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E-raamat: Free-Surface Flow: Computational Methods

(Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, USA)
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  • Ilmumisaeg: 31-Oct-2018
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  • Keel: eng
  • ISBN-13: 9780128154861
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Free-Surface Flow: Computational MethodsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 31-Oct-2018
  • Kirjastus: Butterworth-Heinemann Inc
  • Keel: eng
  • ISBN-13: 9780128154861
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Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow. Closure models for turbulence, such as Reynolds-Averaged Navier-Stokes and Large Eddy Simulation are presented, coupling the aforementioned surface tracking techniques with environmental fluid dynamics. While many computer programs can solve the partial differential equations describing the dynamics of fluids, many are not capable of including free surfaces in their simulations.

  • Provides numerical solutions of the turbulent Navier-Stokes equations in three space dimensions
  • Includes closure models for turbulence, such as Reynolds-Averaged Navier-Stokes, and Large Eddy Simulation
  • Practical applications are presented for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow
Prologue xxi
References xxxiii
1 Basic Concepts
1.1 Introduction
4(5)
1.1.1 "Newton's Rules" for Computational Modeling
5(1)
1.1.2 Computational Models
6(3)
1.2 The Taylor Series
9(5)
1.3 Finite-Difference Approximations
14(7)
1.3.1 Forward Differences
15(1)
1.3.2 Backward Differences
16(1)
1.3.3 Central Differences
16(1)
1.3.4 Second-Order, One-Sided Differences
17(1)
1.3.5 Identity and Shift Operators
18(1)
1.3.6 Linear Difference Equations
18(3)
1.4 Initial-Value Problems for ODE's
21(18)
1.4.1 Basic Numerical Models
22(1)
1.4.2 Truncation Error and Order of Accuracy
23(1)
1.4.3 Stability, Consistency, and Convergence
24(2)
1.4.4 Absolute Stability
26(3)
1.4.5 Runge-Kutta Methods
29(5)
1.4.6 Linear Multi-Step Methods
34(2)
1.4.7 Backward-Difference Methods
36(3)
1.5 Boundary-Value Problems
39(10)
1.5.1 Steady-State Diffusion
39(1)
1.5.2 Solution of a Tri-Diagonal System
40(4)
1.5.3 The Thomas Algorithm
44(1)
1.5.4 Natural Boundary Conditions
45(1)
1.5.5 Variable Grid Computations
46(3)
1.6 Error Norms
49(2)
1.7 Algorithmic Dissipation
51(6)
1.7.1 Backward Difference Model
52(1)
1.7.2 Damping Effect of 2nd Derivative Operator
53(1)
1.7.3 Order of Dissipation
54(1)
1.7.4 Algorithmic Dispersion
54(3)
1.8 von Neumann Stability Analysis
57(14)
1.8.1 Representation of Oscillatory Data-Wave Aliasing
58(2)
1.8.2 Discrete Fourier Series Representation
60(1)
1.8.3 The Fourier Symbol
61(1)
1.8.4 Temporal Evolution
62(2)
1.8.5 Propagation Factor
64(1)
1.8.6 Algorithmic Dissipation-Condition for Stability
65(1)
1.8.7 Algorithmic Celerity-Dispersion
66(1)
1.8.8 Algorithmic Portrait
66(1)
1.8.9 Construction of Phase and Amplitude Graphs
67(2)
1.8.10 PDE's With Variable Coefficients
69(2)
1.9 Stability, Consistency, and Convergence
71(3)
1.9.1 Positivity and Monotonicity
71(3)
1.10 Least-Squares Approximation
74(2)
Problems
76(3)
References
79(3)
2 Finite-Difference Methods for Diffusion
2.1 Introduction
82(2)
2.2 Explicit Scheme for Diffusion (FTCS)
84(12)
2.2.1 Results and Error Estimates
86(2)
2.2.2 Stability
88(1)
2.2.3 Propagation of Information
88(2)
2.2.4 Discretization of Discontinuous Initial Data
90(2)
2.2.5 Boundary Effects
92(1)
2.2.6 Natural Boundary Conditions
92(1)
2.2.7 Simulation of a Point Source
93(1)
2.2.8 Accuracy of FTCS Scheme
94(2)
2.3 Oscillatory Initial Data and Spurious Signals
96(6)
2.3.1 Spurious Waves
97(1)
2.3.2 Stability of FTCS Scheme
98(4)
2.4 Leapfrog Scheme
102(3)
2.4.1 Stability Analysis of Leapfrog Scheme
103(2)
2.5 du Fort-Frankel Scheme
105(2)
2.6 Implicit Scheme for Diffusion
107(4)
2.6.1 Natural Boundary Conditions
108(1)
2.6.2 Accuracy of BTCS Scheme
109(1)
2.6.3 Stability of BTCS Scheme
109(2)
2.7 Crank-Nicolson Implicit Scheme
111(4)
2.7.1 Stability of Crank-Nicolson Scheme
112(1)
2.7.2 Weighted Average Explicit-Implicit Scheme
112(3)
Problems
115(2)
References
117(3)
3 Finite-Difference Methods for Advection
3.1 Introduction
120(2)
3.2 The Numerical Method of Characteristics
122(8)
3.2.1 Curvilinear Characteristic Network
123(3)
3.2.2 Characteristic Scheme on a Cartesian Grid
126(2)
3.2.3 The Effect of Interpolation
128(2)
3.3 Explicit Upwind Scheme (FTBS)
130(7)
3.3.1 Accuracy of Upwind Scheme
131(6)
3.4 The Courant-Friedrichs-Lewy (CFL) Condition
137(3)
3.4.1 Stability of Explicit Upwind Scheme
138(2)
3.5 Centered Explicit Scheme (FTCS)
140(2)
3.6 Implicit Upwind Scheme (BTBS)
142(4)
3.6.1 Stability of the BTBS Scheme
143(3)
3.7 Lax-Friedrichs Scheme
146(4)
3.7.1 Stability Analysis
147(3)
3.8 Leapfrog Scheme
150(11)
3.8.1 Propagation Properties
151(2)
3.8.2 Stability Analysis
153(3)
3.8.3 Dispersion Control
156(5)
3.8.3.1 Leapfrog-Trapezoidal Scheme
157(1)
3.8.3.2 Leapfrog-RAW Scheme
157(4)
3.9 The Lax-Wendroff Scheme
161(5)
3.9.1 Fourier Analysis of Lax-Wendroff Scheme
163(1)
3.9.2 Two-Step Lax-Wendroff-Richtmyer Scheme
164(2)
3.10 Beam and Warming Scheme
166(3)
3.10.1 Stability Analysis
167(2)
3.11 Parasitic Waves, Dissipation, and Dispersion
169(10)
3.11.1 Leapfrog Scheme
170(1)
3.11.2 Lax-Wendroff Scheme
171(1)
3.11.3 Frequency Analysis
172(3)
3.11.4 Group Velocity
175(4)
3.12 Advection Coupled With Diffusion
179(9)
3.12.1 Steady State Solution
181(3)
3.12.2 Generalized Upwind Method
184(4)
3.13 Transient Advection-Diffusion Schemes
188(7)
3.13.1 Centered Explicit Scheme
188(3)
3.13.2 Crank-Nicolson Scheme
191(1)
3.13.3 Stability of Crank-Nicolson Scheme
192(1)
3.13.4 Boundary Conditions
192(3)
Problems
195(2)
References
197(3)
4 Finite-Element and Finite-Volume Methods for Scalar Transport
4.1 Introduction
200(3)
4.1.1 Variational Principles
200(3)
4.1.1.1 Functional for Steady State Diffusion
201(2)
4.2 The Finite-Element Method (FEM)
203(4)
4.2.1 Basis Functions
204(1)
4.2.2 FEM Approximation of the Functional
205(2)
4.3 Method of Weighted Residuals
207(6)
4.3.1 Optimal Least-Squares Distance
207(1)
4.3.2 Inner Product Space
208(1)
4.3.3 Minimization of the Finite-Element Residual
209(1)
4.3.4 Linear Finite Elements
210(1)
4.3.5 Local Coordinates
211(2)
4.4 Diffusion Matrix and Load Vector
213(4)
4.5 Finite-Element Model for Transient Diffusion
217(4)
4.5.1 Time Domain Discretization
218(3)
4.6 Finite-Element Model for Advection
221(5)
4.6.1 Semi-Discrete Form
222(1)
4.6.2 Advection of a Sharp Concentration Front
223(3)
4.7 Petrov-Galerkin Modification
226(13)
4.7.1 Dissipative Galerkin Model
228(1)
4.7.2 Fourier Stability Analysis
229(1)
4.7.3 Phase and Amplitude Portraits
230(1)
4.7.4 Anti-Dissipative Behavior
231(2)
4.7.5 Preserving Monotonicity
233(2)
4.7.6 Selective Dissipation and Shock Capturing
235(2)
4.7.7 Fully Discrete Monotone DG Model
237(2)
4.8 Finite-Volume Method for Diffusion
239(2)
4.9 Finite Volume Method for Advection
241(6)
4.9.1 Conservative Fluxes
242(2)
4.9.2 Upwind Finite Volume Scheme
244(1)
4.9.3 QUICK Scheme for Advection
244(3)
4.10 Total Variation Diminishing
247(1)
4.11 Superbee Limiter for Advection
248(4)
4.11.1 Comparison With the Petrov-Galerkin Finite-Element Model
249(3)
4.12 Discontinuous Galerkin Method
252(5)
4.12.1 Linear Advection Equation
254(1)
4.12.2 Stability Analysis
255(2)
Problems
257(1)
References
258(4)
5 Finite-Difference Methods for Equilibrium Problems
5.1 Introduction
262(1)
5.2 Domain Discretization
263(6)
5.2.1 Choice of Computational Nodes
267(2)
5.3 Equilibrium Problems
269(9)
5.3.1 Finite-Difference Solution of Laplace's Equation
270(1)
5.3.2 Sources and Anisotropic Media
271(1)
5.3.3 Natural Node Ordering
272(1)
5.3.4 The Right Hand Side Vector
273(1)
5.3.5 The Coefficient Matrix of the Discrete Laplacian
274(1)
5.3.6 Fast Poisson Solvers
275(1)
5.3.7 The Residual Equation
276(2)
5.4 Iterative Solution of Sparse Systems
278(14)
5.4.1 Relaxation Methods
278(4)
5.4.2 Over Relaxation
282(1)
5.4.3 Application of SOR to a Square Domain
283(1)
5.4.4 Convergence of the Iterations
284(2)
5.4.5 The Spectral Radius
286(1)
5.4.6 Optimum Relaxation Factor
287(2)
5.4.7 Comparison of Relaxation Methods
289(1)
5.4.8 Impact of Problem Size
290(2)
5.5 Optimization Methods for Solving Sparse Systems of Linear Equations
292(4)
5.5.1 Conjugate Gradient Method
294(2)
5.6 Matrix Preconditioning
296(14)
5.6.1 Preconditioned Conjugate Gradient Method
296(4)
5.6.1.1 Incomplete Factorization
296(3)
5.6.1.2 LDU Factorization
299(1)
5.6.2 Incomplete Factorization
300(1)
5.6.3 Incomplete Cholesky Factorization Algorithm
301(1)
5.6.4 Preconditioned Conjugate Gradient Method
302(2)
5.6.5 Modified Incomplete Cholesky Factorization
304(4)
5.6.6 Convergence Tests
308(2)
5.7 Multigrid Methods
310(22)
5.7.1 Diffusion of Iteration Error
310(3)
5.7.2 Eigenvalues of the Iteration Matrix
313(6)
5.7.2.1 Higher Dimensions
316(3)
5.7.3 Modes of the Jacobi Iteration
319(3)
5.7.4 Behavior on Coarse Grid
322(1)
5.7.5 Elements of Multigrid Method
323(1)
5.7.6 Inter-Grid Operations
324(2)
5.7.6.1 Prolongation
324(2)
5.7.7 Restriction
326(1)
5.7.8 Cycling Schemes
327(3)
5.7.9 Multigrid Solution of Laplace Equation
330(2)
5.8 Multi-Domain Methods
332(6)
5.8.1 Schwarz Alternating Method
332(2)
5.8.1.1 General Boundary Conditions
333(1)
5.8.2 Steklov-Poincare Method
334(2)
5.8.3 Schur Complement and Iterative Substructuring
336(2)
5.9 Irregular Boundaries
338(7)
5.9.1 Dirichlet Boundaries
338(3)
5.9.2 Neumann Boundaries
341(4)
Problems
345(3)
References
348(4)
6 Methods for Two-Dimensional Scalar Transport
6.1 Introduction
352(1)
6.2 Finite-Difference Models for Diffusion
353(7)
6.2.1 Explicit Method (FTCS) for Diffusion
353(2)
6.2.2 Stability of 2D-FTCS
355(1)
6.2.2.1 The Relaxation Analogy
356(1)
6.2.3 Alternating Direction Implicit (ADI) Scheme
356(3)
6.2.4 Stability of ADI Scheme
359(1)
6.3 Finite-Difference Models for Advection
360(17)
6.3.1 The Method of Characteristics for 2D Advection
360(3)
6.3.2 Stability of 2D Method of Characteristics
363(2)
6.3.3 Upwind Method (FIBS) for Advection
365(1)
6.3.4 Stability of 2D-Upwind Scheme for Advection
366(3)
6.3.5 Modified Equation of the Upwind Scheme
369(2)
6.3.6 2D Lax-Friedrichs Scheme
371(1)
6.3.7 Stability Analysis of Lax-Friedrichs Scheme
372(1)
6.3.8 2D Lax-Wendroff Scheme
372(2)
6.3.9 Stability Analysis of 2D Lax-Wendroff Scheme
374(3)
6.4 Advection Coupled With Diffusion
377(6)
6.4.1 Stability of Crank-Nicolson Scheme
377(3)
6.4.2 Cross-Wind Diffusion
380(3)
6.5 Finite-Element Analysis
383(5)
6.5.1 Two-Dimensional Shape Functions
385(3)
6.6 Galerkin Formulation
388(12)
6.6.1 Transformation of Shape Function Derivatives
389(1)
6.6.2 Transformation of Integrals to Local Coordinates
390(1)
6.6.3 Finite Element Equations
390(1)
6.6.4 Gaussian Quadrature
391(2)
6.6.4.1 Transient Advection-Diffusion Problems
392(1)
6.6.5 Petrov-Galerkin Approximation
393(2)
6.6.6 Large-Scale Applications
395(5)
Problems
400(2)
References
402(4)
7 Methods for Open-Channel Flow
7.1 The Method of Characteristics
406(14)
7.1.1 Kinematic Waves
406(2)
7.1.2 Kinematic Shock Model
408(1)
7.1.3 Dynamic Waves
409(3)
7.1.4 Massau's Method
412(3)
7.1.5 Moving Boundaries
415(1)
7.1.6 Hartree's Method
416(4)
7.1.6.1 Moving Boundaries
418(1)
7.1.6.2 Shock Fitting
419(1)
7.2 Finite-Difference Methods
420(21)
7.2.1 Naive FTCS Scheme
420(5)
7.2.1.1 Boundary Conditions
421(2)
7.2.1.2 Stability Analysis
423(2)
7.2.2 Lax-Friedrichs Scheme
425(1)
7.2.3 Lax-Wendroff Scheme
426(5)
7.2.3.1 Two Step Version of LW Scheme
427(1)
7.2.3.2 Boundary Conditions
428(1)
7.2.3.3 Stability Analysis
429(2)
7.2.4 The Preissmann Implicit Scheme
431(6)
7.2.4.1 Double Sweep Method
434(2)
7.2.4.2 Stability Analysis
436(1)
7.2.5 Implicit ENO Method
437(4)
7.2.5.1 Computational Results
439(2)
7.3 FEM for Open-Channel Flow
441(25)
7.3.1 Bubnov-Galerkin Method (BG)
443(6)
7.3.1.1 Computational Results
445(1)
7.3.1.2 Stability Analysis
446(3)
7.3.2 Taylor-Galerkin Method
449(4)
7.3.2.1 Stability Analysis
452(1)
7.3.3 Petrov-Galerkin Method
453(3)
7.3.4 Dissipative Galerkin Scheme (DG)
456(4)
7.3.4.1 Stability Analysis
457(3)
7.3.5 Characteristic Galerkin Scheme (CG)
460(2)
7.3.5.1 Stability Analysis
461(1)
7.3.6 Comparative Analysis of Petrov-Galerkin Schemes
462(4)
7.4 Finite-Volume Methods for Open-Channel Flow
466(18)
7.4.1 The Riemann Problem
467(1)
7.4.2 Numerical Flux Functions
468(3)
7.4.3 Transcritical Depression Waves
471(1)
7.4.4 Source Term Discretization
472(2)
7.4.5 Extension to Second Order Accuracy
474(2)
7.4.6 Flux Limiting
476(1)
7.4.7 Stability Analysis
477(1)
7.4.8 Computational Results
478(1)
7.4.9 Zero-Inertia Deforming-Cell Model
479(5)
7.4.9.1 Inflow Boundary
482(1)
7.4.9.2 Surge Front
482(2)
7.5 Dispersive Waves
484(9)
7.5.1 Stability Analysis
486(1)
7.5.2 Computational Results
487(3)
7.5.3 Serre Equations
490(1)
7.5.4 Finite-Volume Methods
491(2)
Problems
493(2)
References
495(7)
8 Methods for Two-Dimensional Shallow-Water Flow
8.1 Introduction
502(2)
8.2 The Numerical Method of Bicharacteristics
504(22)
8.2.1 Parametric Form of Characteristic Relations
504(1)
8.2.2 Direct Tetrahedral Network
505(1)
8.2.3 Inverse Tetrahedral Network
506(2)
8.2.4 Inverse Pentahedra! Network
508(18)
8.2.4.1 Discrete Compatibility Equations
511(1)
8.2.4.2 Predictor Step
512(1)
8.2.4.3 Corrector Step
513(2)
8.2.4.4 Bicharacteristic Tangency Condition
515(1)
8.2.4.5 Bivariate Interpolation of Initial Data
516(2)
8.2.4.6 Stability Analysis
518(3)
8.2.4.7 Moving Grid Algorithm
521(2)
8.2.4.8 Boundary Conditions
523(1)
8.2.4.9 Computational Results
524(2)
8.3 Finite-Difference Models
526(11)
8.3.1 Leendertse Scheme
526(3)
8.3.1.1 Stability Analysis
529(2)
8.3.2 Computational Results
531(1)
8.3.3 MacCormack Scheme
532(5)
8.3.3.1 Boundary Conditions
533(2)
8.3.3.2 Stability Analysis
535(1)
8.3.3.3 Computational Results
535(2)
8.4 Finite-Element Models
537(9)
8.4.1 Deforming Element Formulation
538(2)
8.4.2 The Dissipative Interface
540(3)
8.4.3 Deforming Flow Domain
543(1)
8.4.4 Computational Results
543(3)
8.5 Finite-Volume Models
546(18)
8.5.1 Structured Grid Model
547(3)
8.5.2 The MUSCL Scheme for Two-Dimensional Flow
550(3)
8.5.3 Boundary Conditions
553(1)
8.5.4 Source Term Discretization
554(2)
8.5.4.1 Hydrostatic Imbalance
555(1)
8.5.5 Critical Flow Sections
556(1)
8.5.6 Stability Analysis
556(1)
8.5.7 Wave Propagation on Dry Terrain
557(3)
8.5.7.1 Steep Slopes With Low Runoff
559(1)
8.5.8 Computational Results
560(4)
Problems
564(1)
References
565(5)
9 Methods for Incompressible Viscous Flow
9.1 Introduction
570(5)
9.2 Projection Method
575(16)
9.2.1 2D Staggered Grid Discretization
577(1)
9.2.2 Time Integration
578(2)
9.2.2.1 Stability Condition
579(1)
9.2.2.2 Semi-Implicit Formulation
580(1)
9.2.3 Spatial Discretization
580(2)
9.2.3.1 Averaging Errors
581(1)
9.2.4 Upwinding of Advective Terms
582(1)
9.2.5 Boundary Conditions
583(1)
9.2.6 Computational Results
584(1)
9.2.7 Higher-Order Projection methods
585(6)
9.2.7.1 Block LU Factorization
587(2)
9.2.7.2 Strong-Stability-Preserving Methods
589(2)
9.3 Finite-Element Methods
591(9)
9.3.1 Mixed Element Formulation
592(3)
9.3.2 Lagrange Multiplier Approach
595(1)
9.3.3 Penalty Methods
596(2)
9.3.4 Artificial Compressibility
598(2)
9.4 Finite-Volume Methods
600(12)
9.4.1 Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
600(5)
9.4.1.1 SIMPLE Algorithm
602(3)
9.4.2 FVM on Collocated Grids
605(2)
9.4.3 Pressure-Implicit With Splitting of Operator (PISO)
607(12)
9.4.3.1 PISO Algorithm
608(1)
9.4.3.2 Stability Analysis
609(3)
Problems
612(1)
References
613(3)
10 Deforming Grid Methods
10.1 Introduction
616(3)
10.2 Finite-Difference Projection Method
619(9)
10.2.1 Flow With Small Density Gradients
619(1)
10.2.2 Staggered Spatial Discretization
620(4)
10.2.3 Computational Results
624(4)
10.3 FEM for Ideal Fluid Flow
628(10)
10.3.1 Finite-Element Solution
630(8)
10.3.1.1 Backwater Subdomain
631(1)
10.3.1.2 Tai !water Subdomain
632(6)
10.4 FEM for Viscous Flow
638(36)
10.4.1 Boundary Conditions
639(2)
10.4.2 Steady, Two-Dimensional Flow
641(12)
10.4.2.1 Domain Discretization
641(1)
10.4.2.2 Method of Weighted Residuals
642(1)
10.4.2.3 Local Coordinates
643(1)
10.4.2.4 Formulation of Global Matrices
644(2)
10.4.2.5 Computation of Free-Surface
646(4)
10.4.2.6 Computational Results
650(3)
10.4.3 Unsteady Viscous Flow
653(7)
10.4.3.1 Formulation of Residuals
653(2)
10.4.3.2 Time Integration Scheme
655(1)
10.4.3.3 Unsteady Flow Simulations
656(4)
10.4.4 Extended Finite Element Method
660(2)
10.4.5 Three-Dimensional Deforming FEM
662(9)
10.4.5.1 Upstream Weighting
665(2)
10.4.5.2 Deforming Element Formulation
667(1)
10.4.5.3 Evaluation of Element Matrices
667(2)
10.4.5.4 Nonlinear System Solver
669(1)
10.4.5.5 Computational Results
670(1)
10.4.6 ALE FEM in Three Dimensions
671(3)
10.5 Structured Finite-Volume Method
674(17)
10.5.1 Conservation Form of Equations
674(1)
10.5.2 Velocity of Nodal Motion
675(1)
10.5.3 Finite Volume Equations
676(2)
10.5.4 Time Integration
678(5)
10.5.4.1 Free Surface Elevation
679(2)
10.5.4.2 The Dynamic Pressure Solver
681(2)
10.5.5 Scalar Transport
683(1)
10.5.6 Spatial Discretization
684(1)
10.5.7 Computational Results
685(6)
10.6 Unstructured Large-Scale Models
691(17)
10.6.1 Vertical Coordinates
691(2)
10.6.2 Governing Equations
693(1)
10.6.3 z-Level Unstructured Grid
694(3)
10.6.4 Numerical Algorithm
697(2)
10.6.4.1 Drag Boundary Conditions
698(1)
10.6.5 Discrete Continuity Equation
699(1)
10.6.6 Advection of Momentum
699(7)
10.6.6.1 Horizontal Diffusion of Momentum
702(1)
10.6.6.2 Non-Hydrostatic Pressure
703(1)
10.6.6.3 Discretized Transport Equations
704(1)
10.6.6.4 Stability Conditions
705(1)
10.6.7 Computational Results
706(2)
Problems
708(1)
References
709(5)
11 Marker and Cell Method
11.1 Introduction
714(2)
11.2 Particle-In-Cell Method
716(3)
11.2.1 Computational Results
718(1)
11.3 Marker-And-Cell Method
719(20)
11.3.1 2D MAC Method
719(4)
11.3.2 Initial and Boundary Conditions
723(8)
11.3.2.1 Inflow Boundary
724(1)
11.3.2.2 Outflow Boundary
725(1)
11.3.2.3 Free-Slip Wall Boundary
725(1)
11.3.2.4 No-Slip Wall Boundary
725(1)
11.3.2.5 Permeable Wall Boundary
726(1)
11.3.2.6 Corner Boundary
726(1)
11.3.2.7 Free-Surface Boundary
727(4)
11.3.3 Modified Free-Surface Condition
731(2)
11.3.4 Particle Movement
733(1)
11.3.5 The Overall Algorithm
734(1)
11.3.6 Stability Conditions
735(1)
11.3.7 Laminar Flow Applications
736(3)
11.4 Turbulent Flow Simulation
739(9)
11.4.1 The Donor Cell Upwind Scheme
742(3)
11.4.1.1 Boundary Conditions for Turbulent Flow
744(1)
11.4.2 Turbulent Flow Applications
745(3)
11.5 Semi-Implicit MAC Method
748(7)
11.5.1 Streamwise Momentum Equation
748(3)
11.5.2 Vertical Momentum Equation
751(3)
11.5.3 Enforcement of Incompressibility
754(1)
11.6 Extension to Inclined Channels
755(5)
11.6.1 Particle Movement
756(1)
11.6.2 Computational Results
757(3)
11.7 Recent Developments
760(3)
Problems
763(1)
References
764(4)
12 Volume of Fluid Method
12.1 Introduction
768(2)
12.2 Simple Line Interface Calculation
770(2)
12.3 Fractional Volume of Fluid
772(13)
12.3.1 Pressure Definition in a Surface Cell
773(1)
12.3.2 Advection of Fractional Volume of Fluid
774(4)
12.3.3 Subgrid Computations
778(1)
12.3.3.1 Computational Results
778(1)
12.3.4 Piece-Wise Linear Interface Calculation
779(3)
12.3.4.1 The Interface Normal
781(1)
12.3.5 Intersection With Cell Edges
782(3)
12.4 Analytical Reconstruction Methods
785(16)
12.4.1 Interface Position
786(3)
12.4.2 Lagrangian Advection of the Interface
789(1)
12.4.3 Extension to Three Dimensions
790(3)
12.4.4 Computational Results
793(1)
12.4.5 Eulerian Advection of the Interface
793(15)
12.4.5.1 Sudden Closing of Sluice Gate
793(2)
12.4.5.2 Fluid-Structure Interaction
795(1)
12.4.5.3 Two-Phase Flow: Breaking Waves
796(1)
12.4.5.4 Two-Phase Flow: Bubble Formation
796(5)
Problems
801(1)
References
802(4)
13 Level Set Method
13.1 Introduction
806(1)
13.2 Implicit Surfaces
807(1)
13.3 Level Set Method
808(8)
13.3.1 The Level Set Function
808(2)
13.3.2 Evolution of the Level Set Function
810(1)
13.3.3 Free-Surface Thickness
810(1)
13.3.4 The Signed Distance Function
811(2)
13.3.5 Re-Initialization of the Level Set Function
813(6)
13.3.5.1 Smoothing the Signed Distance Function
815(1)
13.4 WENO Scheme for Interface Advection
816(3)
13.5 Computational Results
819(7)
13.5.1 Multi-Marker, Level Set Method
819(1)
13.5.2 Iso-Geometric Analysis Model
820(2)
13.5.3 Immersed Boundary-Level Set Method
822(2)
13.5.4 Comparison of Volume of Fluid and Level Set Methods
824(2)
Problems
826(2)
References
828(4)
14 Smoothed Particle Hydrodynamics
14.1 Introduction
832(2)
14.2 Integral Representation of Fluid Properties
834(5)
14.2.1 Selection of SPH Kernel
834(1)
14.2.2 Approximate Kernel Functions
835(2)
14.2.3 Accuracy of SPH Approximation
837(1)
14.2.4 Evaluation of Derivatives
838(1)
14.3 Summation Representation of Fluid Properties
839(4)
14.3.1 Summation Representation of Derivatives
840(3)
14.4 SPH for Viscous Flow
843(5)
14.4.1 Conservation of Mass
843(1)
14.4.2 Conservation of Momentum
844(3)
14.4.2.1 Viscosity Models
845(1)
14.4.2.2 Artificial Viscosity
845(1)
14.4.2.3 Equation of State
846(1)
14.4.3 Adaptive Smoothing Length
847(1)
14.5 Boundary Conditions
848(2)
14.5.1 No-Slip Wall Boundary
848(1)
14.5.2 Free-Slip Wall Boundary
849(1)
14.5.3 Free Surface Boundary
849(1)
14.6 Propagation of Particles
850(5)
14.6.1 Stability Conditions
851(1)
14.6.2 Enhanced SPH Methods
852(3)
14.7 Practical Implementation
855(2)
14.8 Computational Results
857(8)
14.8.1 Two-Dimensional Dam-Break Wave
858(1)
14.8.2 Impact and Ricochet of Plunging Jet
858(1)
14.8.3 Ice-Shelf Dynamics
859(1)
14.8.4 Three-Dimensional Dam-Break Model
860(3)
14.8.5 Simulation of Spillway Flow
863(1)
14.8.6 Combined SPH and Level Set Method
863(2)
Problems
865(1)
References
866(1)
Epilogue 867(2)
Note 869(2)
Bibliography 871(4)
Index 875
Nikolaos D. Katopodes, University Michigan Ann Arbor, Department of Civil & Environmental Engineering, Ann Arbor, United States. Dr. Katopodes has chaired or co-chaired 28 PhD student theses. His research has resulted in over 200 publications, and several software packages that are used worldwide for the analysis and control of free-surface flows.
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