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Numerical Simulation in Fluid Dynamics: A Practical Introduction

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by Michael Griebel, Thomas Dornseifer, and Tilman Neunhoeffer


1997 / xvi + 217 pages / Softcover / ISBN13: 978-0-898713-98-5 / List Price $106.50 / SIAM Member Price $74.55 / Order Code MM03

In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as expository example, the individual steps of scientific computing are presented:

  • the derivation of the mathematical model,
  • the discretization of the model equations,
  • the development of algorithms,
  • parallelization, and
  • visualization of the computed data. 

In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids—the Navier–Stokes equations—the authors look at the simulation of

  • free surface flows,
  • energy and chemical transport, and
  • turbulence. 

The code for the two-dimensional numerical solution of flow problems is located here, and the three-dimensional parallel version is located here.

Detailed hints for the implementation of the various algorithms enable readers to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 93 black-and-white and 17 color illustrations.

Moreover, after reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and to apply their new knowledge of modeling, discretization, parallelization, and visualization to other scientific fields, where numerical simulation has established itself, in addition to theoretical investigations and practical experiments, as a new path for uncovering the laws of nature. Among these fields are the examination of elastic solids, combustion, melting and coating processes, and crystal growth, as well as weather prediction.

The book is written on an advanced undergraduate level and addresses mathematicians, engineers, and natural and computer scientists who are interested in scientific computing. It is well suited for a cross-disciplinary and application-oriented training at the university level as well as for practitioners seeking basic insights into computational fluid dynamics.

Notation; Chapter 1: Numerical Simulationa Key Technology of the Future. Physical Experiments, Mathematical Modeling, and Numerical Simulation; Fluids and Flows; Numerical Flow Simulation; Chapter 2: The Mathematical Description of Flows. The Mathematical Model: The NavierÐStokes Equations; The Derivation of the NavierÐStokes Equations; Dynamic Similarity of Flows; Chapter 3: The Numerical Treatment of the NavierÐStokes Equations. The Discretization; The Algorithm; Implementation; Treatment of General Geometries; Chapter 4: Visualization Techniques. Standard Techniques; Flow Visualization by Particle Tracing and Streaklines; Stream Function and Vorticity; Chapter 5: Example Applications. Lid-Driven Cavity; Flow over a Backward-Facing Step; Flow Past an Obstacle; Pipe Junction; Flow through Complex Geometries; Fluid-Structure Interaction; Chapter 6: Free Boundary Value Problems. Determination of the Domain Shape; Conditions along the Free Boundary; The Extended Algorithm; Implementation; Chapter 7: Example Applications for Free Boundary Value Problems. The Breaking Dam; The Splash of a Liquid Drop; Free-Surface Flow over a Step; Injection Molding; Curtain Coating; Chapter 8: Parallelization. Parallel Computers and Programming Environments; Domain Decomposition as a Parallelization Strategy; Parallelization of the Flow Code; Implementation on a Network of Workstations Using PVM; Measuring Performance; Chapter 9: Energy Transport. Extending the Mathematical Model by the Energy Equation; Derivation of the Energy Equation; On the Validity of the Boussinesq Approximation; Discretization of the Energy Equation and Extension of the Algorithm; Implementation; Visualization of Heat Flow; Example Applications; Chemical Transport; Chapter 10: Turbulence. Turbulent Flows; Turbulence Modeling; Discretization of the k-* Model; Implementation; Numerical Results; Chapter 11: Extension to Three Dimensions. The Continuous Equations; Discretization and Algorithm; Extensions and Modifications; Examples of 3D Simulations; Chapter 12: Concluding Remarks. Appendix A: Guidelines for Parallelization Using PVM; Appendix B: Physical Properties of Fluids; Bibliography; Index

ISBN13: 9780898713985

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