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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Simple, Scalable Large Deformation Solid Mechanics Implementation in the MOOSE Framework

This article describes a large deformation solid mechanics solver implemented as part of the freely available and open source MOOSE finite element simulation framework. The article documents the choices made in developing the solid mechanics framework and describes novel formulations for the gradient operator and constitutive modeling framework made to simplify implementations of different coordinate systems, stabilized gradient operators, and different constitutive model inputs and outputs. In the process, the article describes a new formulation that casts objective integration of the Cauchy stress as a linear transformation of the small stress rate. Finally, the article presents key implementation details and examines the parallel efficiency of the solid mechanics solver implemented in MOOSE. The implementation retains a good weak scaling efficiency beyond 1,000 parallel processes. The article includes a discussion of the factors limiting the parallel efficiency of implicit, large deformation solid mechanics codes on current high-performance computers, with the main current limitation being the scalability of the algebraic multigrid methods used to solve the linearized equilibrium equations.

Applied computing → Computer-aided design↗
DOE OSTI2026

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

COWALKER:EFFECTIVE TRANSPORT PROPERTIES OF COMPOSITE MATERIALS

SF-23-026 This software computes effective transport properties of composite materials involving fibers and nanoparticles using a random-walk algorithm that efficiently scales to an arbitrary number of processes and cores. Effective transport properties (thermal, electrical) are key to bridge the microstructure of complex materials with its macroscopic behavior. Traditional approaches either use effective medium approximations (closed mathematical expressions that are approximation for certain conditions) or continuum simulation models such as finite element or finite volume, which require the generation of a mesh for each configuration explored. cowalker leverages the equivalence between laplacian or heat equation-based models and random walks to compute the asymptotic transport properties from an ensemble of first sojourn times of a random walker moving through the composite material. This allows us to directly define a composite material as a collection of particles and use algorithms developed for molecular dynamics to quickly compute the intersection of the walker with the different interfaces in the material. cowalker is developed in C++, and it relies on the GNU Scientific Library for random generation. cowalker is currently delivered as source code, so the GSL library is not included in cowalker's distribution. A more userfriendly version, cowalker.jl is currently in development and will be released as part of cowalker.

YANGUAS-GIL, ANGEL↗
DOE OSTI2020

Simulating transient heat transfer in graphene at finite Knudsen number via the Boltzmann transport equation and molecular dynamics

The phonon Boltzmann transport equation (BTE) with the relaxation time approximation (RTA) scattering model is used to calculate transient temperature profiles in graphene, and the results are compared to analogous molecular dynamics (MD) simulations. For the BTE calculations, the phonon dispersion relation and frequency-dependent scattering rates are obtained from a combination of MD data and semi-empirical power-law expressions for the normal and Umklapp phonon lifetimes. The dimensions and initial temperature conditions of graphene are varied to study the size and temperature dependence of thermal transport physics at the mesoscopic scale. Good quantitative agreement to within 5% is found between the BTE and MD results, over a wide range of temperatures and lengthscales of the temperature variation in the graphene sheet. Small differences are attributed to the inaccuracy of the RTA as applied to graphene, and to neglecting four-phonon scattering in the BTE simulations. The present results may further understanding in applications such as the transient heating of nanoelectronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Deep learning of accurate force field of ferroelectric HfO 2

The discovery of ferroelectricity in HfO 2 -based thin films opens up new opportunities for using this silicon-compatible ferroelectric to realize low-power logic circuits and high-density nonvolatile memories. The functional performances of ferroelectrics are intimately related to their dynamic responses to external stimuli such as electric fields at finite temperatures. Molecular dynamics is an ideal technique for investigating dynamical processes on large length and time scales, though its applications to new materials are often hindered by the limited availability and accuracy of classical force fields. Here we present a deep neural network–based interatomic force field of HfO 2 learned from ab initio data using a concurrent learning procedure. The model potential is able to predict structural properties such as elastic constants, equation of states, phonon dispersion relationships, and phase transition barriers of various hafnia polymorphs with accuracy comparable with density functional theory calculations. Here, the validity of this model potential is further confirmed by the reproduction of experimental sequences of temperature-driven ferroelectric-paraelectric phase transitions of HfO 2 with isobaric-isothermal ensemble molecular dynamics simulations. We suggest a general approach to extend the model potential of HfO 2 to related material systems including dopants and defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1986

MHD bending waves in a current sheet

Transverse MHD bending waves are considered in an isothermal and compressible two-dimensional current sheet of finite thickness in which the magnetic field changes direction and strength. The general form of the wave equation is obtained. It is shown that rotation of the magnetic field across the current sheet prevents the existence of singular points so that continuous spectrum solutions and the concomitant wave decay disappear. Instead, normal modes exist and closed integral solution for arbitrary current sheet structure are found. The results are discussed in terms of small-scale waves on the heliospheric current sheet.

Musielak, Z. E.↗
NASA NTRS1992

Scaling of low-velocity impact for symmetric composite laminates

The equations governing the problem of low-velocity impact of a simply supported rectangular midplane-symmetric laminated plate are nondimensionalized such that the problem is defined in terms of five dimensionless parameters. A parametric study using the Graeco-Latin Factorial Plan is performed. Semi-empirical formulas for maximum impact force, impact duration, and maximum back surface strains are obtained. It is found that some of the simple impact models provide the bounds for the case of impact on a finite extent plate. A one parameter model is derived for impacts of short duration.

Sankar, Bhavani V.↗
DOE OSTI2026

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗
DOE OSTI2023

Analytical closure to the spatially-filtered Euler equations for shock-dominated flows

To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to derive all necessary viscous/diffusion terms from first principles and then demonstrate the performance of these analytical terms within a centered differencing framework. The physical Euler equations are spatially-filtered with a Gaussian-like filter. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. No SFS terms are present in the continuity or species equations. Here, this approach is tested for several problems involving shocks in one and two dimensions. Implemented within a centered difference code, the SFS terms perform well for a range of flow conditions without introducing excessive diffusion.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions

The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.

Barkeshli, Kasra↗
NASA NTRS1991

Parallel Methods on Large-Scale Structural Analysis and Physics Applications; Symposium, Hampton, VA, Feb. 5, 6, 1991, Selected Papers

Recent advances in parallel methods and algorithms integrated into large-scale codes are presented. Consideration is given to problem decomposition (substructuring), efficient matrix solution algorithms for shared memory architectures, dynamic and transient analysis algorithms for shared memory architectures, and algorithms for distributed and massively parallel architectures. Particular attention is given to partitioning of unstructured problems for parallel processing, parallel-vector computation for linear-structural analysis and nonlinear unconstraint optimization problems, a parallel-vector equation solver for unsymmetric matrices on supercomputers, parallel nonlinear finite element dynamic response, multigrid algorithms for solving structural mechanics problems on supercomputers, structural analysis on massively parallel computers, explicit finite element methods with contact-impact on SIMD computers, and the impact of mapping and sparsity on parallelized finite element method modules.

Storaasli, Olaf O.↗
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗
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

Experiments and simulations of isochorically heated warm dense carbon foam at the Texas Petawatt Laser

An experimental and simulation study of warm dense carbon foams at ambient density (n e ~10 21 cm –3 ) is presented. This study of isochorically heated foams is motivated by their potential application in carbon-atmosphere white-dwarf envelopes, where there are modeling uncertainties due to the equation of state. The foams are heated on an approximately picosecond time scale with a laser-accelerated proton beam. The cooling and expansion of the heated foams can be modeled with appropriately initialized radiation-hydrodynamics codes; xRAGE code is used in this work. The primary experimental diagnostic is the streaked optical pyrometer, which images a narrow band of radiation from the rear surface of the heated material. Presented are xRAGE modeling results for both solid aluminum targets and carbonized resorcinol-formaldehyde foam targets, showing that the foam appears to cool slowly on the pyrometer because of partial transparency. So that simulations of cooling foam are processed properly, it is necessary to account for finite optical depth in the photosphere calculation, and the methods for performing that calculation are presented in depth.

36 MATERIALS SCIENCE↗
DOE OSTI2020

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

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

42 ENGINEERING↗
DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗