High-Resolution Methods for Incompressible and Low-Speed Flows

1. Front Matter

   Pages I-XX

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2. Introduction

   Pages 1-3

3. Fundamental Physical and Model Equations

   1. The Fluid Flow Equations

      Pages 7-25

   2. The Viscous Fluid Flow Equations

      Pages 27-50

   3. Curvilinear Coordinates and Transformed Equations

      Pages 51-65

   4. Overview of Various Formulations and Model Equations

      Pages 67-78

   5. Basic Principles in Numerical Analysis

      Pages 79-97

   6. Time Integration Methods

      Pages 99-119

   7. Numerical Linear Algebra

      Pages 121-143

4. Solution Approaches

   1. Compressible and Preconditioned-Compressible Solvers

      Pages 147-171

   2. The Artificial Compressibility Method

      Pages 173-208

   3. Projection Methods: The Basic Theory and the Exact Projection Method

      Pages 209-235

   4. Approximate Projection Methods

      Pages 237-292

5. Modern High-Resolution Methods

   1. Introduction to Modern High-Resolution Methods

      Pages 295-307

   2. High-Resolution Godunov-Type Methods for Projection Methods

      Pages 309-345

   3. Centered High-Resolution Methods

      Pages 347-372

   4. Riemann Solvers and TVD Methods in Strict Conservation Form

      Pages 373-428

   5. Beyond Second-Order Methods

      Pages 429-476

6. Applications

   1. Variable Density Flows and Volume Tracking Methods

      Pages 479-528

   2. High-Resolution Methods and Turbulent Flow Computation

      Pages 529-555

The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.

• High-resolution
• Incompressible
• Low-speed
• Non-oscillatory
• Turbulence
• computational fluid dynamics
• fluid dynamics
• fluid- and aerodynamics

From the reviews:

"This book presents a wide variety of numerical methods for fluid dynamics. … The material is well organized and quite thorough. The authors should be commended for including material on the actual implementation of methods that other texts do not give. … This book should be a useful reference for computational scientists and engineers engaged in the numerical simulation of fluid flows." (John C. Strikwerda, Mathematical Reviews, 2005k)

"The authors present the current state-of-the-art of numerical techniques for computing low-Mach number fluid flows. … Many subjects are described in full detail, and the reader can find all the necessary information to write a code. … more than 600 given references provide comprehensive information on the state-of-the art that an interested reader may consult. … In conclusion, this book represents a highly valuable tool for researchers involved in the numerical simulation of incompressible flows."(Renzo Arina and Maurizio Pandolfi, Meccanica, Vol. 42, 2007)

• Dept. of Aerospace Science, Cranfield University School of Engineering, Cranfield, UK

  Dimitris Drikakis

• Computer and Computational Sciences Division, Los Alamos National Laboratory, Los Alamos, USA

  William Rider

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