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14 Result(s)
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Romuald Szymkiewicz
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Article
Uncertainty analysis of simplified 1D and 2D shallow water equations via the Karhunen–Loéve expansion and Monte Carlo simulations
The stochastic solution of wave propagation through simplified shallow water equations, described by a system of 1D and 2D linear equations, has been investigated by considering the initial condition as a sour...
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Article
Open AccessInverse Flood Routing Using Simplified Flow Equations
The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hy...
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Article
Open AccessIdentification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
Two nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is con...
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Chapter
One-Dimensional Modeling of Flows in Open Channels
In this chapter, modeling of the unsteady open channel flow using one-dimensional approach is considered. As this question belongs to the well-known and standard problems of open channel hydraulic engineering,...
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Book
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Chapter
Numerical Solution of Ordinary Differential Equations
The initial value problem and the boundary value problem for the ordinary differential equations are discussed in this chapter. Derivation of simple numerical methods as well as a general approach for approxim...
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Chapter
Partial Differential Equations of Hyperbolic and Parabolic Type
This chapter is devoted to the partial differential equations applicable in open channel hydraulics, which can be of hyperbolic or parabolic type. The role of characteristics for hyperbolic equations is underl...
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Chapter
Numerical Solution of the Advection-Diffusion Equation
In this chapter the numerical consequences of hybrid character of the transport equation leading to advection or diffusion dominated problems are shown. The Peclet number is introduced to distinguish the two c...
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Chapter
Simplified Equations of the Unsteady Flow in Open Channel
The system of Saint Venant equations derived in Chapter 1 in the form of Eqs. (1.77) and (1.78) or Eqs. (1.79) and (1.80) is called the dynamic wave model or the complete dynamic model. This model of unsteady ...
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Chapter
Methods for Solving Algebraic Equations and Their Systems
This chapter presents some basic numerical techniques to solve nonlinear algebraic equations and systems of linear and nonlinear equations. For non-linear algebraic equations the bisection, false position, New...
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Chapter
Steady Gradually Varied Flow in Open Channels
This chapter begins with derivation of the governing equations. Instead of the ordinary differential equation with regard to depth, commonly used for prismatic channels, the ordinary differential energy equati...
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Chapter
Numerical Solution of the Advection Equation
This chapter presents a number of schemes for solution of 1D advection equation, which are based on the finite difference method, the finite element method and the method of characteristics. The roots of numer...
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Chapter
Numerical Integration of the System of Saint Venant Equations
This chapter begins with brief review of the numerical methods applicable for the Saint Venant equations. Detailed description of the finite difference Preissmann scheme and of the modified finite element meth...
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Chapter
Open Channel Flow Equations
The chapter begins with the basic definitions and nomenclature used in open channel hydraulics and applied in the book. In the next sections the governing equations for flow and transport are derived, includin...
