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On nonlinear transient free-surface flows over a bottom obstruction (1997)

Zhu, Songping ; Zhang, Yinglong

[S.l.] : American Institute of Physics (AIP)

Physics of Fluids 9 (1997), S. 2598-2604

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ISSN: 1089-7666

Quelle: AIP Digital Archive

Thema: Physik

Notizen: A fully nonlinear integral-equation model based on the potential theory is used to study transient free-surface flow induced by a bump moving along a flat bottom. Comparison is made between the large-time solution of the transient model and the fully nonlinear steady-state solution in Zhang and Zhu [J. Eng. Math. 30, 487 (1996)] for both subcritical and supercritical flows, and asymptotic agreement between the two is observed. For the transcritical flow, some features associated with the resonant flow motion previously found by approximate theories are confirmed. A diagram of the parameter space is presented showing the regions of different solution categories including wave breaking. Through this diagram, a discrepancy between two previous steady-state models can now be clearly explained. Interestingly, the dividing line separating those solutions with or without wave breaking levels out asymptotically for very large Froude numbers, indicating that there is a limiting dimension of the bump, beyond which physically meaningful steady-state solutions do not exist, although they may well be obtained mathematically. © 1997 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.869376

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Digitale Medien

Open channel flow past a bottom obstruction (1996)

Zhang, Yinglong ; Zhu, Songping

Springer

Journal of engineering mathematics 30 (1996), S. 487-499

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ISSN: 1573-2703

Schlagwort(e): Free-surface flows ; nonlinear integral equations ; channel flow ; bottom topography ; hodograph method

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik , Technik allgemein

Notizen: Abstract A new nonlinear integral-equation model is derived in terms of hodograph variables for free-surface flow past an arbitrary bottom obstruction. A numerical method, carefully chosen to solve the resulting nonlinear algebraic equations and a simple, yet effective radiation condition have led to some very encouraging results. In this paper, results are presented for a semi-circular obstruction and are compared with those of Forbes and Schwartz [1]. It is shown that the wave resistance calculated from our nonlinear model exhibits a good agreement with that predicted by the linear model for a large range of Froude numbers for a small disturbance. The small-Froude-number non-uniformity associated with the linear model is also discussed.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00049248

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Improvement on dual reciprocity boundary element method for equations with convective terms (1994)

Zhu, Songping ; Zhang, Yinglong

Chichester : Wiley-Blackwell

Communications in Numerical Methods in Engineering 10 (1994), S. 361-371

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ISSN: 1069-8299

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.

Zusätzliches Material: 5 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/cnm.1640100502

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