SEARCH · Search NASA

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.

SourceResearch connectionFrom yearThrough year

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

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.

Gupta, K. K.↗

NASA NTRS1983

Theoretical and software considerations for nonlinear dynamic analysis

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Schmidt, R. J.↗

NASA NTRS1995

Local multiplicative Schwarz algorithms for convection-diffusion equations

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Cai, Xiao-Chuan↗

NASA NTRS2007

Computational Fluid Dynamics-Based Aeroservoelastic Analysis with Hyper-X Applications

A finite element computational fluids dynamics-based aeroservoelastic analysis methodology is presented in this paper, in which both structural and fluids discretization are achieved by the finite element method, and their interaction is modeled by the transpiration boundary condition technique. In the fluids discipline either inviscid or viscous flow may be accounted for, usually employing unstructured grids.Adescription of a novel viscous flow solver employing unstructured grids is given in detail. Provisions are made for digital as well as analog controllers. These new aeroservoelastic analysis techniques are next applied for the solution of a number of example problems including the novel Hyper-X launch vehicle. Experimental and actual flight test data are also compared with analysis results that signify to the efficacy and accuracy of the newly developed solution procedures.

Gupta, K. K.↗

NASA NTRS2011

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗

NASA NTRS2010

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗

NASA NTRS2013

ONERA-NASA Cooperative Effort on Liner Impedance Eduction

As part of a cooperation between ONERA and NASA, the liner impedance eduction methods developed by the two research centers are compared. The NASA technique relies on an objective function built on acoustic pressure measurements located on the wall opposite the test liner, and the propagation code solves the convected Helmholtz equation in uniform ow using a finite element method that implements a continuous Galerkin discretization. The ONERA method uses an objective function based either on wall acoustic pressure or on acoustic velocity acquired above the liner by Laser Doppler Anemometry, and the propagation code solves the linearized Euler equations by a discontinuous Galerkin discretization. Two acoustic liners are tested in both ONERA and NASA ow ducts and the measured data are treated with the corresponding impedance eduction method. The first liner is a wire mesh facesheet mounted onto a honeycomb core, designed to be linear with respect to incident sound pressure level and to grazing ow velocity. The second one is a conventional, nonlinear, perforate-over-honeycomb single layer liner. Configurations without and with ow are considered. For the nonlinear liner, the comparison of liner impedance educed by NASA and ONERA shows a sensitivity to the experimental conditions, namely to the nature of the source and to the sample width.

Primus, Julien↗

NASA NTRS1996

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Pavarino, Luca F.↗

NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗

NASA NTRS2002

A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

Ransom, Jonathan B.↗

NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗

NASA NTRS2001

Discontinuous Galerkin Methods for NonLinear Differential Systems

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Barth, Timothy↗

NASA NTRS2003

A Comparison of Active and Passive Methods for Control of Hypersonic Boundary Layers on Airbreathing Configurations

Active and passive methods for control of hypersonic boundary layers have been experimentally examined in NASA Langley Research Center wind tunnels on a Hyper-X model. Several configurations for forcing transition using passive discrete roughness elements and active mass addition, or blowing, methods were compared in two hypersonic facilities, the 20-Inch Mach 6 Air and the 31-Inch Mach 10 Air tunnels. Heat transfer distributions, obtained via phosphor thermography, shock system details, and surface streamline patterns were measured on a 0.333-scale model of the Hyper-X forebody. The comparisons between the active and passive methods for boundary layer control were conducted at test conditions that nearly match the nominal Mach 7 flight trajectory of an angle-of-attack of 2-deg and length Reynolds number of 5.6 million. For the passive roughness examination, the primary parametric variation was a range of trip heights within the calculated boundary layer thickness for several trip concepts. The prior passive roughness study resulted in a swept ramp configuration being selected for the Mach 7 flight vehicle that was scaled to be roughly 0.6 of the calculated boundary layer thickness. For the active jet blowing study, the blowing manifold pressure was systematically varied for each configuration, while monitoring the mass flow, to determine the jet penetration height with schlieren and transition movement with the phosphor system for comparison to the passive results. All the blowing concepts tested were adequate for providing transition onset near the trip location with manifold stagnation pressures on the order of 40 times the model static pressure or higher.

Berry, Scott A.↗

NASA NTRS2003

Aircraft Engine Noise Scattering By Fuselage and Wings: A Computational Approach

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far-field. The effects of nonuniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. The approach is based on the discretization of the inviscid flow equations through a collocation form of the Discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Large-scale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic configuration, with and without a wing.

FUSELAGE-NACELLE CONFIGURATION↗

DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗

NASA NTRS1987

Analysis of structures with rotating, flexible substructures

A new methodology has been developed for the dynamic analysis of flexible structures, parts of which may be experiencing discrete motion relative to other parts. This methodology provides the capability of representing the continuum deformations typically treated using finite element methods. In addition, it provides the capability of representing the discrete motion at joints traditionally available with multibody methods. After decomposing the structure into substructures and associating a frame of reference with each substructure, the equations of motion for each substructure can be written explicitly including contributions due to the frame of reference generalized coordinates. By expanding the set of constraints to include constraints that eliminate the redundancy introduced by the frame generalized coordinates, the equations of motion become amenable to solution. The first digital computer program using this methodology, the General Rotorcraft Aeromechanical Stability Program (GRASP), was introduced in 1986. Although GRASP is limited to applications involving steady-state rotation, extension to arbitrary motions (including spin-up) can be accomplished by the selective retention of nonlinear terms in this formulation.

Hopkins, A. Stewart↗

DOE OSTI2025

Modeling supercritical CO2 injection induced rupture of a minor fault embedded in a poroelastic layered reservoir-caprock system

CO2 injection for geologic carbon sequestration involves hydromechanical processes that lead to changes in fluid pressure and stresses that can activate existing faults. This paper presents a new method and workflow of modeling fault activation considering more complex three-dimensional geometry of natural faults using the TOUGH-FLAC multiphase fluid flow and geomechanical simulator. In this method and workflow, FLAC3D mechanical interfaces and TOUGH3 finite volume elements are discretized using computer aided design and gridding software along with a tailored mesh translation routine. The method and workflow are demonstrated with a model of a curved minor fault embedded in a poro-elastic layered reservoir-caprock system. The model is used for a comprehensive sensitivity analysis of fault responses to fault length, injection mass rate, injection schedule, well-fault distance, and well locations versus fault location. Four metrics (CO2 plume, shear state of fault, pressure and stress path at fault monitoring points) are selected to assess CO2 migration, pressure change, and the reactivation of faults. The results reveal that CO2 can bypass around the tip of the minor impermeable fault, building up pressure and poro-elastic stress on both sides that tends to impede fault rupture. Our study shows the benefit of carefully designing the injection to achieve the targeted final storage volume, starting at a relatively low rate for considerable time, and then ramping up the injection rate to the full rate of injection. The initial low injection has two distinct benefits: (1) it allows for the formation of an extensive CO2 plume with a much higher mobility through a low viscosity that will result in a lower pressure for a given injection rate, and (2) it allows for gradual build-up of horizontal poro-elastic stress within the reservoir that will tend to impede activation of steeply dipping faults. The injection scenario starting at a low injection rate, denoted here as conservative injection, can significantly reduce the risk of fault activation as high fluid mobility and reservoir strengthening poro-elastic stress has been established long before reaching the peak injection rates. Moreover, simultaneous injection in two injection wells on both sides of fault can provide further reservoir strengthening through poro-elastic stress buildup acting on a fault under normal faulting stress regime. The findings presented in the paper can provide practical and effective guidance on long-term, safe, and reliable geological CO2 storage.

Cao, Meng↗

NASA NTRS1996

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

Lai, Chen-Yao G.↗