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  • 1
    Electronic Resource
    Electronic Resource
    Towards generalization and optimization of implicit methods (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 357-380 
    Details
    ISSN: 0271-2091
    Keywords: Iterative Methods ; Implicit Procedures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050406
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The parametrized strongly implicit method for solving elliptic difference equations (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 381-391 
    Details
    ISSN: 0271-2091
    Keywords: Matrix Iterative Methods ; Strongly Implicit Procedure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for solving elliptic difference equations is derived based on the strongly implicit method. This parametrized strongly implicit method has three free parameters which may be functions of the field's nodal point. The method has some resemblance to the SOR techniques, but in the present method the off-diagonal entries are also over-relaxed. The main application of this method is for transport equations such as those governing the fluid flow and heat transfer fields.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050407
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Stable second-order accurate iterative solutions for second-order elliptic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 583-598 
    Details
    ISSN: 0271-2091
    Keywords: Upwind ; Second order ; Stable schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper describes a numerical scheme for solving a convection-diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non-linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this scheme.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090508
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Solving numerically the Navier-Stokes equations on parallel systems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 907-923 
    Details
    ISSN: 0271-2091
    Keywords: Parallel computing ; Parallel iterative methods ; Numerical splitting techniques ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new general approach for numerically computing flow fields on parallel computing environments is presented, discussed and analysed. The hierarchy presented here is based on a parallel split of operators. A portion of the theory is presented together with its application to two- and three-dimensional flows. This strategy is applied to a two-dimensional problem for which a specific parallel split, called a parabolized split, is given. The parallel algorithm that results from this split is analysed, leading to reasonably good parallel efficiency, which is close to 50%. Actual experiments lead to similar conclusions. This parallel strategy can also be used together with other parallel computing algorithms, such as domain decomposition, to give an optimal-type parallel algorithm for the Navier-Stokes equations.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100805
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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