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.