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DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures

The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

DOE OSTI2022

PyAlbany: A Python interface to the C++ multiphysics solver Albany

Albany is a parallel C++ finite element library for solving forward and inverse problems involving partial differential equations (PDEs). In this paper we introduce PyAlbany, a newly developed Python interface to the Albany library. PyAlbany can be used to effectively drive Albany enabling fast and easy analysis and post-processing of applications based on PDEs that are pre-implemented in Albany. PyAlbany relies on the library PyBind11 to bind Python with C++ Albany code. Here we detail the implementation of PyAlbany and showcase its capabilities through a number of examples targeting a heat-diffusion problem. In particular we consider the following: (1) the generation of samples for a Monte Carlo application, (2) a scalability study, (3) a study of parameters on the performance of a linear solver, and finally (4) a tool for performing eigenvalue decompositions of matrix-free operators for a Bayesian inference application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

SAM Plug-in Development (Phase I Final Report)

The DOE Office of Nuclear Energy (NE) has created an extensive set of advanced modeling and simulation tools for nuclear engineering analysis. The advanced capabilities of these newer analysis codes require more in-depth training, skills, and knowledge in order to effectively utilize them for the design, analysis, and licensing of advanced nuclear systems and experiments. A high learning curve for inexperienced users may deter organizations from incorporating these tools into their internal processes. This project involved development of a plug-in to the Symbolic Nuclear Analysis Package (SNAP) for the System Analysis Module (SAM) tool. SAM is an advanced system analysis tool for reactor transient analyses being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SNAP provides a highly flexible framework for creating, modifying and documenting input for engineering analysis codes such as SAM as well as extensive functionality for submitting, monitoring, and interacting with the codes through an intuitive graphical user interface (GUI). The common user interface provided by SNAP minimizes the learning curve for engineers starting with a new analysis code and provides an intuitive framework for transitioning between different analysis codes. SNAP provides a powerful but intuitive interface to facilitate access to advanced modeling and simulation tools for inexperienced users. Unlike many “form based” GUI’s, SNAP maps each engineering code’s component input to an internal database which manages all component input parameters along with component interconnections. This level of abstraction permits SNAP to support several advanced capabilities such as renodalization, model validation and consistency checks, embedded documentation, model notebook generation, data ownership and reviewer tracking, and variable assignment for inputs to name a few. SNAP includes a built-in Python interpreter and is interfaced to several commercial and open source packages including CPython, MATLAB/OCTAVE, Microsoft Office, Open Office, and SANDIA’s DAKOTA package which provides Uncertainty Quantification analysis through the SNAP plug-ins. Phase I of this project involved development a fully functional basic SAM plug-in to SNAP. This plug-in provides the ability to import existing models, graphically construct, edit and submit models using SNAP’s extensive functionality.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High- temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes ad- vantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

SAM User’s Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

SAM User's Guide

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1980

TAP 2: A finite element program for thermal analysis of convectively cooled structures

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗

NASA NTRS1991

STARS: An integrated general-purpose finite element structural, aeroelastic, and aeroservoelastic analysis computer program

The details of an integrated general-purpose finite element structural analysis computer program which is also capable of solving complex multidisciplinary problems is presented. Thus, the SOLIDS module of the program possesses an extensive finite element library suitable for modeling most practical problems and is capable of solving statics, vibration, buckling, and dynamic response problems of complex structures, including spinning ones. The aerodynamic module, AERO, enables computation of unsteady aerodynamic forces for both subsonic and supersonic flow for subsequent flutter and divergence analysis of the structure. The associated aeroservoelastic analysis module, ASE, effects aero-structural-control stability analysis yielding frequency responses as well as damping characteristics of the structure. The program is written in standard FORTRAN to run on a wide variety of computers. Extensive graphics, preprocessing, and postprocessing routines are also available pertaining to a number of terminals.

Gupta, Kajal K.↗

NASA NTRS2010

Fully-Implicit Navier-Stokes (FIN-S)

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

Kirk, Benjamin S.↗

NASA NTRSDate not supplied

FUN3D Mesh Adaptation Simulations of 4th AIAA High-Lift Prediction Workshop Case 1a

This paper describes in detail the FUN3D Mesh adaptation simulation results for Case 1a of the 4th AIAA High-Lift Prediction Workshop (HLPW-4). The Stabilized Finite Element library with FUN3D is used along with the Negative Spalart-Allmaras One-Equation Model to simulate fully turbulent free-air flow around the High Lift version of the Common Research Model at three flap settings. Meshes are adapted using multi-scale and goal-oriented metrics. The results are presented and the discussion focuses on the predicted differences between the three flap settings. Coefficients of lift, drag, and pitching moment are predicted within 7% of values measured in the QinetiQ 5m Wind Tunnel at each flap setting. Predicted surface pressures and skin friction distributions show inconsistent discrepancies with measurements across the flap settings. Consequently, flap increments for these figures of merit are not well predicted. These predictions are consistent with submissions to the HLPW-4 from other RANS-SA methods. Visualizations of Liutex vortex cores colored by angular velocity are presented as possible new quantitative and qualitative perspective for solution evaluation.

High-Lift Prediction Workshop↗

DOE OSTI2020

3D full wave fast wave modeling with realistic antenna geometry and SOL plasma

This paper reports the significant advancement of our ability to model and to understand how RF waves interact with the SOL plasma, by simulating the full torus 3D SOL plasma together with the antenna and core plasma. We introduce and use a recently developed and open source code, Petra-M, which was constructed on the scalable MFEM C++ finite element library, and performed 3D full wave simulations in the HHFW regime for both NSTX-U and LAPD plasmas. A first full wave simulation for a full 3D torus including a realistic antenna geometry and SOL plasma region for NSTX-U is presented. A scan of the antenna phasing shows a strong interaction between FWs and the SOL plasma for lower antenna phasing, which is consistent with previous NSTX HHFW observations. The effect of the 3D wave field on the fast ion population from NBI beams in NSTX-U is also discussed by using the 3D field obtained from the Petra-M simulations in the full-orbit following particle SPIRAL code. On LAPD, 3D full wave simulations of a new HHFW 4-strap antenna recently installed by TAE Technologies on LAPD are performed showing a qualitative agreement with experimental data.

Bertelli, Nicola↗

DOE OSTI2020

Comparison between PARFUME and Bison Using the AGR-2 Irradiation Experiment

This report documents comparisons between Fuel Model (PARFUME) model predictions versus Bison for selected compacts from the second irradiation test of the Advanced Gas Reactor (AGR) program that occurred from June 2010 to October 2013 in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). PARFUME is a fuel performance analysis and modeling code, used for evaluating gas-reactor tristructural isotropic (TRISO) coated particle fuel for prismatic, pebble bed, plate, and cylindrical type fuel geometries. PARFUME is an integrated mechanistic computer code that evaluates the thermal, mechanical, and physico-chemical behavior of TRISO coated-fuel particles and the probability for fuel failure given the particle-to-particle statistical variations in physical dimensions and material properties that arise during the fuel fabrication process. Bison is a nuclear fuel performance application built using the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library (Permann 2020). Bison is capable of modeling multiple fuel forms in a wide variety of dimensions and geometries. It solves coupled nonlinear partial differential equations, including heat conduction, mechanics, fission product species transport etc., in a fully implicit manner. Comparisons between PARFUME and Bison were performed using four compacts from the AGR-2 experiment. Selected outputs were chosen based on their impact on the probability of the SiC layer failing. In general there was good agreement between PARFUME and Bison with the exception of predicting the gap formed between the buffer and IPyC. Further comparisons between PARFUME and Bison are planned to further develop Bison’s capabilities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

An HPC-Based Hydrothermal Finite Element Simulator for Modeling Underground Response to Community-Scale Geothermal Energy Production

Geothermal heat, as renewable energy, shows great advantage with respect to its environmental impact due to its significantly lower CO2 emissions than conventional fossil fuel. Open and closed-loop geothermal heat pumps, which utilize shallow geothermal systems, are an efficient technology for cooling and heating buildings, especially in urban areas. Integrated use of geothermal energy technologies for district heating, cooling, and thermal energy storage can be applied to optimize the subsurface for communities to provide them with multiple sustainable energy and community resilience benefits. The utilization of the subsurface resources may lead to a variation in the underground environment, which might further impact local environmental conditions. However, very few simulators can handle such a highly complex set of coupled computations on a regional or city scale. We have developed high-performance computing (HPC) based hydrothermal finite element (FE) simulator that can simulate the subsurface and its hydrothermal conditions at a scale of tens of km. The HPC simulator enables us to investigate the subsurface thermal and hydrologic response to the built underground environment (such as basements and subways) at the community scale. In this study, a coupled hydrothermal simulator is developed based on the open-source finite element library deal.II. The HPC simulator was validated by comparing the results of a benchmark case study against COMSOL Multiphysics, in which Aquifer Thermal Energy Storage (ATES) is modeled and a process of heat injection into ATES is simulated. The use of an energy pile system at the Treasure Island redevelopment site (San Francisco, CA, USA) was selected as a case study to demonstrate the HPC capability of the developed simulator. The simulator is capable of modeling multiple city-scale geothermal scenarios in a reasonable amount of time.

Sun, Xiang↗

DOE OSTI2022

Comparison of Fission Product Release Predictions using PARFUME and BISON with Results from the AGR-3/4 Irradiation Experiment

The PARFUME (PARticle Fuel ModEl) fuel performance modeling code and the BISON nuclear fuel performance application built on the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library were used to predict the fission product release from tristructural isotropic (TRISO) coated fuel particles and compacts during the third and fourth irradiation experiment of the Advanced Gas Reactor (AGR-3/4) Fuel Development and Qualification Program. The fuel performance modeling codes PARFUME and BISON modeled the AGR-3/4 irradiation experiment using the fuel compact time-averaged volume averaged (TAVA) daily temperatures for a total irradiation duration of 369.1 effective full power days (EFPD) to predict the release fraction of the fission product silver (Ag-110m) from a representative TRISO-coated fuel particle from AGR-3/4 compacts. Post-irradiation examination (PIE) measurements provided data on the release of these fission products in the compacts outside of the silicon carbide (SIC) layer. The PARFUME and BISON results were then compared to the silver release measured from compact gamma scanning. The results showed good agreement between PARFUME and BISON but both codes under-predicted the silver release fraction for all the compacts. In addition, BISON was used to model and predict the fission product concentration radial profile outside of the compacts in capsules’ inner and outer rings. These rings were either comprised of matrix and/or structural graphite. To obtain the concentration profiles of silver, cesium, and strontium, a sorption isotherm model was developed in BISON to capture the effects of fission product transport across the gaps between the concentric rings. The general shape of the concentration radial profiles as calculated by BISON were similar in the inner ring (IR) but varied in the outer ring (OR) depending on the fission product of interest or capsule temperature. Using this methodology and model, BISON now has the capability to aid in developing new fission product diffusion coefficients for matrix or structural graphite materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗