Super-critical free-surface flow over a trapezoidal obstacle

Hanna, Sarwat N.; Abdel-Malek, M. N.; Abd‐el‐Malek, Mina B.

doi:10.1016/0377-0427(95)00160-3

Cited by 16 publications

(10 citation statements)

References 17 publications

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“…Figure 15 displays the computed free surface h + ( x ) at time t = T for different values of Froude number varying from 2.02 to 5.05, where T = 10800 s. The maximum height of the free surface decreases while the Froude number increases. The results are similar to those shown by Hanna et al [1996].…”

Section: Numerical Experiments For Supercritical Flowssupporting

confidence: 91%

Boundary value problems for the shallow water equations with topography

Shiue¹,

Laminie²,

Témam³

et al. 2011

J. Geophys. Res.

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Nonviscous shallow water equations with topography are considered in one spatial dimension. The aim is to find boundary conditions which are physically suitable; that is, they let the waves move freely out of the domain and do not reflect them at the boundary in a nonphysical way (or a way that is believed to be nonphysical). Two types of boundary conditions, called linear and nonlinear, are proposed for two types of flows, namely subcritical and supercritical flows. The second aim in this article is to numerically implement these boundary conditions in a numerically effective way. This is achieved by a suitable extension of the central‐upwind method for the spatial discretization and the Runge‐Kutta method of second order for the time discretization. Several successful numerical experiments for which we tested the proposed boundary conditions and the numerical schemes are described. The topography was added to render the examples studied physically more interesting.

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Section: Numerical Experiments For Supercritical Flowssupporting

confidence: 91%

Boundary value problems for the shallow water equations with topography

Shiue¹,

Laminie²,

Témam³

et al. 2011

J. Geophys. Res.

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“…This interesting topic has been studied intensively in several types of physical problems, such as the free surface flow over a polygonal obstacle [2][3][4][5][6][7], over a step [8], over a semi-circular obstruction [9,10], as well as a waterfall [11 -15]. Some other applications in the engineering field can be found in References [16 -21].…”

Section: Introductionmentioning

confidence: 99%

“…Some other applications in the engineering field can be found in References [16 -21]. Most of these studies are based on a conformal mapping technique, which maps a variety of standard domains, such as an upper-half plane [2,6,14,19], a unit disk [16], the upper-half of a unit disk [7,18,19] and an infinite strip [4,8], onto the physical domain with an unknown boundary. The special features of this technique are 1.…”

Section: Introductionmentioning

confidence: 99%

Numerical studies on non-linear free surface flow using generalized Schwarz-Christoffel transformation

Chuang

2000

Int. J. Numer. Meth. Fluids

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“…In the past, researchers explored the wave patterns of flow passing through a submerged object based on the assumption of steady flow at supercritical or subcritical flows. For example, Hanna et al [17] applied the Schwartz-Christoffel transformation technique and a series truncation based computational procedure to solve the problem of a steady supercritical flow over a trapezoidal obstacle. Furthermore, a steady turbulent flow model was used by Tzabiras [18] to study the super-and subcritical flows over a hump.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analyses of Wave Generation and Vortex Formation under the Action of Viscous Fluid Flows over a Depression

Chang

2019

JMSE

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Transient free-surface deformations and evolving vortices due to the passage of flows over a submerged cavity are simulated. A two-dimensional stream function–vorticity formulation with a free-surface model is employed. Model results are validated against the limiting case of pure lid-driven cavity flow with comparisons of the vortical flow pattern and velocity profiles. The verification of the free-surface computations are also carried out by comparing results with published potential flow solutions for cases of flows over a depressed bottom topography. The agreements are generally good. Investigations are extended to other viscous flow conditions, where the cavity is set to have the normalized dimension of one by one when scaled by the still water depth. The free-surface elevations and streamline patterns for cases with Froude numbers ranging from 0.5 to 1.1 and different Reynolds numbers (Re = 5000 and 500) are calculated. At the condition of near-critical flow (Fr ≈ 1.0), the phenomenon of upstream advancing solitons is produced. Viscous effects on the free-surface profile reveal that at a lower value of Re (e.g., Re = 500) larger advancing solitary waves are generated. Vortical flow patterns in the cavity are examined for the cases with Fr = 1.0 and various values of Re. When Re = 5000, the vortex pattern includes a primary and a weak, but dominated secondary vortices at the time reaching a nearly quasi-steady motion. For the case of lower Re (e.g., Re = 500), a steady-state vortex pattern can be established with a clockwise primary vortex mostly occupied inside the cavity.

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Super-critical free-surface flow over a trapezoidal obstacle

Cited by 16 publications

References 17 publications

Boundary value problems for the shallow water equations with topography

Boundary value problems for the shallow water equations with topography

Numerical studies on non-linear free surface flow using generalized Schwarz-Christoffel transformation

Numerical Analyses of Wave Generation and Vortex Formation under the Action of Viscous Fluid Flows over a Depression

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