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  • NUMERICAL ANALYSIS  (3)
  • FLUID MECHANICS AND HEAT TRANSFER  (2)
  • 1985-1989  (5)
  • 1960-1964
  • 1
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    A new approach for solving the three-dimensional steady Euler equations. I - General theory (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 60; 23-61
    Format: text
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  • 2
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    Steady inviscid three-dimensional flows (1985)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The present analysis combines some of the theoretical concepts suggested by Hawthorne (1955) with a numerical integration procedure suggested by Martin (1978). The resulting algorithm is for inviscid subsonic flows. Thus, it is restricted to high Reynolds number flows. Chang and Adamczyk (1983) have provided a detailed derivation of the present algorithm along with a discussion of its stability bounds. The present paper represents a summary of this work. The integration of the continuity equation is considered along with an evaluation of the entropy, total temperature, and vorticity field. Attention is given to the shear-flow algorithm construction, and an application to a shear flow in a turning channel. A description of numerical results is also provided. The discussed algorithm represents a new procedure for solving inviscid subsonic three-dimensional rotational flows.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 3
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    Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method (1986)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2530 , E-2528-1 , NAS 1.60:2530
    Format: application/pdf
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  • 4
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    Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method (1986)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2529 , E-2461-1 , NAS 1.60:2529 , International Conference on Numerical Methods in Fluid Dynamics; Jun 25, 1984 - Jun 29, 1984; Saclay; France
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  • 5
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    An embedding method for the steady Euler equations (1986)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: Certain difficulties arise in connection with the numerical solution of a direct finite difference representation of the steady Euler equations. Johnson (1979, 1981, 1982) has, therefore, proposed a surrogate-equation technique, in which the first-order steady Euler equations are embedded in a certain second-order system of equations. The present paper is concerned with the theoretical justification for such an embedding approach. For the numerical solution of the two-dimensional steady Euler equations, it is shown that, under a continuity restriction, it is possible to solve a second-order embedded system together with appropriate additional boundary conditions. The result indicates that a more direct and potentially more efficient approach to the steady solutions exists than the alternative of solving the unsteady equations.
    Keywords: NUMERICAL ANALYSIS
    Type: Journal of Computational Physics (ISSN 0021-9991); 63; 191-200
    Format: text
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