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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....
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
IWA Pub.,
©2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
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 ODE2.2.2 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 Derrivatives4.4 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 method5.1 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 approximationChapter 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.