Shallow Flows Over a Permeable Medium: The Hydrodynamics of Submerged Aquatic Canopies

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

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Cementing Deepwater, Low-Temperature Gulf of Mexico Formations Prone to Shallow Flows

10.2118/87161-ms ◽

2004 ◽

Cited By ~ 1

Author(s):

Jim O'Leary ◽

Juan Carlos Flores ◽

Paulo Rubinstein ◽

Greg Garrison

Keyword(s):

Low Temperature ◽

Gulf Of Mexico ◽

Shallow Flows

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Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamicsThis paper is one of a selection of papers in this Special Issue in honour of Professor M. Selim Yalin (1925–2007).

Canadian Journal of Civil Engineering ◽

10.1139/l09-033 ◽

2009 ◽

Vol 36 (10) ◽

pp. 1605-1621 ◽

Cited By ~ 14

Author(s):

Rui M. L. Ferreira ◽

Mário J. Franca ◽

João G. A. B. Leal ◽

António H. Cardoso

Keyword(s):

Sediment Transport ◽

Mathematical Modelling ◽

Conceptual Models ◽

Numerical Solutions ◽

Shear Stresses ◽

Shallow Flows ◽

River Modelling ◽

Morphologic Evolution ◽

Sediment Mixtures ◽

Selection Of

Mathematical modelling of river processes is, nowadays, a key element in river engineering and planning. River modelling tools should rest on conceptual models drawn from mechanics of sediment transport, river mechanics, and river hydrodynamics. The objectives of the present work are (i) to describe conceptual models of sediment transport, deduced from grain-scale mechanics of sediment transport and turbulent flow hydrodynamics, and (ii) to present solutions to specific river morphology problems. The conceptual models described are applicable to the morphologic evolution of rivers subjected to the transport of poorly sorted sediment mixtures at low shear stresses and to geomorphic flows featuring intense sediment transport at high shear stresses. In common, these applications share the fact that sediment transport and flow resistance depend, essentially, on grain-scale phenomena. The idealized flow structures are presented and discussed. Numerical solutions for equilibrium and nonequilibrium sediment transport are presented and compared with laboratory and field data.

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