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  • 1975-1979  (17)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Relaxation Methods in Fluid Mechanics (1975)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 7 (1975), S. 63-88 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.07.010175.000431
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    Paper (German National Licenses)
    Fulltext
  • 2
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    Relaxation Methods in Fluid Mechanics (1975)
    Annual Reviews
    Details
    Publication Date: 1975-01-01
    Print ISSN: 0066-4189
    Electronic ISSN: 1545-4479
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Annual Reviews
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    PAPER CURRENT
  • 3
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    On the convergence of certain finite-difference schemes by an inverse-matrix method (1975)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.
    Keywords: NUMERICAL ANALYSIS
    Type: Journal of Computational Physics; 17; Feb. 197
    Format: text
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    NASA TECHNICAL REPORTS
  • 4
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    Relaxation methods in fluid mechanics (1975)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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    NASA TECHNICAL REPORTS
  • 5
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    Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations (1978)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: Although the Navier-Stokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several time-accurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservation-law form have certain eigenvalue-eigenvector properties which may be used to construct conservative-form coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computer Methods in Applied Mechanics and Engineering; 13; Feb. 197
    Format: text
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    NASA TECHNICAL REPORTS
  • 6
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    Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations (1979)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: Elliptic partial differential equations are used to generate a smooth grid that permits a one-to-one mapping in such a way that mesh lines of the same family do not cross. Problems that arise due to lack of clustering at crucial points or intersections of mesh lines at highly acute angles, are examined and various forcing or source terms are used (to correct the problems) that are either compatible with the maximum principle or are so locally controlled that mesh lines do not intersect. Attention is given to various schematics of unclustered grids and grid detail about (highly cambered) airfoils.
    Keywords: NUMERICAL ANALYSIS
    Type: Journal of Computational Physics; 33; Dec. 197
    Format: text
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  • 7
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    On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm (1978)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-78495 , A-7474
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 8
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    Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-73252 , A-6950
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 9
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    Implicit approximate-factorization schemes for the low-frequency transonic equation (1975)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-X-73082 , A-6373
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 10
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    Implicit finite-difference procedures for the computation of vortex wakes (1976)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flow-field gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described and qualitatively compared with existing experimental data.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 76-385 , Fluid and Plasma Dynamics Conference; Jul 14, 1976 - Jul 16, 1976; San Diego, CA
    Format: text
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    NASA TECHNICAL REPORTS
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