Computational Engineering Introduction to Numerical Methods

Transcription

1 Michael Schafer Computational Engineering Introduction to Numerical Methods With 204 Figures 4y Springer

2 ire discussed. The following, structural mechanics, fluid 1 grids, finite-volume meth- n, properties of discrete sys- ir systems, coupling of varilization. for elasto-mechanical probe flows, simulation of turbuner, such that besides basic ad linear algebra no further itive studies hints for correve chapter are given. application examples. Many > follow and understand the ;er give the possibility of rere provided on the web page itable either for self-study or lectures. It can be useful for computational engineers in ed are integrated in the flow im the author. re notes for different courses anical Engineering at Darmthe German book Numerik, but includes several modiof the department who have jcial thanks are addressed to RS at Marseille for the warm which helped a lot in comto Rekik Alehegn Mekonnen ;ast the author would like to cooperation. Michael Schdfer 1 Introduction Usefulness of Numerical Investigations Development of Numerical Methods Characterization of Numerical Methods 6 2 Modeling of Continuum Mechanical Problems Kinematics Basic Conservation Equations Mass Conservation Momentum Conservation Moment of Momentum Conservation 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 Hyperelasticity Fluid Mechanical Problems Incompressible Flows Inviscid Flows Coupled Fluid-Solid Problems Modeling Examples of applications 49 Exercises for Chap. 2 56

3 VIII 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 74 Exercises for Chap 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 100 Exercises for Chap 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-Dimensional Elements Variable Transformation for Triangular Elements Linear Triangular Elements Numerical Example 132

4 IX [Integrals hs 118 fcbutions pangular Elements Bilinear Parallelogram Elements Other Two-Dimensional Elements Numerical Integration 143 Exercises for Chap Time Discretization Basics Explicit Methods Implicit Methods Numerical Example 161 Exercises for Chap 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 182 Exercises for Chap Properties of Numerical Methods Properties of Discretization Methods Consistency Stability Convergence Conservativity Boundedness Estimation of Discretization Error Influence of Numerical Grid Cost Effectiveness 206 Exercises for Chap Finite-Element Methods in Structural Mechanics Structure of Equation System Finite-Element Discretization Examples of Applications 215 Exercises for Chap

5 X 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 251 Exercises for Chap 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 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 Efncieny Considerations and Example Computations Exercises for Chap List of Symbols 307 References 313 Index 317