A posteriori error estimates for mixed finite element and finite volume methods
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nuclear (including radiation effects), carbon sequ↗
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Computational Homogenization of Polycrystals
This paper reviews the current state of the art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modeling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Lastly, current challenges and future research directions in this field are summarized.
36 MATERIALS SCIENCE↗
Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization
Here we present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.
97 MATHEMATICS AND COMPUTING↗
Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure
A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
Tsiveriotis, K.↗
Yearly report for the period Jan. 2018 – Jan. 2019 IC Project: w17_unedetection - “Simulation of underground nuclear explosions using the combined finite discrete element method” and “Fracture Formation and Permeability Evolution at in situ Pressure, Temperature and Stress Conditions”
Understanding the underlying physical processes associated with an underground nuclear explosion (UNE) can help with detection and identification of a suspected event. The Underground Nuclear Explosion Signatures Experiment (UNESE) is a collaborative effort between national laboratories aimed towards improving our understanding of physical and radiochemical signatures associated with a UNE. One primary objective of this effort is to perform hydrodynamic modeling of a UNE, with the purpose of estimating the extent of damage caused by such an event. Estimating the damage associated with an event is important for: a) detection of possible physical signatures at the surface of the earth such as fractures, spallation, and cratering and (b) damage to subsurface structures such as tunnels. Additionally, the damage produced by the hydrodynamic models play can be used to inform subsurface flow and transport models. The Combined Finite-Discrete Element Method (FDEM), implemented as an in-house code known as HOSS (Hybrid Optimization Software Suite), is used to model the damage associated with a UNE in various geological settings.
42 ENGINEERING↗
Development of a Modeling Approach to Describe Thermal Conductivity of Prototypic SiC-SiC tubes for LWR Fuel Cladding
SiC-SiC composites are a promising material intended to be used as a for fuel cladding for Light Water Reactors (LWRs). This material has a high steam oxidation resistance, high strength and low neutron cross section. Thermal conductivity is one of the most important physical properties for assessing the performance of SiC based fuel cladding. However, there is a significant lack of data for tube materials because measurement is challenging owing to the specimen geometry. This report summarizes the modeling methodology, experimental methodologies and software that will be used to study the thermal conductivity of different SiC-SiC composite tubes. The proposed experiments described here, are directed to create a baseline of thermal conductivity values to validate experimental simulations. In order to obtain the thermal conductivity of these materials the Laser Flash Analysis (LFA) will be implemented to obtain the thermal diffusivity of flat and sections of round shape specimens. Thermal diffusivity experiments will be complemented by Finite Element Method (FEM) simulations and a branch of this methodology known as Image-Based Finite Element Method (IBFEM). The FEM simulations will help to identify the possible limitations of experimental measurements in round shape specimens and verify the results of experiments in flat shape samples. The results of the IBFEM will help to quantify the possible effects of porosity in SiC-SiC composites. The findings of the aforementioned activities will be also applied to SiC-SiC neutron irradiated tube samples in order to capture the damage produced by this ageing mechanism.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Trends in computerized structural analysis and synthesis; Proceedings of the Symposium, Washington, D.C., October 30-November 1, 1978
The subjects considered are related to future directions of structural applications and potential of new computing systems, advances and trends in data management and engineering software development, advances in applied mathematics and symbolic computing, computer-aided instruction and interactive computer graphics, nonlinear analysis, dynamic analysis and transient response, structural synthesis, structural analysis and design systems, advanced structural applications, supercomputers, numerical analysis, and trends in software systems. Attention is given to the reliability and optimality of the finite element method, computerized symbolic manipulation in structural mechanics, a standard computer graphics subroutine package, and a drag method as a finite element mesh generation scheme.
Noor, A. K.↗
An isogeometric variational multiscale method for large-eddy simulation of coupled multi-ion transport in turbulent flow
Highlights: •We present a computational method for coupled multi-ion transport in turbulent flow. •The underlying formulation is a variational multiscale finite element method. •It is combined with the isogeometric concept for electrochemical systems. •Coupled multi-ion transport in fully turbulent Taylor–Couette flow is simulated. •This example is an important model problem for rotating cylinder electrodes. -- Abstract: Electrochemical processes, such as electroplating of large items in galvanic baths, are often coupled to turbulent flow. In this study, we propose an isogeometric residual-based variational multiscale finite element method for multi-ion transport in dilute electrolyte solutions under turbulent flow conditions. In other words, this means that the concepts of isogeometric discretization and variational multiscale methods are successfully combined for developing a method capable of simulating the challenging problem of coupled multi-ion transport in turbulent flow. We present a comprehensive three-dimensional computational method taking into account, among others, coupled convection–diffusion-migration equations subject to an electroneutrality constraint in combination with phenomenological electrode-kinetics modeling. The electrochemical subproblem is one-way coupled to turbulent incompressible flow via convection. Ionic mass transfer in turbulent Taylor–Couette flow is investigated, representing an important model problem for rotating-cylinder-electrode configurations. Multi-ion transport as considered here is an example for mass transport at high Schmidt number (Sc=1389). An isogeometric discretization is especially advantageous for the present problem, since (i) curved boundaries can be represented exactly, and (ii) it has been proven to provide very accurate solutions for flow quantities when being applied in combination with residual-based variational multiscale modeling. We demonstrate that the method is robust and provides results which are in good agreement with direct numerical simulation results as well as empirical mass-transfer correlations reported in literature.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4
Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.
97 MATHEMATICS AND COMPUTING↗
Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science
Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.
Ransom, Jonathan B.↗
On Multifunctional Collaborative Methods in Engineering Science
Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.
Ransom, Jonathan B.↗
Stress-intensity factors for internal surface cracks in cylindrical pressure vessels
The paper presents stress-intensity factors for a wide range of semi-elliptical surface cracks on the inside of pressurized cylinders. The ratio of crack depth to crack length ranged from 0.2 to 1; the ratio of crack depth to wall thickness ranged from 0.2 to 0.8; and the ratio of wall thickness to vessel radius was 0.1 to to 0.25. The stress-intensity factors were calculated by a three-dimensional finite-element method using singularity elements along the crack front and linear-strain elements elsewhere. An equation for the stress-intensity factors was obtained which applies over a wide range of configuration parameters and was within about 5 percent of the present results. A comparison was also made between the results and other analyses of internal surface cracks in cylinders. The results from a boundary-integral equation method were in agreement and those from another finite-element method were in fair agreement (+ or - 8 percent) with the results.
Newman, J. C., Jr.↗
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↗
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↗
An enriched finite element model with q-refinement for radiative boundary layers in glass cooling
Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.
97 MATHEMATICS AND COMPUTING↗
Modeling holes and voids in three dimensions using a single element within the Extended Finite Element framework
This paper introduces a highly efficient computational approach using the extended finite element method to model three-dimensional mechanics of holes and voids. The defect is encapsulated within a single element with a tailored exponential enrichment function that captures the behavior near the discontinuity boundary and can account for the pressure acting on the void’s surface through an equivalent nodal force vector. The method’s results were compared against analytical solutions and conventional finite element method results for problems involving single and multiple holes. The comparison demonstrated that the method provides accurate stress concentration estimates while adhering to computational constraints.
Adnan Shahriar↗
Coupling finite and boundary element methods for two-dimensional potential problems
A finite element-boundary element (FE-BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modeled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effects of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE-TR interface and zero values on the FE-TR interface. The present FE-BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.
Krishnamurthy, T.↗
Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects
This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.
Deshpande, Manohar↗