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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 815-834 
    ISSN: 0271-2091
    Keywords: vertical discretization ; sigma co-ordinates ; localized sigma co-ordinates ; tidal flow ; numerical experimentation ; 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: We propose an empirical law for vertical nodal placement in tidal simulations that depends on a single parameter p. The influence of dimensionless numbers on the optimal value of pis analysed through a series of numerical experiments for an individual vertical and a single value of pis found to be adequate for all cases. The proposed law can lead to gains in accuracy of over two orders of magnitude relative to a uniform grid and compares favourably with non-uniform grids previously used in the literature. In practical applications the most effective use of this law may require each vertical to have a different number of nodes. Criteria for the distribution of the total number of nodes among different verticals are also proposed, based on the concept of equalizing errors across the domain. The usefulness of the overall approach is demonstrated through a two-dimensional laterally averaged application to a synthetic estuary.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 183-204 
    ISSN: 0271-2091
    Keywords: transport equation ; Eulerian-Lagrangian methods ; stability analysis ; accuracy analysis ; numerical experimentation ; 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: Selected finite element Eulerian-Lagrangian methods for the solution of the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines. Within the methods analyzed, those that approach such treatment with the perspective of ‘integration’ rather than ‘interpolation’ tend to have superior accuracy. Exact integration leads to unconditional stability and excellent accuracy. Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulness of quadrature integration methods in a range of practical applications. While conclusions cannot be extended directly to multiple dimensions and complex flows and geometries, results should provide useful insight to the development and behaviour of specific Eulerian-Lagrangian transport models.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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