networks (DNNs). The framework consists of three modules: earth model classification, parameter extraction, and surrogate construction. Separate DNNs are trained and tested for different modules. The accuracy and efficiency of the DNN assisted fast modeling are validated by several experiments. Here, this study finds that the fast modeling assisted by DNNs is able to calculate the tool responses and reconstruct the subsurface formations in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Pronghorn Porous Media Model Validation with Pressure Drop Measurements

The verification and validation (V&V) of Pronghorn is imperative to assert its accuracy when predicting the fluid velocity, temperature, and pressure in high temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, and multidimensional thermal-hydraulics (TH) code developed by the Idaho National Laboratory (INL). New pebble bed experiments are used to observe the details of the fluid motion and pressure drop in the porous bed under the reactor normal operation. This paper focuses on the validation of the Pronghorn compressible and incompressible Navier-Stokes equations using the pressure drop measurements performed at the engineering-scale pebble bed facility at the Texas A&M university (TAMU). Various pressure drop correlations and porosity functions are implemented in both Pronghorn and STAR-CCM+ to compare the pressure drop due to the combined viscous and inertial resistances in the porous bed. The correlations accounting for the near-wall effect are also utilized to observe if the pressure drop estimates can be improved. Pronghorn porous media models predict the pressure drop well relative to the STAR-CCM+ simulation results and 1D correlations, and both the finite element method (FEM) and finite volume method (FVM) perform accurately. Pronghorn models are also validated with the experimental measurements given the different Reynolds number ranges and specific aspect ratios. The likelihood of the statistical significance between the pressure drop measurements and specific correlations or simulations is low provided that the overlap of their confidence intervals is more than the half of a single arm. Several validation metrics are reasonable in regard to the similar studies from other literature. The precise average pebble bed porosity estimation has much impact on the pressure drop, and the Foumeny and Montillet (dense packing) models carry out the accurate pressure drop prediction by considering the near-wall effect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗
DOE OSTI2022

Using porous random fields to predict the elastic modulus of unoxidized and oxidized superfine graphite

Nuclear graphite is a candidate material for Generation IV nuclear power plants. Porous materials such as graphite can contain complex networks of pores that influence the material's mechanical and irradiation response. A methodology known as the random finite element method (RFEM) was adapted to create synthetic microstructures and predict the influence of porosity on the elastic properties of graphite during oxidation. RFEM combines random field theory and the finite element method in a Monte Carlo framework to estimate the mechanical response of a given grade of graphite. In this research, the random fields were verified through experimental characterization to predict the elastic response of three nuclear graphite grades, ETU-10, IG-110, and 2114. Finite element models (FEM) were generated using segmentations of x-ray computed tomography (XCT) data known as image-based models (IBMs) to validate and compare with the RFEM results and better understand the effects of uniform oxidation in these graphite grades. The RFEM predictions appear to correlate well with the experimental values of the measured Young’s modulus of the three graphite grades and display the same trends as IBMs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗