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  • Other Sources  (28)
  • 1
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    New alternating direction procedures in finite element analysis based upon EBE approximate factorizations (1983)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in computational mechanics. A variety of techniques are compared on problems of structural mechanics, heat conduction and fluid mechanics. The results obtained suggest considerable potential for the methods described.
    Keywords: NUMERICAL ANALYSIS
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  • 2
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    A one-dimensional shock capturing finite element method and multi-dimensional generalizations (1985)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Multi-dimensional generalizations of a one-dimensional finite element shock capturing scheme are proposed. A scalar model problem is used to emphasize that 'preferred directions' are important in multi-dimensional applications. Schemes are developed for the two-dimensional Euler equations. One, based upon characteristics, employs the Mach lines and streamlines as preferred directions.
    Keywords: NUMERICAL ANALYSIS
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  • 3
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    Numerical simulation of electrophoresis separation processes (1986)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.
    Keywords: INORGANIC AND PHYSICAL CHEMISTRY
    Type: NASA-CR-180124 , NAS 1.26:180124
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  • 4
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    Finite element solution techniques for large-scale problems in computational fluid dynamics (1987)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: 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.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-172004 , NAS 1.26:172004
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  • 5
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    Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation (1987)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-CR-172005 , NAS 1.26:172005
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  • 6
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    Finite element computation of incompressible flows (1992)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Among the solution techniques presented for FEM computation of incompressible flows are stabilized formulations designed to prevent the numerical oscillations that may be generated by (1) the presence of dominant advection terms in the governing equations, or (2) the failure to use an acceptable combination of interpolation functions to represent velocity and pressure fields. It is shown that the space-time formulation, in conjunction with the Galerkin-least squares methods, can be used to compute steady incompressible flows involving moving boundaries and interfaces; it is recommended that iteration methods be used to reduce the associated computational costs.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Computational nonlinear mechanics in aerospace engineering (A93-12151 02-31); p. 417-449.
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  • 7
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    Finite element computation of compressible flows with the SUPG formulation (1991)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.
    Keywords: AERODYNAMICS
    Type: In: Advances in finite element analysis in fluid dynamics - 1991; Proceedings of the Symposium, ASME Winter Annual Meeting, Atlanta, GA, Dec. 1-6, 1991 (A93-29773 10-34); p. 21-27.
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  • 8
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    Unsteady incompressible flow computations with the finite-element method (1992)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: While the methods thus far developed for vorticity-streamfunction formulation are thus far restricted to 2D flows, they are applicable to both viscous and inviscid flows, including problems with multiply-connected domains. The present solution techniques for the velocity-pressure formulation can be extended to 3D problems. Attention is given to (1) two multistep formulations that use piecewise bilinear functions for the velocity and piecewise constant functions for the pressure, and (2) a novel multistep velocity-pressure formulation based on the equal-order interpolation of velocity and pressure.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Finite elements in fluids. Vol. 8 (A93-45962 19-34); p. 177-209.
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  • 9
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    Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations (1984)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A Petrov-Galerkin finite element formulation is presented for first-order hyperbolic systems of conservation laws with particular emphasis on the compressible Euler equations. Applications of the methodology are made to one- and two-dimensional steady and unsteady flows with shocks. Results obtained suggest the potential of the type of methods developed.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computer Methods in Applied Mechanics and Engineering (ISSN 0045-7825); 45; 218-284
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  • 10
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    Analysis of some fully-discrete algorithms for the one-dimensional heat equation (1985)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The present investigation is concerned with a fully discrete accuracy and stability analysis of the one-dimensional heat equation, taking into account the evaluation of two-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices. Schemes of the considered characteristics are not amenable to uncoupled semidiscrete and ordinary differential equation analyses. The obtained results illustrate that superior behavior may be achieved by schemes of the employed type when compared with the performance of the standard one-pass explicit schemes. The key idea in the considered approach is related to the utilization of a reduced-quadrature capacity matrix in the evaluation of the right-hand-side residual.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Journal for Numerical Methods in Engineering (ISSN 0029-5981); 21; 163-168
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