Computational hydraulics : an introduction


Computational hydraulics : an introduction

Cornelis B. Vreugdenhil

Springer-Verlag, 1989

  • : Berlin
  • : New York

大学図書館所蔵 件 / 28



Bibliography: p. [178]-179

Includes index



What is Computational Hydraulics? Computational hydraulics is one of the many fields of science in which the application of computers gives rise to a new way of working, which is intermediate between purely theoretical and experimental. It is concerned with simulation ofthe flow of water, together with its consequences, using numerical methods on com- puters. There is not a great deal of difference with computational hydrodynamics or computational fluid dynamics, but these terms are too much restricted to the fluid as such. It seems to be typical of practical problems in hydraulics that they are rarely directed to the flow by itself, but rather to some consequence of it, such as forces on obstacles, transport of heat, sedimentation of a channel or decay of a pollutant. All these subjects require very similar numerical methods and this is why they are treated together in this book. Therefore, I have preferred to use the term computational hydraulics. Accordingly, I have attempted to show the wide field of application by giving examples of a great variety of such practical problems. Purpose of the Book It is getting a normal situation that an engineer is required to solve some engineering problem involving fluid flow, using standard and general-purpose computer programs available in many organizations. In many instances, the software has been designed with the claim that no numerical or computer-science expertise is needed in using them.


1. Introduction.- 2. Water quality in a Lake.- 2.1. Mathematical Formulation.- 2.2. Exercises.- 3. Numerical solution for Box Model.- 3.1 Principle.- 3.2 Stability and Accuracy.- 3.3. Example.- 3.4. Implicit Method.- 3.5. Exercises.- 4. Transport of a Dissolved Substance.- 4.1. Mathematical Formulation.- 4.2. Numerical Solution.- 4.3. Exercises.- 5. Explicit Finite-Difference Methods.- 5.1. Two-Level Methods.- 5.2. The Leap-Frog Method.- 5.3. The CFL Condition.- 5.4. Truncation Error.- 5.5. Wave Propagation.- 5.6. Exercises.- 6. Kinematic waves.- 6.1. Theory.- 6.2. Example.- 7. Diffusion.- 7.1. Groundwater Flow in a Horizontal Layer.- 7.2. Explicit Finite-Difference Method.- 7.3. Implicit Finite-Difference Method.- 7.4. The Thomas Algorithm.- 7.5. Application.- 7.6. Exercises.- 8. Numerical Accuracy for Diffusion Problems.- 8.1. Fourier Series.- 8.2. Transfer Function.- 8.3. Numerical Representation.- 8.4. Exercises.- 9. Diffusion Model for Coastline Development.- 9.1. Mathematical Formulation.- 9.2. Initial and Boundary Conditions.- 9.3. Example.- 9.4. Exercises.- 10. Consolidation of Soil.- 10.1. Mathematical Formulation.- 10.2. Numerical Example.- 11. Convection-Diffusion.- 11.1. Transport of a Dissolved Substance.- 11.2. Numerical Method.- 11.3. Application.- 11.4. Exercises.- 12. Numerical Accuracy for Convection-Diffusion.- 12.1. Wave Propagation.- 12.2. Example.- 12.3. Numerical Diffusion.- 12.4. Example.- 12.5. Convection only.- 12.6. Wiggles.- 12.7. Exercises.- 13. Salt intrusion in Estuaries.- 13.1. Formulation.- 13.2. Accuracy Mean Concentration.- 13.3. Accuracy for Tidal Fluctuation.- 14. Boundary Layers.- 14.1. Suspended Sediment Transport.- 14.2. Example.- 14.3. Boundary-Layer Flows.- 14.4. Pressure Gradient.- 14.5. Developing Flow in a River.- 14.6. Exercises.- 15. Long Waves.- 15.1. Simplified Formulation.- 15.2. Characteristics.- 15.3. Weakly Reflecting Boundary Conditions.- 15.4. Example.- 15.5. Wave Propagation.- 15.6. Example.- 15.7. Exercises.- 16. Numerical Methods for Long Waves.- 16.1. Leap-Frog Method.- 16.2. Stability of the Leap-Frog Method.- 16.3. Example.- 16.4. Implicit Methods.- 16.5. Numerical Wave Propagation.- 16.6. Example.- 16.7. Exercises.- 17. Long Waves in Two-Dimensional Areas.- 17.1. Mathematical Formulation.- 17.2. Wave Propagation and Characteristics Ill.- 17.3. Boundary Conditions.- 17.4. Example.- 18. Finite-Difference Methods for Two-Dimensional Long Waves.- 18.1. Grids.- 18.2. Explicit Method.- 18.3. Alternating-Direction Implicit Method.- 18.4. Stability.- 18.5. Wave Propagation.- 18.6. Example.- 18.7. Exercises.- 19. Potential Flow.- 19.1. Irrotational Flow.- 19.2. Potential and Stream Function.- 19.3. Characteristics and Boundary Conditions.- 19.4. Pressure.- 19.5. Exercises.- 20. Finite-Difference Method for Potential Flow.- 20.1. Difference Equation.- 20.2. Accuracy.- 20.3. Example..- 20.4. Exercises.- 21. Finite-Element Method.- 21.1. Principle.- 21.2. The Galerkin Method.- 21.3. Boundary Conditions.- 21.4. Comparison with Finite-Difference Method.- 21.5. Groundwater Flow.- 21.6. Exercises.- Appendices.- Al. Long Waves.- A 1.1. Mathematical Formulation for Rivers.- A 1,2. Mathematical Formulation in Two Dimensions.- A 1.3. Characteristics.- A 1.4. Linearization.- A 1.5. Wave Propagation.- A2. Linear Triangular Finite Elements.- References.- Subject Index 181s.

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