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
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
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
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
One-dimensional cubic elements
Two-dimenssional elements
Variable transformation for triangular elements
Linear triangular elements
Bilinear parallelogram elements
Other two-dimensional elements
Numerical integration
6 Time discretization
Basics
Explicit methods
Implicit methods
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
8 Properties of numerical methods
Properties of discretization methods
Consistency
Stability
Convergence
Conservativity
Boundedness
Estimation of discretization error
Influence of numerical grid
Cost effectiveness
9 Finite-element methods in structural mechanics
Structure of equation system
10 Finite-volume methods for incompressible flows
Finite-volume discretization
Solution algorithms
Pressure-correction methods
Pressure-velocity coupling
Under-relaxation
Pressure-correction variants
Example of application
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
List of symbols
References
Index
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