Preface	5
	Contents	7
	1 Introduction	11
	1.1 Usefulness of Numerical Investigations	11
	1.2 Development of Numerical Methods	14
	1.3 Characterization of Numerical Methods	16
	2 Modeling of Continuum Mechanical Problems	21
	2.1 Kinematics	21
	2.2 Basic Conservation Equations	25
	2.3 Scalar Problems	30
	2.4 Structural Mechanics Problems	36
	2.5 Fluid Mechanical Problems	52
	2.6 Coupled Fluid-Solid Problems	56
	3 Discretization of Problem Domain	67
	3.1 Description of Problem Geometry	67
	3.2 Numerical Grids	70
	3.3 Generation of Structured Grids	76
	3.4 Generation of Unstructured Grids	81
	4 Finite-Volume Methods	87
	4.1 General Methodology	87
	4.2 Approximation of Surface and Volume Integrals	91
	4.3 Discretization of Convective Fluxes	94
	4.4 Discretization of Diffusive Fluxes	99
	4.5 Non-Cartesian Grids	101
	4.6 Discrete Transport Equation	104
	4.7 Treatment of Boundary Conditions	105
	4.8 Algebraic System of Equations	107
	4.9 Numerical Example	110
	5 Finite-Element Methods	116
	5.1 Galerkin Method	116
	5.2 Finite-Element Discretization	119
	5.3 One-Dimensional Linear Elements	121
	5.4 Practical Realization	127
	5.5 One-Dimensional Cubic Elements	132
	5.6 Two-Dimensional Elements	137
	5.7 Numerical Integration	152
	6 Time Discretization	158
	6.1 Basics	158
	6.2 Explicit Methods	163
	6.3 Implicit Methods	166
	6.4 Numerical Example	170
	7 Solution of Algebraic Systems of Equations	176
	7.1 Linear Systems	176
	7.2 Non-Linear and Coupled Systems	191
	8 Properties of Numerical Methods	195
	8.1 Properties of Discretization Methods	195
	8.2 Estimation of Discretization Error	207
	8.3 In.uence of Numerical Grid	210
	8.4 Cost Effectiveness	214
	9 Finite-Element Methods in Structural Mechanics	217
	9.1 Structure of Equation System	217
	9.2 Finite-Element Discretization	219
	9.3 Examples of Applications	223
	10 Finite-Volume Methods for Incompressible Flows	230
	10.1 Structure of Equation System	230
	10.2 Finite-Volume Discretization	231
	10.3 Solution Algorithms	237
	10.4 Treatment of Boundary Conditions	254
	10.5 Example of Application	258
	11 Computation of Turbulent Flows	266
	11.1 Characterization of Computational Methods	266
	11.2 Statistical Turbulence Modeling	268
	11.3 Large Eddy Simulation	278
	11.4 Comparison of Approaches	282
	12 Acceleration of Computations	284
	12.1 Adaptivity	284
	12.2 Multi-Grid Methods	288
	12.3 Parallelization of Computations	302
	List of Symbols	314
	References	320
	Index	323
	More eBooks at www.ciando.com	0