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NUMERICAL METHODS IN CIVIL ENGINEERING
Contents
1 Introduction
Usefulness of numerical investigations
Development of numerical methods
Characterization of numerical methods
2 Modeling of continuum mechanical problems
Kinematics
Basic conservation equations
Mass conservation
Momentum conservation
Moment of momentum conversation
Energy conservation
Material laws
Scalar problems
Simple field problems
Heat transfer problems
Structural mechanics problems
Linear elasticity
Bars and beams
Disks and plates
Linear thermo-elasticity
Hyper elasticity
Fluid mechanical problems
Incompressible flows
Inviscid flows
Coupled fluids –solid problems
Modeling
Examples of applications
Exercises for chap
3 Discretization of problem domain
Description of problem geometry
Numerical grids
Grid types
Grid structure
Generation of structured grids
Algebraic grid generation
Elliptic grid generation
Generation of unstructured grids
Advancing front methods
Delaunay triangulations
Exercises for chap
4 Finite volume methods
General methodology
Approximation of surface and volume integrals
Discretization of convective fluxes
Central differences
Upwind techniques
Flux-blending technique
Discretization of diffusive fluxes
Non-cartesian grids
Discrete transport equation
Treatment of boundary conditions
Algebraic system of equations
Numerical example
Exercises for chap
5 Finite-element methods
Galerkin method
Finite-element discretization
One-dimensional linear elements
Discretization
Global and local view
Practical realization
Assembling of equation systems
Computation of element contributions
Numerical example
One-dimensional cubic elements
Discretization
Numerical example
Two-dimenssional elements
Variable transformation for triangular elements
Linear triangular elements
Numerical example
Bilinear parallelogram elements
Other two-dimensional elements
Numerical integration
Exercises for chap
6 Time discretization
Basics
Explicit methods
Implicit methods
Numerical example
Exercises for chap
7 Solution of algebraic systems of equations
Linear systems
Direct solution methods
Basic iterative methods
ILU methods
Convergence of iterative methods
Conjugate gradient methods
Preconditioning
Comparison of solution methods
Non-linear and coupled systems
Exercises for chap
8 Properties of numerical methods
Properties of discretization methods
Consistency
Stability
Convergence
Conservativity
Boundedness
Estimation of discretization error
Influence of numerical grid
Cost effectiveness
Exercises for chap
9 Finite-element methods in structural mechanics
Structure of equation system
Finite-element discretization
Examples of applications
Exercises for chap
10 Finite-volume methods for incompressible flows
Structure of equation system
Finite-volume discretization
Solution algorithms
Pressure-correction methods
Pressure-velocity coupling
Under-relaxation
Pressure-correction variants
Treatment of boundary conditions
Example of application
Exercises for chap
11 Computation of turbulent flows
Characterization of computational methods
Statistical turbulence modeling
The k-E turbulence model
Boundary conditions
Discretization and solution methods
Large eddy simulation
Comparison of approaches
12 Acceleration of computations
Adaptivity
Refinement strategies
Error indicators
Multi-grid methods
Principle of multi-grid method
Two-grid method
Grid transfers
Multigrid cycles
Examples of computations
Parallelization of computations
Parallel computer systems
Parallelization strategies
Efficiency considerations and example computations
Exercises for chap
List of symbols
References
Index