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A variational principle for ideal flow over a spillway (1980)

O'carroll, M. J.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 15 (1980), S. 767-772

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ISSN: 0029-5981

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: 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.

Zusätzliches Material: 2 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nme.1620150511

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Digitale Medien

Types of stationary points in a variational formulation of shallow-water flows (1984)

Toro, E. F. ; O'Carroll, M. J.

Springer

Journal of engineering mathematics 18 (1984), S. 195-205

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ISSN: 1573-2703

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik , Technik allgemein

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00039188

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Numerical computations of critical flow over a weir (1984)

O'Carroll, M. J. ; Toro, E. F.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 4 (1984), S. 499-509

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ISSN: 0271-2091

Schlagwort(e): Critical Flow Rate ; Finite Elements ; Free Surface ; Weir ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Maschinenbau

Notizen: 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.

Zusätzliches Material: 6 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/fld.1650040604

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A Kantorovich computational method for free surface gravity flows (1984)

Toro, E. F. ; O'Carroll, M. J.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 4 (1984), S. 1137-1148

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ISSN: 0271-2091

Schlagwort(e): Free Surface Flows ; Computation ; Kantorovich Method ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Maschinenbau

Notizen: 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.

Zusätzliches Material: 5 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/fld.1650041204

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