Introduction to computational engineering hydraulics

Introduction to computational engineering hydraulics

rok wydania: 2016, wydanie pierwsze
ilość stron: 308
ISBN:  978-83-7348-672-0

Opis
Niniejsza książka pomyślana jest jako pomoc dydaktyczna w zakresie metod obliczeniowych stosowanych w inżynierii wodnej. Aby ułatwić korzystanie z podręcznika jego treść podzielona została na dwie części. W pierwszej części Czytelnik znajdzie syntetyczny opis standardowych metod i technik numerycznych, szczególnie często stosowanych w obliczeniach z zakresu inżynierii wodnej. W części drugiej przedstawiono opisy wybranych i raczej typowych zagadnień związanych z przepływami wody i transportu rozpuszczonych w niej domieszek w kanałach otwartych, w gruncie oraz w rurociągach.

Aby ułatwić korzystanie z podręcznika podstawowe równania i zależności znane z kursów mechaniki płynów, hydrauliki, hydrologii i hydrogeologii zostały wyprowadzone w sposób możliwie prosty. Wybrane przypadki przepływu wody opisane tymi równaniami rozwiązano opisanymi w części pierwszej metodami numerycznymi. Dla wielu, raczej typowych, zagadnień przedstawiono również tabulogramy podprogramów lub programów w języku FORTRAN.

Książka adresowana jest do studentów i doktorantów studiujących budownictwo wodne i inżynierię środowiska w języku angielskim zarówno w Politechnice Gdańskiej, jak i w Nankai University w Chinach.

Spis treści
PREFACE / 7      
Part 1. BASIC NUMERICAL TECHNIQUES APPLIED IN HYDRAULIC ENGINEERING
1. SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS / 11    
1.1. Introduction  to the problem / 11    
1.2. Direct methods / 14    
1.2.1. Systems with triangular matrices / 14  
1.2.2. Gauss elimination method / 15  
1.2.3. LU decomposition method / 19  
1.3. Iterative methods /25    
1.3.1. Simple iterative methods / 25    
1.3.2. Representation of sparse matrices / 28
1.3.3. Conjugate gradient method / 29
1.3.4. Bi-conjugate gradient stabilized method / 31
1.4. Ill-conditioned systems of equations / 33
2. SOLUTION OF NONLINEAR ALGEBRAIC EQUATIONS AND THEIR SYSTEMS / 35  
2.1. Introduction to the problem / 35    
2.2. Methods for solving nonlinear algebraic equations / 37    
2.2.1. Bisection method / 37
2.2.2. False position method / 39  
2.2.3. Newton method / 41
2.2.4. Simple fixed point iteration / 46  
2.2.5. Steffenson method / 50
2.2.6. Wegstein method / 50
2.3. Methods for solving systems of nonlinear algebraic equations / 51  
2.3.1. Newton method / 52
2.3.2. Picard method / 54    
3. CURVE FITTING USING LEAST SQUARES METHOD / 56    
4. SEARCHING EXTREME POINT FOR FUNCTION f(x) / 60  
4.1. Optimization problem as solution of nonlinear algebraic equation / 61
4.2. Solution of optimization problem by dividing of interval containing the extreme point / 61
4.2.1. Dividing on three equal parts  /62
4.2.2. Dividing using golden number /64  
5. SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND THEIR SYSTEMS / 68
5.1. Introduction to numerical solution of ordinary differential equations / 68
5.2. Numerical solution of the initial value problem for ordinary differential equation / 69
5.3. Single step explicit methods / 72    
5.3.1. Euler explicit method / 72
5.3.2. Improved Euler explicit method / 73    
5.3.3. Runge-Kutta method / 74
5.4. Single step implicit methods / 76    
5.4.1. Euler implicit method / 76  
5.4.2. Implicit trapezoidal rule / 77
5.4.3. Generalization of 1-step implicit formulas / 78  
5.4.4. Solution of nonlinear equations provided by implicit formulas / 79  
5.5. Solution of initial value problem for system of ordinary differential equations / 79
5.6. Solution of boundary value problem for ordinary differential equations / 82  
6. INTRODUCTION TO SOLUTION PROBLEM OF PARTIAL DIFFERENTIAL  EQUATIONS / 86    
6.1. Classification of 2nd order PDE with 2 independent variables / 86  
6.2. Formulation of solution problem for PDEs / 88  
6.3. Numerical  solution of PDEs  / 93    
6.3.1. Solution of PDEs using FDM / 94  
6.3.2. Solution of PDEs using FEM / 98
6.3.3. Properties of numerical methods for PDEs: convergence, consistency and stability / 107
Part 2.  HYDRAULIC ENGINEERING PROBLEMS SOLVED USING NUMERICAL TECHNIQUES
7. BASIC DEFINITIONS, RELATIONS AND EQUATIONS USED IN HYDRAULIC   
ENGINEERING / 111  
7.1. Discharge and average flow velocity / 111  
7.2. Bernoulli equation / 112  
7.3. Reynolds number / 115  
7.4. Steady  flow in conduits / 115  
7.4.1. Steady flow in closed conduit / 115  
7.4.2. Steady uniform flow in open channel / 120  
8. ORIFICES, WEIRS AND SPILLWAYS / 123  
8.1. Discharge through orifices  / 123  
8.2. Unsteady outflow of water from tank / 125  
8.3. Flow over weirs and spillways / 129
8.4. Hydraulic jump and stilling basin / 132
9. FLOW IN PIPES / 134  
9.1. Steady flow in pipes of water supply system / 134  
9.2. Unsteady flow in system: reservoir – conduit – chamber / 139
10. STEADY OPEN CHANNEL FLOW / 145  
10.1. Normal depth in open channel / 145
10.2. Critical, subcritical and supercritical flow / 151  
10.3. Designing of open channel cross section  / 155  
10.4. Natural open channel / 159  
10.5. Rating curve Q(h) / 160  
10.6. Steady gradually varied flow in open channel  / 164  
10.6.1. Governing equations for steady gradually varied flow / 164
10.6.2. Solution of initial value problem forsteady gradually varied flow equation / 167
10.6.3. Solution of boundary value problem for steady gradually varied flow equations / 172
11. UNSTEADY OPEN CHANNEL FLOW / 180  
11.1. Derivation of governing equations /180  
11.1.1. Continuity equation / 180
11.1.2. Dynamic equation / 182  
11.2. Simplified open channel flow equations / 185  
11.3. Storage equation / 188  
11.4. Numerical solution of advection equation / 196  
11.4.1. Classification of advection equation and required auxiliary conditions  / 196
11.4.2. Solution of linear advection equation using method of characteristics / 198
11.4.3. Solution of linear advection equation using finite difference up-wind scheme / 202
11.4.4. Accuracy analysis of numerical solution of linear advection equation using modified equation approach / 204  
11.5. Solution of Saint-Venant equations  / 206  
11.6. Solution of nonlinear kinematic wave equation  / 211  
12. GROUNDWATER FLOW / 217
12.1. Introduction to the problem / 217
12.2. Flow in saturated zone / 219  
12.3. Flow in unsaturated zone / 226  
12.4. Numerical solution of 1D groundwater flow equation using FDM / 229  
12.4.1. Solution using explicit scheme / 231
12.4.2. Solution using Crank-Nicolson scheme / 236  
12.4.3. Solution of nonlinear equation using fully implicit scheme / 240
12.5. Solution of 1D Richards equation for water flow in unsaturated soils / 243
12.6. Numerical solution of 2D groundwater flow equation / 254  
12.6.1. Solution using explicit scheme / 254
12.6.2. Solution  using implicit scheme / 256  
12.6.3. Solution using alternating direction implicit method / 258  
12.7. Numerical solution of 2D groundwater steady flow equation / 261  
12.7.1. Solution of Poisson equation using FDM / 261  
12.7.2. Solution of steady groundwater flow in confined aquifer using FEM / 271  
13. POLLUTANTS TRANSPORT IN FLOWING WATER / 280  
13.1. Transport of substances dissolved in water / 280  
13.2. Heat transport by flowing water / 283
13.3. Simplified forms of 1D transport equation / 285  
13.4. Numerical solution of 1D advection – diffusion transport equation / 286  
13.4.1. Solution using implicit scheme of FDM / 287  
13.4.2. Numerical diffusion in solution of advection-diffusion equation / 291
13.4.3. Solution of advection-diffusion transport equation using modified FEM / 294
13.5. Characteristics of processes represented in 1D transport equation / 301  
13.6. Advection-diffusion transport equation in environmental engineering / 304
REFFERENCES / 306