Computational Fluid Dynamics Recipes

Outline & Worked Examples

Preface

Computational fluid dynamics (CFD) has been the main tool for the analysis of fluid flow problems for the last sixty years or so. The basic idea of CFD is the same as any numerical method, namely solving complicated problems with basic arithmetic operations doable by computers. These methods have changed dramatically during last half of century. With the advances in the available computational power, CFD has evolved to a robust tool of the science and indeed the art of fluid flow simulation.

Having being a student, researcher, designer and teacher, I have found that examples play a pivotal role in increasing one’s learning efficiency, at least at the entry level. Therefore, this book is based on a hand’s on "learn trough examples" concept. The basic methods are briefly introduced and then applied to different examples with detailed solution steps and FORTRAN codes in each section. I hope this effort will not only make the subject more accessible and understandable to students, but also helps them to concentrate on the conceptual and noble aspects of CFD methods.

All the methods presented here provide an insight into the engine behind CFD packages such as FLUENT, ANSYSCFX, STARCD. Understanding these methods will help users of these packages to adapt intrinsic routines or even develop their own subroutines inside them, whenever necessary and possible.

In explaining all the methods and writing the codes, clarity, and ease of understanding, rather than elegance, compactness and computational efficiency, has been the main guide. The algorithms and the codes can be drafted in more generic, compact and efficient way.

Who should use this book?

The approach adopted in this book makes it suitable for not only a textbook for undergraduate courses, but also as an aid for teachers, researchers, designers and workers in the field.

The structure of the book

Part I deals with bare needs for tackling any fluid mechanics problems, such as vector and matrix algebra.

Part II introduces general scalar transport equation and concentrates on simple steady state diffusion problems. Before attempting the NavierStokes equations.

Part III outlines basic fluid dynamics equations and detailed discussion of the incompressible flow model, using primitive variables as well as vorticitystreamfunction, is presented.

Part IV, revisits the diffusion dominated problems through tackling low Reynolds number (creeping) flows. Part V introduces the convection terms into the scene. Different discretization schemes, including first and second order upwind methods, hybrid and CONDIF methods, as well as thirdorder QUICK scheme, are discussed.

Part VI, addresses the incompressible NavierStokes equation and introduces the primitive variables formulation, staggered grid with emphasis on the SIMPLE family and PIOS algorithms.

Finally, in the last part of the book, Part VII details the more complicated cases of unsteady fluid flows. First, unsteady scalar transport equation, using conduction and creeping flow examples, is addressed. Then, the methods to solve the primitive variable formulation of the NavierStokes equations are outlined.

The codes in this book have been compiled by GNU FORTRAN and the results are plotted using Tecplot.

It is intended to follow this book by two additional volumes. The second volume will deal with the grid generation, and compressible flow problems. The third volume will cover special topics, such as multigrid methods, reacting flows, turbulence, flows with interfaces, and flow through porous media. With the limitations of a book like this, many topics have not been covered in details or at all. However, many outstanding text books are written by talented authors, which undoubtedly cover the shortcomings of a book like this.

No doubt, despite all earnest efforts, errors remain within the text and I will be grateful to hear from readers who discover any errors or their comments.

Thomas Selerland

London

June, 2012

t.selerland@cfdrecipes.com