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  • 1
    Electronic Resource
    Electronic Resource
    Types of stationary points in a variational formulation of shallow-water flows (1984)
    Springer
    Journal of engineering mathematics 18 (1984), S. 195-205 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary Free-surface gravity flows are stationary points of a functional J when the problem is formulated variationally. Here we are concerned with the problem of determining the nature of the stationary point, that is, whether it is a minimum, a maximum, a saddle point or whether a singularity occurs. This is a problem of both theoretical and computational importance. Within a variational approximation of shallow-water type developed by the authors, we prove some new results on the problem. The analysis is carried out by studying the second variation of the functional J and the corresponding Jacobi's equation. Reference is also made to numerical experiments which confirm the findings. The experiments also suggest that such findings may well extend to flows outside the class of shallow-water flows governed by the model used in the analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00039188
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical computations of critical flow over a weir (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 499-509 
    Details
    ISSN: 0271-2091
    Keywords: Critical Flow Rate ; Finite Elements ; Free Surface ; Weir ; 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: Computing critical flows in hydraulics involves three problems in one: the internal flow problem, the location of the free surface and the determination of the critical flow rate. The subject can involve such difficulties as non-uniqueness, non-existence, ill-conditioning and catastrophes.This paper discusses the difficulties relating to computing critical flows over weirs. A new rapidly convergent method of determining the critical flow rate is presented and various results are shown using it with finite element discretization and with a new streamline shifting method. Numerical results are in good agreement with published data, both numerical and experimental.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040604
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  • 3
    Electronic Resource
    Electronic Resource
    A Kantorovich computational method for free surface gravity flows (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1137-1148 
    Details
    ISSN: 0271-2091
    Keywords: Free Surface Flows ; Computation ; Kantorovich Method ; 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: Computing free surface gravity flows involves basically two coupled problems, namely, the location of the free surface position and the determination of the internal flow field (for assumed values H0 and Q of the total head and discharge, respectively).Solution techniques are invariably based on iterative procedures, but those that iterate between the two coupled problems may become unstable.In this paper we present a computational method in which the coupling is kept throughout the process of iteration. This is achieved by converting the coupled problems (by means of the Kantorovich method) into the single problem of finding a set of streamlines, including that of the free surface. These streamlines are moved (iteratively) to satisfy the stationary conditions of the governing variational principle.The algorithm is very stable and converges rapidly. It is also easy to implement to solve various types of steady flows with a free surface under gravity.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650041204
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  • 4
    Electronic Resource
    Electronic Resource
    A variational principle for ideal flow over a spillway (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 767-772 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational principle is presented which represents steady ideal flow with a free surface under gravity in terms of the stream function with Dirichlet boundary conditions. A different principle of Ikegawa and Washizu is shown to require restricted variations not consistent with the mass flow specification. The new principle is a special case of the of O'Carroll and Harrison in terms of enthalpy discontinuity between two streams. It is also reciprocal to a velocity potential functional. Finite element procedures and the determination of critical flow are discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150511
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    Paper (German National Licenses)
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