Intro
Preface to the Second Edition
Preface to the First Edition
Contents
1 Introduction
1.1 Usefulness of Numerical Investigations
1.2 Development of Numerical Methods
1.3 Characterization of Numerical Methods
2 Modeling of Continuum Mechanical Problems
2.1 Kinematics
2.2 Basic Conservation Equations
2.2.1 Mass Conservation
2.2.2 Momentum Conservation
2.2.3 Moment of Momentum Conservation
2.2.4 Energy Conservation
2.2.5 Material Laws
2.3 Scalar Problems
2.3.1 Simple Field Problems
2.3.2 Heat Transfer Problems

2.4 Structural Mechanics Problems
2.4.1 Linear Elasticity
2.4.2 Bars and Beams
2.4.3 Disks and Plates
2.4.4 Linear Thermo-Elasticity
2.4.5 Hyperelasticity
2.5 Fluid Mechanical Problems
2.5.1 Incompressible Flows
2.5.2 Inviscid Flows
2.6 Aeroacoustics Problems
2.7 Coupled Fluid-Solid Problems
2.7.1 Modeling
2.7.2 Examples of Applications
3 Discretization of Problem Domain
3.1 Description of Problem Geometry
3.2 Numerical Grids
3.2.1 Grid Types
3.2.2 Grid Structure
3.3 Generation of Structured Grids
3.3.1 Algebraic Grid Generation

3.3.2 Elliptic Grid Generation
3.4 Generation of Unstructured Grids
3.4.1 Advancing Front Methods
3.4.2 Delaunay Triangulations
4 Finite-Volume Methods
4.1 General Methodology
4.2 Approximation of Surface and Volume Integrals
4.3 Discretization of Convective Fluxes
4.3.1 Central Differences
4.3.2 Upwind Techniques
4.3.3 Flux-Blending Technique
4.4 Discretization of Diffusive Fluxes
4.5 Non-Cartesian Grids
4.6 Discrete Transport Equation
4.7 Treatment of Boundary Conditions
4.8 Algebraic System of Equations
4.9 Numerical Example

5 Finite-Element Methods
5.1 Galerkin Method
5.2 Finite-Element Discretization
5.3 One-Dimensional Linear Elements
5.3.1 Discretization
5.3.2 Global and Local View
5.4 Practical Realization
5.4.1 Assembling of Equation Systems
5.4.2 Computation of Element Contributions
5.4.3 Numerical Example
5.5 One-Dimensional Cubic Elements
5.5.1 Discretization
5.5.2 Numerical Example
5.6 Two-Dimensional Elements
5.6.1 Variable Transformation for Triangular Elements
5.6.2 Linear Triangular Elements
5.6.3 Numerical Example
5.6.4 Bilinear Parallelogram Elements

5.6.5 Other Two-Dimensional Elements
5.7 Numerical Integration
6 Other Discretization Methods
6.1 Spectral Methods
6.1.1 Chebyshev Ansatz
6.1.2 Error
6.1.3 Extensions
6.1.4 Numerical Examples
6.2 Mesh-Free Methods
6.3 Discontinuous Galerkin Methods
7 Time Discretization
7.1 Basics
7.2 Explicit Methods
7.3 Implicit Methods
7.4 Numerical Example
8 Solution of Algebraic Systems of Equations
8.1 Linear Systems
8.1.1 Direct Solution Methods
8.1.2 Basic Iterative Methods
8.1.3 ILU Methods
8.1.4 Convergence of Iterative Methods