Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Discrete Element Method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

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

Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement

In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Sierra/SolidMechanics 4.56 Capabilities In Development

This user's guide documents capabilities in Sierra/SolidMechanics which remain "in-development" and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.56 User's Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and J-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sierra/SolidMechanics 5.0 Capabilities in Development

This user’s guide documents capabilities in Sierra/SolidMechanics which remain “in-development” and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 5.0 User’s Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the conforming reproducing kernel (CRK) method, numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and $\textit{J}$-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Sierra/SolidMechanics 4.58. Capabilities In Development

This user’s guide documents capabilities in Sierra/SolidMechanics which remain “in-development” and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.58 User’s Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and /-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Adaptive Framework for Extreme Deformation and Failure in Solids

Recent developments at Sandia in meshfree methods have delivered improved robustness in solid mechanics problems that prove difficult for traditional Lagrangian, mesh-based finite elements. Nevertheless, there remains a limitation in accurately predicting very large material deformations. It seems robust meshfree discretizations and integration schemes are necessary, but not sufficient, to close this capability gap. This state of affairs directly impacts current and future LEPs, whose simulation needs are not well met for extremely large deformation problems. We propose to use a new numerical framework, the Optimal Transportation Meshfree (OTM) method enhanced by meshfree adaptivity, as we believe that a combination of both will provide a novel way to close this capability gap.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The MFiX Particle-in-Cell Method (MFiX-PIC) Theory Guide

MFiX (Multiphase Flow with Interphase eXchanges) is an open-source multiphase flow solver developed at the National Energy Technology Laboratory. Within the code, users have access to a single phase or interpenetrating continua-based multiphase two-fluid model (TFM), a discrete element model (DEM), and a particle-in-cell model (PIC). TFM, DEM, and PIC can all be used to create multiphase simulations that include hydrodynamics, chemical reactions, and heat transfer.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Predicting large-scale pool fire dynamics using an unsteady flamelet- and large-eddy simulation-based model suite

A low-Mach, unstructured, large-eddy-simulation-based, unsteady flamelet approach with a generalized heat loss combustion methodology (including soot generation and consumption mechanisms) is deployed to support a large-scale, quiescent, 5-m JP-8 pool fire validation study. The quiescent pool fire validation study deploys solution sensitivity procedures, i.e., the effect of mesh and time step refinement on capturing key fire dynamics such as fingering and puffing, as mesh resolutions approach O(1) cm. A novel design-order, discrete-ordinate-method discretization methodology is established by use of an analytical thermal/participating media radiation solution on both low-order hexahedral and tetrahedral mesh topologies in addition to quadratic hexahedral elements. Here, the coupling between heat losses and the flamelet thermochemical state is achieved by augmenting the unsteady flamelet equation set with a heat loss source term. Soot and radiation source terms are determined using flamelet approaches for the full range of heat losses experienced in fire applications including radiative extinction. The proposed modeling and simulation paradigm are validated using pool surface radiative heat flux, maximum centerline temperature location, and puffing frequency data, all of which are predicted within 10% accuracy. Simulations demonstrate that under-resolved meshes predict an overly conservative radiative heat flux magnitude with improved comparisons as compared to a previously deployed hybrid Reynolds-averaged Navier–Stokes/eddy dissipation concept-based methodology.

42 ENGINEERING↗
DOE OSTI2026

Finite-element boundary-integral simulation of thin wires and inhomogeneous penetrable bodies in subsurface multilayered anisotropic media

With the prevailing presence of drilling wells near the subsurface in mature oil and gas fields, the application of electromagnetic methods can be particularly challenging where the electromagnetic field is affected by the steel casing. In the past decades, borehole-to-surface and crosswell electromagnetic methods have been utilized for monitoring of reservoir and underground CO 2 storage. This paper presents a unified finite-element boundary-integral (FEBI) method capable of simultaneously modeling the complex electromagnetic interactions between thin metallic wires (representing steel casings) with 3D trajectory and arbitrary 3D inhomogeneous penetrable bodies (such as CO 2 plumes or hydrocarbon reservoirs) within anisotropic multilayered subsurface environments. Unlike existing approaches that treat these components separately or require dense discretization, or are limited to vertical wells, our unified formulation preserves flexible electromagnetic coupling while delivering improved computational efficiency. Assuming the background formation is multilayered anisotropic media, the surface integral equation method is applied to model the thin wires and boundaries of the inhomogeneous bodies. Meanwhile, the finite element method is applied to model the volume of inhomogeneous bodies. Here, the performance of the proposed FEBI method is assessed through comparison with reference numerical results and its practical significance is demonstrated through CO 2 plume monitoring scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

DEM analysis of the effect of interface transition zone on dynamic splitting tensile behavior of high-strength concrete based on multi-phase model

Highlights: • Crushable aggregates with the real geometry shape are generated by using clump-cluster method. • Flat-Joint Model is adopted as the constitutive law. • The tensile strength is almost not affected by ITZ strength when its strength exceeds 0.8 times that of mortar. • A modified formula that can reflect the functional relationship between the ITZ strength and the TDIF is proposed. The tensile strength is one of the main parameters in the design of concrete structures and has an important influence on the cracking performance and durability of concrete materials. As the weak region in concrete, the strength of the interface transition zone (ITZ) directly affects the dynamic mechanical response of concrete. Meanwhile, considering that the tensile performance of concrete is far weaker than its compressive performance, the study of the strength of ITZ is of great significance to the dynamic tensile fracture characteristics and mechanical properties of concrete. In this paper, a method combining 3D scanning technology and Clump-Cluster was proposed to generate a real geometry shape model of crushable aggregate. On this basis, the 3D discrete element model (DEM) of high-strength concrete was constructed using the Flat-Joint Model (FJM). The effects of the ITZ strength on the failure mode, number of microcracks, tensile strength and strain rate effect of high-strength concrete under strain rates from 0.01/s to 100/s were studied by splitting tensile test. The simulation results indicate that the number of microcracks generated decreases with the increase of ITZ strength, and the proportion of ITZ cracks decreases obviously. When the ITZ strength exceeds the critical value of 0.8 times that of mortar, the tensile strength is almost not affected by ITZ strength. In addition, based on the numerical simulation results, a modified formula that can reflect the functional relationship between the ITZ strength and the dynamic increasing factor of the concrete tensile strength (TDIF) is proposed, and the rationality of the TDIF modified formula is verified.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.

Rudi, Johann↗
DOE OSTI2022

NekRS, a GPU-accelerated spectral element Navier–Stokes solver

The development of NekRS, a GPU-oriented thermal-fluids simulation code based on the spectral element method (SEM) is described. For performance portability, the code is based on the open concurrent compute abstraction and leverages scalable developments in the SEM code Nek5000 and in libParanumal, which is a library of high-performance kernels for high-order discretizations and PDE-based miniapps. Critical performance sections of the Navier–Stokes time advancement are addressed. Performance results on several platforms are presented here, including scaling to 27,648 V100s on OLCF Summit, for calculations of up to 60B gridpoints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Physics-Informed Machine Learning-Aided System Space Discretization

Decision-making is the process of identifying and choosing alternatives based on an agreed-upon set of metrics and preferences established by the decision-maker. There are options to be considered during the decision-making process and each option offers a different trajectory and associated success profile in moving from a given system state to the desired system state. The decision-making process typically involves uncertainties associated with the current component and system states. In this sense, probabilistic risk assessment (PRA) can be an analytical method and tool for accomplishing the probabilistic aspect of the decision-making process. Dynamic PRA is an evolution of conventional PRA methodology in which driving forces on modeled plant elements and the element behaviors are explicitly modeled over time. In the recent past, risk assessment methodologies have evolved to address risk issues in a continuously evolving environment and a novel probabilistic dynamics framework in continuous time and state-space discretization forms has been proposed. While state-space discretization has shown its strength in both consequence and causal reasoning modes, several challenges, including the computational requirement and physically meaningful system state identification, exist. Conventional system space discretization has usually been done by either the equal width discretization method or a data-driven method. Those methods naturally possess challenges coming from the physical understanding of discretized system space (i.e., system state) and the trajectory moving from a given system state to another system state. The purpose of this paper is to present a physics-based and data-driven system state discretization method such that one can justify what the discretized system space implies and understand the state trajectory from the viewpoint of operational actions.

Kim, Junyung↗
DOE OSTI2020

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗