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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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite-difference-like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using a tensor product construction on quadrilateral elements. The GD basis can be used to define the solution space for a discontinuous Galerkin finite element discretization of partial differential equations. In this work we propose two approaches to handling complex geometries within this setting: (1) using nonconforming, curvilinear GD elements and (2) coupling affine GD elements with curvilinear simplicial elements. In both cases the (semidiscrete) discontinuous Galerkin method is provably energy stable even when variational crimes are committed. Additionally, for both element types a weight-adjusted mass matrix is used, which ensures that only the reference mass matrix must be inverted. We also present sufficient conditions on the treatment of metric terms for the curvilinear, nonconforming GD elements to ensure that the scheme is both constant preserving and conservative. Numerical experiments confirm the stability results and demonstrate the accuracy of the coupled schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enhanced Collisional Losses from a Magnetic Mirror Using the Lenard-Bernstein Collision Operator

Collisions are crucial in governing particle and energy transport in plasmas confined in a magnetic mirror trap. Modern gyrokinetic codes model transport in magnetic mirrors, but some utilize approximate model collision operators. This study focuses on a Pastukhov-style method of images calculation of particle and energy confinement times using a Lenard-Bernstein model collision operator. Prior work on parallel particle and energy balances used a different Fokker-Planck plasma collision operator. The method must be extended in non-trivial ways to study the Lenard-Bernstein operator. To assess the effectiveness of our approach, we compare our results with a modern finite element solver. Our findings reveal that the particle confinement time scales like a exp( a 2 ) using the Lenard-Bernstein operator, in contrast to the more accurate scaling that the Coulomb collision operator would yield a 2 exp( a 2 ), where a 2 is approximately proportional to the ambipolar potential. We propose that codes solving for collisional losses in magnetic mirrors utilizing the Lenard-Bernstein or Dougherty collision operator scale their collision frequency of any electrostatically confined species. This study illuminates the collision operator’s intricate role in the Pastukhov-style method of images calculation of collisional confinement.

fusion plasma↗
NASA NTRS1985

Finite element simulation of temperature dependent free surface flows

The method of Engelman and Sani (1984) for a finite-element simulation of incompressible surface flows with a free and/or moving fluid interface, such as encountered in crystal growth and coating and polymer technology, is extended to temperature-dependent flows, including the effect of temperature-dependent surface tension. The basic algorithm of Saito and Scriven (1981) and Ruschak (1980) has been generalized and implemented in a robust and versatile finite-element code that can be employed with relative ease for the simulation of free-surface problems in complex geometries. As a result, the costly dependence on the Newton-Raphson algorithm has been eliminated by replacing it with a quasi-Newton iterative method, which nearly retains the superior convergence properties of the Newton-Raphson method.

Engelman, M. S.↗
NASA NTRS1995

Combining Comparison Functions and Finite Element Approximations in CFD

In a variety of potential flow applications, the modal element method has been shown to significantly reduce the numerical grid, employ a more precise grid termination boundary condition, and give theoretical insight to the flow physics. The method employs eigenfunctions to replace the numerical grid over significant portions of the flow field. Generally, a numerical grid is employed around obstacles with complex geometry while eigenfunctions are applied to regions in the flow field where the boundary conditions can easily be satisfied. To handle a wider class of computational fluid dynamics (CFD) problems, the present paper extends the modal element to include function approximations which do not satisfy the governing differential equation. To accomplish this task, a double modal series approximation and weighted residual constraints are developed to force the comparison functions to satisfy the governing differential equation and to interface properly with the finite element solution. As an example, the method is applied to the problem of potential flow in a channel with two-dimensional cylindrical like obstacles. The calculated flow fields are in excellent agreement with exact analytical solutions.

Baumeister, Kenneth J.↗
NASA NTRS1992

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Jiang, Bo-Nan↗
DOE OSTI2024

Performance-based earthquake early warning for tall buildings

The ShakeAlert Earthquake Early Warning (EEW) system aims to issue an advance warning to residents on the West Coast of the United States seconds before the ground shaking arrives, if the expected ground shaking exceeds a certain threshold. However, residents in tall buildings may experience much greater motion due to the dynamic response of the buildings. Therefore, there is an ongoing effort to extend ShakeAlert to include the contribution of building response to provide a more accurate estimation of the expected shaking intensity for tall buildings. Currently, the supposedly ideal solution of analyzing detailed finite element models of buildings under predicted ground-motion time histories is not theoretically or practically feasible. The authors have recently investigated existing simple methods to estimate peak floor acceleration (PFA) and determined these simple formulas are not practically suitable. Instead, this article explores another approach by extending the Pacific Earthquake Engineering Research Center (PEER) performance-based earthquake engineering (PBEE) to EEW, considering that every component involved in building response prediction is uncertain in the EEW scenario. Additionally, while this idea is not new and has been proposed by other researchers, it has two shortcomings: (1) the simple beam model used for response prediction is prone to modeling uncertainty, which has not been quantified, and (2) the ground motions used for probabilistic demand models are not suitable for EEW applications. In this article, we address these two issues by incorporating modeling errors into the parameters of the beam model and using a new set of ground motions, respectively. We demonstrate how this approach could practically work using data from a 52-story building in downtown Los Angeles. Using the criteria and thresholds employed by previous researchers, we show that if peak ground acceleration (PGA) is accurately estimated, this approach can predict the expected level of human comfort in tall buildings.

58 GEOSCIENCES↗
NASA NTRS1989

Probabilistic structural analysis methods of hot engine structures

Development of probabilistic structural analysis methods for hot engine structures is a major activity at Lewis Research Center. Recent activities have focused on extending the methods to include the combined uncertainties in several factors on structural response. This paper briefly describes recent progress on composite load spectra models, probabilistic finite element structural analysis, and probabilistic strength degradation modeling. Progress is described in terms of fundamental concepts, computer code development, and representative numerical results.

Chamis, C. C.↗
NASA NTRS2018

A Higher-Order Space-Time Finite-Element Method for Moving-Body and Fluid-Structure Interaction Problems

We present a high-order finite-element method for moving body and fluid/structure interaction problems. Our solution strategy is based on a space-time discontinuous Galerkin (DG) spectral-element discretization which extends to arbitrary order of accuracy. The space-time DG discretization is a natural choice for moving body and fluid-structure interaction problems as moving surfaces are incorporated simply by considering curved space-time elements whose space-time faces align with the moving body. We present a discontinuous-Galerkin in time discretization for six-degree of motion modeling of rigid bodies, and a continuous-Galerkin discretization for equations of linear elasticity to generate curved space-time meshes. Numerical results for several simple 2D test cases are presented in order to verify the implementation of the different models. Finally we present a preliminary dynamic simulation of a parachute.

High-Order↗
NASA NTRS1985

Selecting step sizes in sensitivity analysis by finite differences

This paper deals with methods for obtaining near-optimum step sizes for finite difference approximations to first derivatives with particular application to sensitivity analysis. A technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously. Both the original and extended FD algorithms are applied to sensitivity analysis for a data-fitting problem in which derivatives of the coefficients of an interpolation polynomial are calculated with respect to uncertainties in the data. The methods are also applied to sensitivity analysis of the structural response of a finite-element-modeled swept wing. In a previous study, this sensitivity analysis of the swept wing required a time-consuming trial-and-error effort to obtain a suitable step size, but it proved to be a routine application for the extended FD algorithm herein.

Iott, J.↗
DOE OSTI2022

Context-Aware Learning for Inverse Design in Photovoltaics

This document describes progress in the ARPA-E DIFFERENTIATE project titled “Context-Aware Learning for Inverse Design in Photovoltaics” during the period of May 2019 to May 2022. This project is being performed at Iowa State University, New York University, Stanford University, and National Renewable Energy Laboratory. The project aims to develop a new machine learning (ML) framework to significantly accelerate the design of organic microstructures for improved organic photovoltaic performance. In this project, we had developed an inverse design framework using Deep Learning called InvNets for generating microstructures with desired physics-driven properties. As a preliminary product, in Milestone 3, we demonstrated how InvNets show 20% improvement in the performance of the microstructures and over 100X speedup in the performance compared to traditional processes for physics-driven inverse design. Later, in Milestone 6, we demonstrated that InvNets work for more complex physics properties, specifically, generating microstructures for organic photovoltaic cells with desired current-voltage characteristics. Further, in Milestone 4, we explored the idea of using physics-aware surrogates for obtaining solutions of partial differential equations(PDE) called as DiffNets(now called as NeuFENets to avoid ambiguity of names). The connection between both frameworks is that DiffNet surrogates form the physics-aware surrogate in the InvNet framework. Finally in Milestone 8, we extend our framework for other physics domains. Specifically, we explore building geometry-aware NeuFENets by developing physics surrogates that exploit ideas from traditional immersed boundary finite element methods. With these updates, we are able to achieve all the Milestones.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Acoustic-Liner Admittance in a Duct

Method calculates admittance from easily obtainable values. New method for calculating acoustic-liner admittance in rectangular duct with grazing flow based on finite-element discretization of acoustic field and reposing of unknown admittance value as linear eigenvalue problem on admittance value. Problem solved by Gaussian elimination. Unlike existing methods, present method extendable to mean flows with two-dimensional boundary layers as well. In presence of shear, results of method compared well with results of Runge-Kutta integration technique.

Watson, W. R.↗
NASA NTRS1991

The first ANDES elements: 9-DOF plate bending triangles

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Militello, Carmelo↗
DOE OSTI2017

Final Report of the Project "From the finite element method to the virtual element method"

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Mortandad Canyon seismic modeling (Progress Report)

The goal of this project is to assess site amplification for LANL through modeling of site and topography effects. Such assessment is difficult due to the lack of data documenting site effects for large normal faulting earthquakes such as the Pajarito Fault System that was found to be governing the seismic hazard at LANL. LANL site is also characterized by unique geologic settings, a series of mesa at the edge of the huge volcanic complex of the Jemez caldera. The latter has produced a series of successive and intertwined deposits of volcanic flow and sedimentary layer. Such layering of material with different elastic properties is expected to create large amplification effects magnified further by the presence at the surface of tuff materials. In 2014, a seismic campaign was performed in the Mortandad Canyon with a network of sensors on and near a local mesa. That campaign was designed to provide experimental data to estimation and prediction of amplification and site effects at LANL. An analysis on the seismic noise records of that campaign shows evidence of amplification of the seismic amplitude for the stations on the top of the mesa. Our goal is to reproduce the effect observed (both retrieving the resonance frequencies and amplification levels). We also plan to test if amplification effects observed for seismic noise can be extended to shaking produced by earthquakes. We are using a 3D modeling tool based on the Spectral Element Method (SEM) that is a particular type of high-order finite element modeling. Two types of seismic sources will be considered: (1) earthquakes for purpose of seismic hazard evaluation, (2) ambient noise. We show 2 series of numerical computations: (1) seismic waves are generated by random sources to simulate ambient noise. (2) seismic waves are planar waves to simulate a distant earthquake. We plan in the future to model rupture scenario on the Pajarito Fault System.

58 GEOSCIENCES↗
DOE OSTI2018

Path integral Monte Carlo calculation of the momentum distribution of the homogeneous electron gas at finite temperature

Path integral Monte Carlo (PIMC) simulations are employed to calculate the momentum distribution of the homogeneous electron gas at finite temperature. Open paths are introduced to sample off-diagonal elements of the real-space density matrix. Here it is demonstrated how the restricted PIMC method can be extended to incorporate open paths in order to allow for the simulations in fermionic systems where a sign problem is present. The computed momentum distribution shows significant deviations from behavior of free fermions when strong correlations are present but agrees with predictions from variational methods.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Dynamic Delamination Buckling In Composite Laminates

Procedure for mathematical modeling of dynamic delamination buckling and propagation of delamination, with plate bending elements and multipoint constraints, developed and incorporated into finite-element computer program. Predicts time at which delamination buckling occurs, shape of dynamic-buckling mode, and strain-energy-release rate due to extension of delamination crack. Method extended to handle such other defects as transply and edge cracks.

Grady, Joseph E.↗
NASA NTRS1991

Application of a robust linear control design to a truss structure with nonlinear joints

An efficient nonlinear equivalent beam finite-element method for the application of a full state feedback design is described, which is robust to plant uncertainties to a beamlike truss structure with nonlinear elements. The method may be extended to model nonlinear structures with other types of control systems, such as model-based compensators.

Webster, Mark↗