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Stabilization method for the Saint-Venant equations by boundary control
Transactions of the Institute of Measurement and Control, 2020In this paper, we are interested in the stabilization of the flow modeled by the Saint-Venant equations. We have solved two problems in this study. The first, we have proved that the operator associated to the Saint-Venant system has a finite number of unstable eigenvalues. Consequently, the system is not exponentially stable on the space [Formula: see
Hassen Arfaoui
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Lattice Boltzmann method for the Saint–Venant equations
Journal of Hydrology, 2015Summary The Saint–Venant equations represent the hydrodynamic principles of unsteady flows in open channel network through a set of non-linear partial differential equations. In this paper, a new lattice Boltzmann approach to solving the one-dimensional Saint–Venant equations (LABSVE) is developed, demonstrating the variation of discharge and ...
Yu Ding, Haifei Liu
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Numerical solution of Saint-Venant equations
AIP Conference Proceedings, 2021In this paper, we have developed numerical calculation of stable solutions for the quasilinear hyperbolic system of Saint-Venant equations, which describes the motion of unsteady river fiows. Carrying out numerical experiments, we took as an example a rectangular channel with a constant coefficient of friction, the slope is not constant. When the slope
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On Lyapunov stability of linearised Saint-Venant equations for a sloping channel
Networks and Heterogeneous Media, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Michel Coron +2 more
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Green’s Function of the Linearized de Saint-Venant Equations
Journal of Engineering Mechanics, 2006We derive and discuss the Green’s function of the linearized de Saint-Venant equations (LSVEs) for shallow water waves in channels and rivers. The analysis offers a unified description of previous results on LSVEs regarding, in particular, the existence of three simple linear waves whose interplay determines all the evolution of the solution, the role ...
RIDOLFI, LUCA +2 more
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Automatica, 2019 International audienceThe exponential stability problem of the nonlinear Saint-Venant equations is addressed in this paper. We consider the general case where an arbitrary friction and space-varying slope are both included in the system, which lead to ...
Amaury Hayat, Peipei Shang
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Persistence of Roll Waves for the Saint Venant Equations
SIAM Journal on Mathematical Analysis, 2009The purpose of the article is to study the linear and nonlinear “stability” of roll-waves that are periodic and discontinuous entropic travelling wave solutions of the Saint Venant equations. More precisely, we prove that the Cauchy problem with initial data close to a roll-wave and satisfying suitable compatibility conditions has a solution on a ...
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Numerical Solution of Saint-Venant Equations
Journal of the Hydraulics Division, 1970The general, one-dimensional Saint-Venant equations are presented for a rigid open channel of arbitrary form, not necessarily prismatic, containing a flow that may be spatially varied. The theoretical basis for the method of characteristics is reviewed and used to show that, in the general case, the speed of long-wave disturbances is given by the slope
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Upwind Conservative Scheme for the Saint Venant Equations
Journal of Hydraulic Engineering, 2004An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method.
Xinya Ying +2 more
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Bifurcations and Dynamics of Traveling Wave Solutions for the Regularized Saint-Venant Equation
International Journal of Bifurcation and Chaos, 2020This paper studies the bifurcations of phase portraits for the regularized Saint-Venant equation (a two-component system), which appears in shallow water theory, by using the theory of dynamical systems and singular traveling wave techniques developed in [Li & Chen, 2007] under different parameter conditions in the two-parameter space.
Jibin Li 0001, Guanrong Chen, Jie Song
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