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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1992

Finite element simulations involving simultaneous multiple interface fronts in phase change problems

The present paper describes the simulation of phase change problems involving simultaneous multiple interface fronts employing the finite element method. Much of the past investigations employing finite elements have been restricted to primarily a single phase change situation. The existence of more than one phase, that is, the presence of multiple phase fronts poses certain challenges and further complications. However, the results provide a very interesting thermal behavior for this class of problems. In this paper, attention is focused on fixed grid methods and the trapezoidal family of one-step methods using the enthalpy formulations. Illustrative examples which handle simultaneous multiple fronts in phase change problems are presented.

Ouyang, Tianhong↗
NASA NTRS2002

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

Kang, Kab S.↗
DOE OSTI2014

Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Surface effects are critical to the accurate simulation of electromagnetics (EM) as current tends to concentrate near material surfaces. Sandia EM applications, which include exploding bridge wires for detonator design, electromagnetic launch of flyer plates for material testing and gun design, lightning blast-through for weapon safety, electromagnetic armor, and magnetic flux compression generators, all require accurate resolution of surface effects. These applications operate in a large deformation regime, where body-fitted meshes are impractical and multimaterial elements are the only feasible option. State-of-the-art methods use various mixture models to approximate the multi-physics of these elements. The empirical nature of these models can significantly compromise the accuracy of the simulation in this very important surface region. We propose to substantially improve the predictive capability of electromagnetic simulations by removing the need for empirical mixture models at material surfaces. We do this by developing an eXtended Finite Element Method (XFEM) and an associated Conformal Decomposition Finite Element Method (CDFEM) which satisfy the physically required compatibility conditions at material interfaces. We demonstrate the effectiveness of these methods for diffusion and diffusion-like problems on node, edge and face elements in 2D and 3D. We also present preliminary work on h -hierarchical elements and remap algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Two-Level Least Squares Methods in Krylov Subspaces

Two-level least squares acceleration approaches are applied to the Chebyshev acceleration method and the restarted conjugate residual method in solving systems of linear algebraic equations with sparse unsymmetric coefficient matrices arising from finite volume or finite element approximations of boundary-value problems on irregular grids. Application of the proposed idea to other iterative restarted processes also is considered. The efficiency of the algorithms suggested is investigated numerically on a set of model Dirichlet problems for the convection-diffusion equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Phase-space finite elements in a least-squares solution of the transport equation

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Recent advances and progress towards an integrated interdisciplinary thermal-structural finite element technology

An integrated finite element approach is presented for interdisciplinary thermal-structural problems. Of the various numerical approaches, finite element methods with direct time integration procedures are most widely used for these nonlinear problems. Traditionally, combined thermal-structural analysis is performed sequentially by transferring data between thermal and structural analysis. This approach is generally effective and routinely used. However, to solve the combined thermal-structural problems, this approach results in cumbersome data transfer, incompatible algorithmic representations, and different discretized element formulations. The integrated approach discussed in this paper effectively combines thermal and structural fields, thus overcoming the above major shortcomings. The approach follows Lax-Wendroff type finite element formulations with flux and stress based representations. As a consequence, this integrated approach uses common algorithmic representations and element formulations. Illustrative test examples show that the approach is effective for integrated thermal-structural problems.

Namburu, Raju R.↗
DOE OSTI2018

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In this work, we introduce a framework for modeling dynamic fracture problems using cohesive polygonal finite elements. Random polygonal meshes provide a robust, efficient method for generating an unbiased network of fracture surfaces. Further, these meshes have more facets per element than standard triangle or quadrilateral meshes, providing more possible facets per element to insert cohesive surfaces. This property of polygonal meshes is advantageous for the modeling of pervasive fracture. We use both Wachspress and maximum entropy shape functions to form a finite element basis over the polygons. Fracture surfaces are captured through dynamically inserted cohesive zone elements at facets between the polygons in the mesh. Contact is enforced through a penalty method that is applied to both closed cohesive surfaces and general interpenetration of two polygonal elements. Finally, several numerical examples are presented that illustrate the capabilities of the method and demonstrate convergence of solutions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Solution of axisymmetric fluid structure interaction problems with NASTRAN

The solution of axisymmetric acoustic fluid structure interaction problems, employing the NASTRAN computer program is presented. A previously developed 3-D Cartesian Coordinates pressure element formulation is adapted especially for axisymmetric elements. Analogous to the 3-D Cartesian Coordinate predecessor, the fluid portion of the problem is modeled with finite elements wherein one of the displacement components serves as a dummy variable for the pressure unknowns. Two alternatives for implementation of the analogy are presented: (1) an approximate method by which dummy values of G, and nu are used to approximately invoke the analogy wherein the accuracy of the approximation is made as close as desired to the proper analogy within an arbitrary small parameter epsiton; (2) an exact method whereby the NASTRAN FORTRAN coding is slightly changed to invoke the analogy exactly. Comparison of the finite element solution to the exact solution to the same problem is given.

Kalinowski, A. J.↗
NASA NTRS1989

Probalistic Finite Elements (PFEM) structural dynamics and fracture mechanics

The purpose of this work is to develop computationally efficient methodologies for assessing the effects of randomness in loads, material properties, and other aspects of a problem by a finite element analysis. The resulting group of methods is called probabilistic finite elements (PFEM). The overall objective of this work is to develop methodologies whereby the lifetime of a component can be predicted, accounting for the variability in the material and geometry of the component, the loads, and other aspects of the environment; and the range of response expected in a particular scenario can be presented to the analyst in addition to the response itself. Emphasis has been placed on methods which are not statistical in character; that is, they do not involve Monte Carlo simulations. The reason for this choice of direction is that Monte Carlo simulations of complex nonlinear response require a tremendous amount of computation. The focus of efforts so far has been on nonlinear structural dynamics. However, in the continuation of this project, emphasis will be shifted to probabilistic fracture mechanics so that the effect of randomness in crack geometry and material properties can be studied interactively with the effect of random load and environment.

Liu, Wing-Kam↗
NASA NTRS1983

Finite element formulation for transient heat treat problems

The macrothermomechanical behavior of materials subjected to rapid thermal or mechanical loading such as occurs in most heat treatments is described. The equations are developed for Lagrangian, Eulerian, and intermediary kinematic descriptions and are independent of the constitutive laws and the equation of state; they can be solved numerically for a specified material and boundary conditions. The coupled transport effects between dissipation and energy are included. The conventional linearized stability approach indicates the numerical procedure to be stable, with certain restriction on the time step size.

Mullen, R. L.↗
NASA NTRS1974

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Osias, J. R.↗
NASA NTRS1992

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Collins, J. D.↗