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  • 1
    Electronic Resource
    Electronic Resource
    Unsteady axial mixing by natural convection in a vertical column (1992)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 38 (1992), S. 1825-1834 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Unsteady axial mixing due to addition of a batch of sodium chloride solution at the top of a water-filled tube (2.63 cm i.d.) has been studied by measuring the developing concentration profile and the advancing front with dye added to the brine. Data have also been obtained with added baffle plates, with the use of a viscous aqueous solution, and in smaller diameter (1.48, 1.91 cm) tubes. Results can be approximately correlated by means of a model based on unsteady one-dimensional turbulent dispersion. Laminar flow affects the behavior of the advancing front at which the salt concentration is lowest.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690381113
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient multigrid solution of boundary element models of cracks and faults (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 15 (1991), S. 549-572 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: We consider the multigrid solution of a discretized singular integral equation whose solution represents the displacement discontinuity distribution across a pressurized crack or the slip on a fault subjected to a prescribed shear stress. The multigrid technique reduces the operation count for a crack model having N degrees of freedom from O(N3) operations for standard stationary iterative methods to O(N2) operations. In the numerical simulations performed the multigrid approach proves to be extremely efficient even for small values of N. We use Fourier analysis to determine the spectral properties of the coarse grid correction process and the effect of a number of different interpolation operators on the multigrid algorithm. We show that the multigrid technique can be combined with the process of lumping remote influences to yield an algorithm that involves O(N) operations. The performance of multigrid iteration in a nonlinear environment is explored by considering seams filled with nonlinear material. For this purpose a segmented multigrid algorithm is developed that allows for different seam constitutive relations to be used along different line segments. The O(N2) operation count characteristic of linear multigrid iteration is shown to persist in this nonlinear environment and the segmented multigrid approach is shown to provide significant computational savings for values of N well within the range for typical problems that occur in practice.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610150804
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 4009-4034 
    Details
    ISSN: 0029-5981
    Keywords: boundary elements ; damage mechanics ; fracture growth ; multipole algorithms ; plasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we introduce a method to reduce the solution cost for Boundary Element (BE) models from O(N3)operations to O(N2logN) operations (where N is the number of elements in the model). Previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh. We have developed the Spectral Multipole Method (SMM) which can be used not only for problems with arbitrary geometries but also with a variety of element types. The memory necessary to store the required influence coefficients for the spectral multipole method is O(N) whereas the memory required for the traditional Boundary Element method is O(N2). We demonstrate the savings in computational speed and fast memory requirements in some numerical examples. We have established that the break-even point for the method can be as low as 500 elements, which implies that the method is not only suitable for extremely large-scale problems, but that it also provides a useful bridge between the small-scale and large-scale problems. We also demonstrate the performance of the multipole algorithm on the solution of large-scale granular assembly models. The large-scale BE capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620382307
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    Paper (German National Licenses)
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