scholarly journals A solution method for one-dimensional shallow water equations using flux limiter centered scheme for open Venturi channels

2018 ◽  
Vol 10 (4) ◽  
pp. 228-238 ◽  
Author(s):  
Prasanna Welahettige ◽  
Knut Vaagsaether ◽  
Bernt Lie
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Experimental Results ◽  
Pressure Force ◽  
One Dimensional ◽  
Advection Term ◽  
Fourth Order Method ◽  
Contraction And Expansion

The one-dimensional shallow water equations were modified for a Venturi contraction and expansion in a rectangular open channel to achieve more accurate results than with the conventional one-dimensional shallow water equations. The wall-reflection pressure–force coming from the contraction and the expansion walls was added as a new term into the conventional shallow water equations. In the contraction region, the wall-reflection pressure–force acts opposite to the flow direction; in the expansion region, it acts with the flow direction. The total variation diminishing scheme and the explicit Runge–Kutta fourth-order method were used for solving the modified shallow water equations. The wall-reflection pressure–force effect was counted in the pure advection term, and it was considered for the calculations in each discretized cell face. The conventional shallow water equations produced an artificial flux due to the bottom width variation in the contraction and expansion regions. The modified shallow water equations can be used for both prismatic and nonprismatic channels. When applied to a prismatic channel, the equations become the conventional shallow water equations. The other advantage of the modified shallow water equations is their simplicity. The simulated results were validated with experimental results and three-dimensional computational fluid dynamics result. The modified shallow water equations well matched the experimental results in both unsteady and steady state.

A domain decomposition method for the three-dimensional shallow water equations

1995 ◽  
Vol 3 (4-5) ◽  
pp. 307-325 ◽  
Author(s):  
E.D. de Goede ◽  
J. Groeneweg ◽  
K.H. Tan ◽  
M.J.A. Borsboom ◽  
G.S. Stelling
Keyword(s):  
Domain Decomposition ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Three Dimensional

Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear

2013 ◽  
Vol 723 ◽  
pp. 289-317 ◽  
Author(s):  
Andrew L. Stewart ◽  
Paul J. Dellar
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Shear Instability ◽  
Vertical Shear ◽  
Vortex Sheets ◽  
Multilayer Shallow Water Equations ◽  
Complete Coriolis Force

AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.

The evolution of a localized vortex disturbance in external shear flows. Part 1. Theoretical considerations and preliminary experimental results

1995 ◽  
Vol 289 ◽  
pp. 159-177 ◽  
Author(s):  
Vladimir Levinski ◽  
Jacob Cohen
Keyword(s):  
Boundary Layers ◽  
Shear Flows ◽  
Flow Direction ◽  
Linear Equations ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Experimental Results ◽  
Instability Criterion ◽  
Hairpin Vortices ◽  
Plane Normal

The evolution of a finite-amplitude three-dimensional localized disturbance embedded in external shear flows is addressed. Using the fluid impulse integral as a characteristic of such a disturbance, the Euler vorticity equation is integrated analytically, and a system of linear equations describing the temporal evolution of the three components of the fluid impulse is obtained. Analysis of this system of equations shows that inviscid plane parallel flows as well as high Reynolds number two-dimensional boundary layers are always unstable to small localized disturbances, a typical dimension of which is much smaller than a dimensional length scale corresponding to an O(1) change of the external velocity. Since the integral character of the fluid impulse is insensitive to the details of the flow, universal properties are obtained. The analysis predicts that the growing vortex disturbance will be inclined at 45° to the external flow direction, in a plane normal to the transverse axis. This prediction agrees with previous experimental observations concerning the growth of hairpin vortices in laminar and turbulent boundary layers. In order to demonstrate the potential of this approach, it is applied to Taylor-Couette flow, which has additional dynamical effects owing to rotation. Accordingly, a new instability criterion associated with three-dimensional localized disturbances is found. The validity of this criterion is supported by our experimental results.

A Numerical Analysis of Phonation Using a Two-Dimensional Flexible Channel Model of the Vocal Folds

2001 ◽  
Vol 123 (6) ◽  
pp. 571-579 ◽  
Author(s):  
Tadashige Ikeda ◽  
Yuji Matsuzaki ◽  
Tatsuya Aomatsu
Keyword(s):  
Channel Model ◽  
Flow Direction ◽  
Speech Sound ◽  
Three Dimensional ◽  
Vocal Folds ◽  
Two Dimensional ◽  
Threshold Values ◽  
One Dimensional ◽  
Frequency Components ◽  
Main Flow Direction

A two-dimensional flexible channel model of the vocal folds coupled with an unsteady one-dimensional flow model is presented for an analysis of the mechanism of phonation. The vocal fold is approximated by springs and dampers distributed in the main flow direction that are enveloped with an elastic cover. In order to approximate three-dimensional collision of the vocal folds using the two-dimensional model, threshold values for the glottal width are introduced. The numerical results show that the collision plays an important role in speech sound, especially for higher resonant frequency components, because it causes the source sound to include high-frequency components.

scholarly journals Wind-induced baroclinic response of Lake Constance

2000 ◽  
Vol 18 (11) ◽  
pp. 1488-1501 ◽  
Author(s):  
Y. Wang ◽  
K. Hutter ◽  
E. Bäuerle
Keyword(s):  
Numerical Modeling ◽  
Finite Difference ◽  
Eigenvalue Problem ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Measured Data ◽  
Lake Constance ◽  
Stratified Lake ◽  
Implicit Finite Difference

Abstract. We present results of various circulation scenarios for the wind-induced three-dimensional currents in Lake Constance, obtained with the aid of a semi-spectral semi-implicit finite difference code developed in Haidvogel et al. and Wang and Hutter. Internal Kelvin and Poincaré-type oscillations are demonstrated in the numerical results, whose periods depend upon the stratification and the geometry of the basin and agree well with measured data. By solving the eigenvalue problem of the linearized shallow water equations in the two-layered stratified Lake Constance, the interpretation of the oscillations as Kelvin and Poincaré-type waves is corroborated.Key words: Oceanography: general (limnology; numerical modeling) – Oceanography: physical (internal and inertial waves)

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