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  • NUMERICAL ANALYSIS  (5)
  • 1
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    Finite elements: Theory and application (1988)
    In:  Other Sources
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    Publication Date: 2016-03-09
    Description: Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
    Keywords: NUMERICAL ANALYSIS
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  • 2
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    Temporal and spatial inconsistencies of time-split finite-difference schemes (1981)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: The properties of an implicit time-split algorithm, which utilizes locally one dimensional spatial steps, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified. A consistent, implicit splitting approach is developed. The relationship between this method and other time-split implicit schemes is explained, and stability problems encountered with the method in three dimensions are discussed.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-1790 , L-13941
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  • 3
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    Improving the convergence rate of parabolic ADI methods (1983)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 83-1897 , Computational Fluid Dynamics Conference; Jul 13, 1983 - Jul 15, 1983; Danvers, MA
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  • 4
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    An efficient iteration strategy for the solution of the Euler equations (1985)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 85-1529 , Computational Fluid Dynamics Conference; Jul 15, 1985 - Jul 17, 1985; Cincinnati, OH
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  • 5
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    Accuracy and stability of time-split finite-difference schemes (1981)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: In a recently published work by Abarbanel and Gottlieb (1980), a new class of explicit time-split algorithms designed for application to the compressible Navier-Stokes equations was developed. These algorithms, which utilize locally-one-dimensional (LOD) spatial steps, were shown to possess stability characteristics superior to those of other time-split schemes. In the present work, the properties of an implicit LOD method, analogous to the Abarbanel-Gottlieb algorithm, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified, and a new consistent, implicit splitting approach is developed and applied to the linear Burgers' equation. The relationship between this new method and other time-split implicit schemes is explained and stability problems encountered with the method in three dimensions are discussed.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 81-1005 , Computational Fluid Dynamics Conference; Jun 22, 1981 - Jun 23, 1981; Palo Alto, CA
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