Computational hydraulics : numerical methods and modelling

Computational hydraulics numerical methods and modelling

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment....

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Detalles Bibliográficos
Otros Autores: Popescu, Ioana, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: London, England : IWA Publishing 2014
2014.
Edición:1st ed
Materias:
Hydraulics > Mathematics.
Hydraulics > Data processing.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009430299906719
Tabla de Contenidos:
  • Cover
  • Copyright
  • Contents
  • About the author
  • Preface
  • Chapter 1: Modelling theory
  • 1.1 Context and Nature of Modelling
  • 1.1.1 Classification of models
  • 1.1.2 Computational Hydraulics
  • 1.2 Conceptualiation: Building a Model
  • 1.3 Mathematical Modelling in Practice
  • 1.3.1 Selecting a proper model
  • 1.3.2 Testing a model
  • 1.4 Development and Application of Models
  • Chapter 2: Modelling water related problems
  • 2.1 Basic Conservation Equations
  • 2.1.1 Conservation of mass
  • 2.1.2 Conservation of momentum
  • 2.1.3 Conservation of energy
  • 2.2 Mathematical Classification of Flow Equations
  • 2.2.1 Solutions of ODE
  • 2.2.2 Solutions of PDE
  • 2.3 Navier-Stokes and Saint-Venant Equations
  • 2.3.1 Navier-Stokes equations
  • 2.3.2 Saint-Venant equations
  • 2.3.3 Characteristic form of Saint-Venant equations
  • Chapter 3: Discretization of the fluid flow domain
  • 3.1 Discrete Solutions of Equations
  • 3.2 Space Discretization
  • 3.2.1 Structured grids
  • 3.2.2 Unstructured grids
  • 3.2.3 Grid generation
  • 3.2.4 Physical aspects of space discretization
  • 3.3 Time Discretization
  • Chapter 4: Finite difference method
  • 4.1 General Concepts
  • 4.2 Approximation of the First Order Derrivative
  • 4.3 Approximation of Higher Order Derrivatives
  • 4.4 Finite Differences for Ordinary Differential Equations
  • 4.4.1 Problem position
  • 4.4.2 Explicit schemes (Euler method)
  • 4.4.3 Implicit schemes (Improved Euler method)
  • 4.4.4 Mixed schemes
  • 4.4.5 Weighted averaged schemes
  • 4.4.6 Runge-Kutta methods
  • 4.5 Numerical Schemes for Partial Differential Equations
  • 4.5.1 Principle of FDM for PDEs
  • 4.5.2 Hyperbolic PDEs
  • 4.5.3 Parabolic PDEs
  • 4.5.4 Elliptic PDEs
  • 4.6 Examples
  • 4.6.1 ODE: Solution of the linear reservoir problem
  • 4.6.2 PDE: Simple wave propagation
  • 4.6.3 PDE: Diffusion equation.
  • Chapter 5: Finite volume method
  • 5.1 General Concept
  • 5.2 FVM Application Details
  • 5.2.1 Step by step application of the FVM
  • 5.2.2 Surface and volume integrals
  • 5.2.3 Discretization of convective fluxes
  • 5.2.4 Discretization of diffusive fluxes
  • 5.2.5 Evaluation of the time derivative
  • 5.2.6 Boundary conditions
  • 5.2.7 Solving algebraic system of equations
  • 5.3 Example of Advection-Diffusion Equation in 1D
  • 5.3.1 Constant unknown function
  • 5.3.2 Linear variation approximation of the unknown function
  • 5.3.3 Parabolic variation approximation of the unknown function
  • 5.3.4 Error of the approximation
  • Chapter 6: Properties of numerical methods
  • 6.1 Properties of Numerical Methods
  • 6.1.1 Convergence
  • 6.1.2 Consistency
  • 6.1.3 Stability
  • 6.1.4 Lax's theorem of equivalence
  • 6.2 Convergence of FDM Schemes
  • 6.2.1 Convergence for ODEs
  • 6.2.2 Convergence for PDEs
  • 6.2.3 Amplitude and phase errors
  • 6.3 Convergence of FVM Schemes
  • 6.3.1 Convective fluxes
  • 6.3.2 Diffusive fluxes
  • 6.4 Examples
  • 6.4.1 Stability region of a simple ODE
  • 6.4.2 Convergence of an ODE: Emptying of a groundwater reservoir
  • 6.4.3 PDE: Convergence analysis for Preissmann scheme applied to advection equation
  • 6.4.4 PDE: Convergence analysis for diffusion equation
  • Chapter 7: River system modelling and flood propagation
  • 7.1 Introduction
  • 7.2 River Systems Modelling
  • 7.2.1 Preissmann solution
  • 7.2.2 Abbott-Ionescu solution
  • 7.2.3 Initial and boundary conditions
  • 7.2.4 River networks
  • 7.3 Modelling Floods
  • 7.4 River Routing Example
  • Chapter 8: Water quality modelling
  • 8.1 Introduction
  • 8.2 Processes Described in Water Quality Models
  • 8.3 River Water Quality Models
  • 8.4 Lakes Water Quality Modelling
  • 8.5 Examples of Lake Hydrodynamics and Water Quality Models
  • 8.5.1 Sontea-Fortuna wetland system.
  • 8.5.2 Lake Taihu water quality
  • References
  • Index.

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