Book

Introduction to Numerical Modelling of Two-Dimensional Free Surface Flows

M. Jovanović

Book1.webp


M. Jovanović

Introduction to Numerical Modelling of Two-Dimen-sional Free Surface Flows

(in Serbian)


Faculty of Civil Engineering

Belgrade, 1998.

ISBN 86-80049-83-2

Pages: 395


About the book:

This book originated from the author's lectures on the subject of River hydra-ulics, on the post-graduate studies at the Faculty of Civil Engineering in Bel-grade. In the hope that the book will be also useful to practicing engineers, this book is based more on a sowewhat "engineering-intuitive" approach to ex-plaining numerical procedures, and less on strictly proving the existence of numerical solutions. "Classical" nume-rical methods of finite differences, as well as methods of finite and boundary elements are presented. Understan-ding them can help engineers to effectively use commercial software and to form a critical awareness of the capabilities and limitations of numeri-cal modeling of open channel flows.

Contents:

1. Equations of Two-Dimensional Free Surface Flows

  • Navier-Stokes equations
  • Reynolds equations
  • Depth-averaged equations
  • Closure problem
  • Modelling of dispersion terms

2. Shear stress modelling

  • Shear stress distribution in boundary layer
  • Velocity distribution in boundary layer
  • Empirical frictional resistance formulas
  • Bottom and free surface shear stresses

3. Turbulence modelling

  • Turbulent viscosity and diffusion
  • Zero equation turbulence modelling
  • One-equation model ("k-model")
  • Two-equations model ("k-epsilon")
  • K-epsilon model for free-surface flows
  • Large eddy simulation (LES)

4. Method of Characteristics

  • Long waves in shallow water
  • Flow equations
  • Solution for flow in one space dimension
  • Solution for flow in two space dimensions

5. The Finite Difference Method

  • Finite-difference approximations
  • Consistency, stability, convergence
  • Finite-difference meshes
  • Principles of numerical solution
  • Solution of equations of 2D free-surface flows
  • The fractional step method
  • Modelling of discontinous flows (weak solutions)

6. The Finite Element Method

  • General considerations
  • Approximate solutions
  • Types of finite elements
  • Consistency and continuity
  • Local coordinate systems
  • Conventional Lagrange polynomial elements
  • Hermite polynomial elements
  • Special elements
  • Integral formulations of FEM
  • Matrix formulation of FEM
  • Integral equation for the reference element
  • One example
  • Numerical integration
  • Algorithmic structure of FEM
  • Assembling of the global matrix
  • Introduction of the boundary conditions
  • Numerical solution of non-linear problems
  • Application of FEM to 2D free-surface flow problems

7. The Boundary Element Method

  • Theoretical background
  • Solution of integral equations
  • Application of BEM to 2D free-surface flow problems
  • Examples

Appendix A: Classification of partial differential equations

Appendix B: The Von Neumann stability analysis


Subject and author index