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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Effects of finite element discretization and model simplification on calculations of ductile failure initiation

The finite element method is a scheme to discretize the infinite number of degrees of freedom in continuum-level problems down to a finite number of degrees of freedom. This discretization is done in conjunction with methods that also reduce the field differential equations to sets of algebraic ones that can be solved by arithmetical operations. Therefore, solutions attained by finite element models are approximations to the exact solutions of the field equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem

We study a multigrid method for solving large linear systems of equations with tensor product structure here. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the steady-state diffusion problem with random coefficients. When the variance in the problem is not too large, the solution can be well approximated by a low-rank object. In the proposed multigrid algorithm, the matrix iterates are truncated to low rank to reduce memory requirements and computational effort. The technique is proved convergent with an analytic error bound. Numerical experiments show its effectiveness in solving the Galerkin systems compared to the original multigrid solver, especially when the number of degrees of freedom associated with the spatial discretization is large.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Fractional Operators Applied to Geophysical Electromagnetics

A growing body of applied mathematics literature in recent years has focused on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is presumed attributable to long–range correlations of material properties within an inherently complex, and in some cases self-similar, conducting medium. Rather than considering an exquisitely discretized (and computationally intractable) representation of the medium, the complex and spatially correlated heterogeneity is represented through reformulation of the governing equation for the relevant transport physics such that its coefficients are, instead, smooth but paired with fractional–order space derivatives. Here we apply these concepts to the scalar Helmholtz equation and its use in electromagnetic interrogation of Earth’s interior through the magnetotelluric method. We outline a practical algorithm for solving the Helmholtz equation using spectral methods coupled with finite element discretizations. Execution of this algorithm for the magnetotelluric problem reveals several interesting features observable in field data: long–range correlation of the predicted electromagnetic fields; a power–law relationship between the squared impedance amplitude and squared wavenumber whose slope is a function of the fractional exponent within the governing Helmholtz equation; and, a non–constant apparent resistivity spectrum whose variability arises solely from the fractional exponent. In geologic settings characterized by self–similarity (e.g. fracture systems; thick and richly–textured sedimentary sequences, etc.) we posit that these diagnostics are useful for geologic characterization of features far below the typical resolution limit of electromagnetic methods in geophysics.

58 GEOSCIENCES↗
DOE OSTI2017

ECP Milestone Report: Identify initial kernels, bake-off problems (benchmarks) and miniapps (CEED-MS6)

The CEED co-design center is developing a number of kernels, bake-off / benchmark problems (BPs) and mini-applications (miniapps) that capture the unique requirements of high-order finite element algorithms and use them to influence standards, best practices and vendors to generate more portable, better performing code across diverse hardware designs. This is a main activity in CEED’s Hardware, Applications and Finite Element thrusts. CEED’s miniapps, a.k.a. CEEDlings, are small, standalone applications - surrogates for sub-components of interest from the selected first wave of applications (the MARBL/LLNLApp and ExaSMR projects). The BPs are even smaller standalone programs that solve a simple physical problem, including discretization, linear and/or nonlinear solve, and potentially a relatively small number of time steps. A BP may be a proxy/surrogate for part of a miniapp or another problem of general interest. In CEED, both miniapps and BPs will be used extensively in the project to evaluate and compare the performance of algorithms in specific contexts. The parts of the miniapps and BPs that play an important role in their overall performance will be identified and separated as standalone kernels. These kernels and their interaction inside BPs, miniapps and the actual applications, will be the main focus of our optimization efforts. All three standalone pieces of software (miniapps, BPs, and kernels) will serve as a basis for engaging and collaborating with hardware vendors and software technologies (ST) projects. These partners can start at the bottom of the hierarchy, e.g. with the kernels, and easily transition to BPs and miniapps as all three families will be produced in the same CEED environment. In this milestone we identified the initial kernels, bake-off problems and miniapps and delivered software and documentation for them through the new CEED website, http://ceed.exascaleproject.org. We specifically identified the Nekbone miniapp for the ExaSMR application and developed a new miniapp, Laghos, for the MARBL/LLNLApp application. We also formulated four initial benchmark problems (BP1- BP4) with clearly defined performance metrics and performed an initial bake-off comparison between the Nek5000 (spectral element) and MFEM (high-order finite element) technologies. As part of the milestone, we also engaged vendors (AMD) and ST projects (MPICH, STRUMPACK). In this document we are reporting some details and results from these R&D activities, as well as additional project-wide activities performed in Q3 of FY17, including: making CEED software available on GitHub, developing the project website, and the preparation of CEED’s first annual meeting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

BIGHORN Computational Fluid Dynamics Theory, Methodology, and Code Verification & Validation Benchmark Problems

This document presents the theoretical background for a hybrid finite-element / finite-volume fluid flow solver, namely BIGHORN, based on the Multiphysics Object Oriented Simulation Environment (MOOSE) computational framework developed at the Idaho National Laboratory (INL). An overview of the numerical methods used in BIGHORN are discussed and followed by a presentation of the formulation details. The document begins with the governing equations for the compressible fluid flow, with an outline of the requisite constitutive relations. A second-order finite volume method used for solving the compressible fluid flow problems is presented next. A Pressure-Corrected Implicit Continuous-fluid Eulerian (PCICE) formulation for time integration is also presented. The multi-fluid formulation is being developed. Although multi-fluid is not fully-developed, BIGHORN has been designed to handle multi-fluid problems. Due to the flexibility in the underlying MOOSE framework, BIGHORN is quite extensible, and can accommodate both multi-species and multi-phase formulations. This document also presents a suite of verification & validation benchmark test problems for BIGHORN. The intent for this suite of problems is to provide baseline comparison data that demonstrates the performance of the BIGHORN solution methods on problems that vary in complexity from laminar to turbulent flows. Wherever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using BIGHORN.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Progress toward a new implementation of the mortar finite element method in MOOSE

The mortar finite element method has been used for many years in a variety of applications, including the enforcement of continuity conditions across decomposed domains, the implementation of Dirichlet boundary conditions, obtaining improved estimates of surface fluxes, and for solving large deformation contact mechanics problems. There is a currently great deal of interest in developing more robust mechanical and thermal contact solution strategies in the MOOSE framework and physics modules, and schemes based on the mortar finite element approach appear to be a promising avenue of development. There are a number of challenges associated with the development of a robust Lagrange multiplier based formulation of the mortar finite element method which can be tackled using the relatively simple framework of thermal contact problems, before tackling more complicated applications such as thermomechanical contact. In this report, we describe several aspects of our mortar finite element method implementation for solving thermal contact problems. The approach and notation used are based primarily based on the work of Bin Yang et al. ("Two dimensional mortar contact methods for large deformation frictional sliding," International Journal for Numerical Methods in Engineering 62(9), 2005).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Study of the Effects of Materials Selection for the Closeout Structure on the Service Life of a Liquid Rocket Engine Thrust Chamber

The external structure of rocket engines thrust chambers for aerospace applications should be designed in order to provide adequate stiffness to the thrust chamber; however, it affects in a significant way the engine service life since it acts as a structural bound for the internal structure which is subjected to very high temperature values. The adoption of thin closeout structures allows to have lighter structures and to significantly increase the service life of the thrust chamber. The aim of the present work is to perform numerical investigations on the influence of the closeout geometry and materials on the number of cycles to failure of the thrust chamber. Furthermore, a study on the impact of creep phenomenon on the service life is illustrated. In particular, the present paper is focused on the thermomechanical study of the closeout structure, in terms of material choice, thickness, joining process with the inner liner, etc. Transient thermal and static structural nonlinear analyses are conducted by means of a commercial finite element code (ANSYS), in order to evaluate the number of cycles to failure for the investigated configurations. Viscoplastic models are adopted in order to simulate the highly nonlinear and rate-dependent phenomena occurring in the inner liner structure.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Chemical modelling of Delayed Ettringite Formation for assessment of affected concrete structures

Delayed Ettringite Formation (DEF) modelling is addressed in the context of structural analysis. First, a chemical model is specified to simulate the effects of the heating of concrete in terms of reactions involving sulfates, aluminates and alkalis. It can be decomposed into: dissolution of primary sulfoaluminates at high temperature, fixation of aluminates in hydrogarnet or carboaluminates, and formation of delayed ettringite at low temperature. The influences of alkalis, temperature and water saturation on these reactions are taken into account. The main result of this model is the amount of delayed ettringite. The parameters of the proposed chemical model are fitted on a large number of experiments taken from the literature. The chemical model is then coupled with a nonlinear mechanical model based on poro-mechanics modelling. An application of chemo-mechanical coupling shows the features and benefits of such modelling to help practitioners in the management of structures affected by DEF.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Towards improved speed and accuracy of laser powder bed fusion simulations via multiscale spatial representations

Due to the growing popularity of laser powder bed fusion (LPBF) as a metal additive manufacturing technique, there is a strong need to be able to accurately predict build outcomes. Full fidelity simulations of this process are not feasible due to the vast range of length and time scales inherent to it. While part-scale codes for simulating residual stress and distortion have shown reasonable predictive capability, they often neglect many aspects of the process occurring over smaller length/time scales, and thus are unable to capture effects of process parameter adjustments or the behavior of fine features. One way of capturing aspects at more refined length scales is through the use of adaptive mesh refinement (AMR). AMR allows for the process to be simulated at scales approaching the physical spatial dimensions without drastically increasing the total degrees of freedom in the simulation. This manuscript describes the implementation of an AMR algorithm within a multiphysics, parallelized finite element code, and its application to the LPBF problem. In this work, part-scale examples are provided where the use of AMR has allowed for higher fidelity thermal and thermomechanical simulations, as compared to experimental measurements. Results from these higher resolution simulations show that while AMR is a necessary component for increased accuracy in a computationally efficient manner, other improvements are also necessary, including handling of the multiple time scales inherent to the problem and the need for improved AM-specific material models.

42 ENGINEERING↗
DOE OSTI2014

Simulation of the temperature distribution in the selective beam melting process for polymer material

In the present contribution the temperature distribution in the selective beam melting process for polymer materials is simulated to better understand the influence of process parameters on the properties of the produced part. The basis for the developed simulation tool is the nonlinear heat equation including temperature dependent functions for the heat capacity and the heat conduction which were obtained by experimental measurements. The effect of latent heat occurring in the process is also taken into account. The heat equation is discretized in time and space where a Runge-Kutta method of Radau IIA type is used for time integration. An adaptive finite element method is applied for the discretization in space and the model is implemented into the finite element library deal.II. The heat and cooling rate as important process parameters are simulated for different beam velocities. The ability for computing these process parameters makes the simulation tool suited for optimizing the process management of selective beam melting plants.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Simulation of the dissipated and stored energy under deformation and failure of metallic materials

This work is devoted to the development of the statistical model of the structural defect evolution which was developed at the Institute of continuous media mechanics UB RAS. This model takes into account stochastic properties of the defect evolution process, nonlinear interaction of defects, and connection between microplasticity and damage accumulation. The obtained constitutive equations allow us to propose a model of the energy storage and dissipation in the process of plastic deformation and failure of metallic materials. The obtained relations were adapted for standard finite-element package. Applicability of this model was demonstrated in three-dimensional simulation of the strain localization and crack propagation in metals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. Furthermore, we demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

density functional theory↗
DOE OSTI2015

Simulation of Powder Layer Deposition in Additive Manufacturing Processes Using the Discrete Element Method

This document serves as a final report to a small effort where several improvements were added to a LLNL code GEODYN-­L to develop Discrete Element Method (DEM) algorithms coupled to Lagrangian Finite Element (FE) solvers to investigate powder-­bed formation problems for additive manufacturing. The results from these simulations will be assessed for inclusion as the initial conditions for Direct Metal Laser Sintering (DMLS) simulations performed with ALE3D. The algorithms were written and performed on parallel computing platforms at LLNL. The total funding level was 3-­4 weeks of an FTE split amongst two staff scientists and one post-­doc. The DEM simulations emulated, as much as was feasible, the physical process of depositing a new layer of powder over a bed of existing powder. The DEM simulations utilized truncated size distributions spanning realistic size ranges with a size distribution profile consistent with realistic sample set. A minimum simulation sample size on the order of 40-­particles square by 10-­particles deep was utilized in these scoping studies in order to evaluate the potential effects of size segregation variation with distance displaced in front of a screed blade. A reasonable method for evaluating the problem was developed and validated. Several simulations were performed to show the viability of the approach. Future investigations will focus on running various simulations investigating powder particle sizing and screen geometries.

36 MATERIALS SCIENCE↗
DOE OSTI2016

SIERRA Multimechanics Module: Aria User Manual – Version 4.40

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities. Aria is based upon the Sierra Framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

NEAMS-IPL MOOSE Framework Activities

The Multiapp Picard iteration Milestone’s purpose was to support a framework level “tight-coupling” method within the hierarchical Multiapp’s execution scheme. This new solution scheme gives developers new choices for running multiphysics applications, particularly those with very strong nonlinear effects or those requiring coupling across disparate time or spatial scales. Figure 1 shows a typical Multiapp setup in MOOSE. Each node represents a separate simulation containing a separate equation system. MOOSE solves the equation system on each node in turn, in a user-controlled manner. Information can be aggregated or split and transferred from parent to child or child to parent as needed between solves. Performing a tightly coupled execution scheme using this method wasn’t possible in the original implementation. This is was due to the inability to back up to a previous state once a converged solution was accepted at a particular Multiapp level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

SIERRA Multimechanics Module: Aria User Manual (V.4.44)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

GeneratorSE: A Sizing Tool for Variable-Speed Wind Turbine Generators

This report documents a set of analytical models employed by the optimization algorithms within the GeneratorSE framework. The initial values and boundary conditions employed for the generation of the various designs and initial estimates for basic design dimensions, masses, and efficiency for the four different models of generators are presented and compared with empirical data collected from previous studies and some existing commercial turbines. These models include designs applicable for variable-speed, high-torque application featuring direct-drive synchronous generators and low-torque application featuring induction generators. In all of the four models presented, the main focus of optimization is electromagnetic design with the exception of permanent-magnet and wire-wound synchronous generators, wherein the structural design is also optimized. Thermal design is accommodated in GeneratorSE as a secondary attribute by limiting the winding current densities to acceptable limits. A preliminary validation of electromagnetic design was carried out by comparing the optimized magnetic loading against those predicted by numerical simulation in FEMM4.2, a finite-element software for analyzing electromagnetic and thermal physics problems for electrical machines. For direct-drive synchronous generators, the analytical models for the structural design are validated by static structural analysis in ANSYS.

17 WIND ENERGY↗
DOE OSTI2016

SIERRA Multimechanics Module: Aria User Manual Version 4.42

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.

97 MATHEMATICS AND COMPUTING↗