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The properties and effects of flows are important in many areas of science and engineering - their prediction can be achieved through analytical, experimental and computational fluid mechanics. In this essential, Karim Ghaib introduces computational fluid dynamics. After an overview of mathematical principles, the author formulates the conservation equations of fluid mechanics and explains turbulence models. He describes the most important numerical methods and then gives types and evaluation criteria of computational meshes. This essential book is thus recommended to both the beginner and the user in the field of computational fluid dynamics.

This book on computational techniques for thermal and fluid-dynamic problems arose from seminars given by the author at the Institute of Nuclear Energy Technology of Tsinghua University in Beijing, China. The book is composed of eight chapters-- some of which are characterized by a scholastic approach, others are devoted to numerical solution of ordinary differential equations of first order, and of partial differential equations of first and second order, respectively. In Chapter IV, basic concepts of consistency, stability and convergence of discretization algorithms are covered in some detail. Other parts of the book follow a less conventional approach, mainly informed by the author's experience in teaching and development of computer programs. Among these is Chapter III, where the residual method of Orthogonal Collocations is presented in several variants, ranging from the classical Galerkin method to Point and Domain Collocations, applied to numerical solution of partial differential equations of first order. In most cases solutions of fluid dynamic problems are led through the discretization process, to the numerical solutions of large linear systems. Intended to impart a basic understanding of numerical techniques that would enable readers to deal with problems of Computational Fluid Dynamics at research level, the book is ideal as a reference for graduate students, researchers, and practitioners.

This book serves as a preliminary reference for the principles of thermal radiation and its modelling in computational fluid dynamics (CFD) simulations.Radiation Heat Transfer Modelling with Computational Fluid Dynamics covers strategies and processes for synthesizing radiation with CFD setups, computational techniques for solving the radiative transfer equation, the strengths and weaknesses thereof, boundary and initial conditions and relevant guidelines. Describing the strategic planning of a typical project, the book includes the spectroscopic properties of gases, some particulates and porous media.FEATURES Fills a gap between existing CFD and thermal radiation textbooks and elaborates on some aspects of user manuals. Aims at (1) CFD practitioners who are newcomers to thermal radiation and are looking for a preliminary introduction thereon and (2) modellers familiar with thermal radiation looking for a precursory introduction to CFD. The book is tilted somewhat towards the first group. Provides guidelines for choosing the right model, the strategic planning of the modelling and its implementation. Outlines the pitfalls of some solution techniques. Describes how radiation is included in the variety of boundary condition types offered by CFD codes. Helps to develop the practical skills required to plan, implement and interpret thermal radiation within the typical CFD code. Addresses a wide variety of physical circumstances in which thermal radiation plays a role. Offers ample references for readers searching for additional details. Includes several examples of practical applications, including fire, a utility boiler and car headlights in cold environments. This book is intended for researchers and professionals who wish to simulate problems that involve fluid flow and heat transfer with thermal radiation.

This textbook presents the basic methods, numerical schemes, and algorithms of computational fluid dynamics (CFD). Readers will learn to compose MATLAB® programs to solve realistic fluid flow problems.Newer research results on the stability and boundedness of various numerical schemes are incorporated. The book emphasizes large eddy simulation (LES) in the chapter on turbulent flow simulation besides the two-equation models. Volume of fraction (VOF) and level-set methods are the focus of the chapter on two-phase flows.The textbook was written for a first course in computational fluid dynamics (CFD) taken by undergraduate students in a Mechanical Engineering major.Access the Support Materials: https://www.routledge.com/9780367687298.

This unique text provides engineering students and practicing professionals with a comprehensive set of practical, hands-on guidelines and dozens of step-by-step examples for performing state-of-the-art, reliable computational fluid dynamics (CFD) and turbulence modeling. Key CFD and turbulence programs are included as well. The text first reviews basic CFD theory, and then details advanced applied theories for estimating turbulence, including new algorithms created by the author. The book gives practical advice on selecting appropriate turbulence models and presents best CFD practices for modeling and generating reliable simulations. The author gathered and developed the book's hundreds of tips, tricks, and examples over three decades of research and development at three national laboratories and at the University of New Mexico—many in print for the first time in this book. The book also places a strong emphasis on recent CFD and turbulence advancements found in the literature over the past five to 10 years. Readers can apply the author's advice and insights whether using commercial or national laboratory software such as ANSYS Fluent, STAR-CCM, COMSOL, Flownex, SimScale, OpenFOAM, Fuego, KIVA, BIGHORN, or their own computational tools. Applied Computational Fluid Dynamics and Turbulence Modeling is a practical, complementary companion for academic CFD textbooks and senior project courses in mechanical, civil, chemical, and nuclear engineering; senior undergraduate and graduate CFD and turbulence modeling courses; and for professionals developing commercial and research applications.

This book describes recently developed research methods used to study complex problems in fluid engineering, especially optical flow measurement, flow visualization and numerical methods. It includes a wealth of diagrams and images, and the content is presented in a step-by-step manner from beginning to end, helping readers grasp the central points of the book.The book also presents a number of practical cases, illustrating how the research methods covered can be concretely implemented. Lastly, the book offers a valuable point of departure for pursuing further research.

This book introduces design techniques developed to increase the safety of aircraft engines, and demonstrates how the application of stochastic methods can overcome problems in the accurate prediction of engine lift caused by manufacturing error. This in turn addresses the issue of achieving required safety margins when hampered by limits in current design and manufacturing methods. The authors show that avoiding the potential catastrophe generated by the failure of an aircraft engine relies on the prediction of the correct behaviour of microscopic imperfections. This book shows how to quantify the possibility of such failure, and that it is possible to design components that are inherently less risky and more reliable.This new, updated and significantly expanded edition gives an introduction to engine reliability and safety to contextualise this important issue, evaluates newly-proposed methods for uncertainty quantification as applied to jet engines.Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines will be of use to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students in aerospace or mathematical engineering may also find it of interest.

Computational fluid-structure interaction and flow simulation are challenging research areas that bring solution and analysis to many classes of problems in science, engineering, and technology. Young investigators under the age of 40 are conducting much of the frontier research in these areas, some of which is highlighted in this book. The first author of each chapter took the lead role in carrying out the research presented. The topics covered include Computational aerodynamic and FSI analysis of wind turbines,Simulating free-surface FSI and fatigue-damage in wind-turbine structural systems,Aorta flow analysis and heart valve flow and structure analysis,Interaction of multiphase fluids and solid structures,Computational analysis of tire aerodynamics with actual geometry and road contact, andA general-purpose NURBS mesh generation method for complex geometries.This book will be a valuable resource for early-career researchers and students — not only those interested in computational fluid-structure interaction and flow simulation, but also other fields of engineering and science, including fluid mechanics, solid mechanics and computational mathematics – as it will provide them with inspiration and guidance for conducting their own successful research. It will also be of interest to senior researchers looking to learn more about successful research led by those under 40 and possibly offer collaboration to these researchers.

This book deals with numerical simulations and computations of the turbulent flow around high-lift configurations commonly used in aircraft. It is devoted to the Computational Fluids Dynamics (CFD) method using full Navier-Stokes solvers typically used in the simulation of high-lift configuration. With the increase of computational resources in the aeronautical industry, the computation of complex flows such as the aerodynamics of high-lift configurations has become an active field not only in academic but also in industrial environments. The scope of the book includes applications and topics of interest related to the simulation of high-lift configurations such as: lift and drag prediction, unsteady aerodynamics, low Reynolds effects, high performance computing, turbulence modelling, flow feature visualization, among others. This book gives a description of the state-of-the-art of computational models for simulation of high-lift configurations. It also shows and discusses numerical results and validation of these computational models. Finally, this book is a good reference for graduate students and researchers interested in the field of simulation of high-lift configurations.

This book focuses on CFD (Computational Fluid Dynamics) techniques and the recent developments and research works in thermo-mechanics applications. It is devoted to the publication of basic and applied studies broadly related to this area. The chapters present the development of numerical methods, computational techniques, and case studies in the thermo-mechanics applications. They offer the fundamental knowledge for using CFD in real thermo-mechanics applications and complex flow problems through new technical approaches. Also, they discuss the steps in the CFD process and provide benefits and issues when using the CFD analysis in understanding of complicated flow phenomena and its use in the design process. The best practices for reducing errors and uncertainties in CFD analysis are also discussed. The presented case studies and development approaches aim to provide the readers, such as engineers and PhD students, the fundamentals of CFD prior to embarking on any real simulation project. Additionally, engineers supporting or being supported by CFD analysts can benefit from this book. ​

This book reports on the EU-funded 7th Framework project, Go4Hybrid (Grey Area Mitigation for Hybrid RANS-LES Methods). It presents new findings concerning the accuracy and reliability of current hybrid RANS-LES methods. It describes improved formulations of both non-zonal and embedded hybrid strategies, together with their validation in a broad range of flow cases, and highlighting some key industrial applications. The book provides students, researchers and professionals in the field of applied computational fluid dynamics with a timely, practice-oriented reference guide.

This volume offers a tool for High Performance Computing (HPC). A brief historical background on the subject is first given. Fluid Statics dealing with Pressure in fluids at rest, Buoyancy and Basics of Thermodynamics are next presented. The Finite Volume Method, the most convenient process for HPC, is explained in one-dimensional approach to diffusion with convection and pressure velocity coupling. Adiabatic, isentropic and supersonic flows in quasi-one dimensional flows in axisymmetric nozzles is considered before applying CFD solutions. Though the theory is restricted to one-dimensional cases, three-dimensional CFD examples are also given. Lastly, nozzle flows with normal shocks are presented using turbulence models. Worked examples and exercises aregiven in each chapter. Fluids transport thermal energy for its conversion to kinetic energy, thus playing a major role that is central to all heat engines. With the advent of rotating machinery in the 20th century, Fluid Engineering was developed in the form of hydraulics and hydrodynamics and adapted in engineering Schools across the world until recent times. With the High Performance Computing (HPC) in recent years, Simulation Based Engineering Science (SBES) has gradually replaced the conventional approach in Fluid Flow Design bringing Science directly into Engineering without approximations. Hence this SpringerBrief in Applied Sciences and Technology. This book brings SBES to an entry level allowing young students to quickly adapt to modern design practices.

This book concerns the most up-to-date advances in computational transport phenomena (CTP), an emerging tool for the design of gas-solid processes such as fluidized bed systems. The authors examine recent work in kinetic theory and CTP and illustrate gas-solid processes'many applications in the energy, chemical, pharmaceutical, and food industries. They also discuss the kinetic theory approach in developing constitutive equations for gas-solid flow systems and how it has advanced over the last decade as well as the possibility of obtaining innovative designs for multiphase reactors, such as those needed to capture CO2 from flue gases. Suitable as a concise reference and a textbook supplement for graduate courses, Computational Transport Phenomena of Gas-Solid Systems is ideal for practitioners in industries involved with the design and operation of processes based on fluid/particle mixtures, such as the energy, chemicals, pharmaceuticals, and food processing.

This book discusses basic thermodynamic behaviors and'abnormal'properties from a thermo-physical perspective, and explores basic heat transfer and flow properties, the latest findings on their physical aspects and indications, chemical engineering properties, microscale phenomena, as well as transient behaviors in fast and critical environments. It also presents the most and challenging problems and the outlook for applications and innovations of supercritical fluids.

Heat transfer enhancement has seen rapid development and widespread use in both conventional and emerging technologies. Improvement of heat transfer fluids requires a balance between experimental and numerical work in nanofluids and new refrigerants. Recognizing the uncertainties in development of new heat transfer fluids, Advances in New Heat Transfer Fluids: From Numerical to Experimental Techniques contains both theoretical and practical coverage.

This book introduces a new generation of superfast algorithms for the treatment of the notoriously difficult velocity-pressure coupling problem in incompressible fluid flow solutions. It provides all the necessary details for the understanding and implementation of the procedures. The derivation and construction of the fully-implicit, block-coupled, incomplete decomposition mechanism are given in a systematic, but easy fashion. Worked-out solutions are included, with comparisons and discussions. A complete program code is included for faster implementation of the algorithm. A brief literature review of the development of the classical solution procedures is included as well.

This book addresses the evaluation and optimization of key elements in concentrating solar thermal (CST) technologies, such as solar receivers and working fluids, using computational fluid dynamics (CFD) modeling. It discusses both general and specific aspects, explaining the methodology used to analyze and evaluate the influence of different parameters on the facility performance. This information provides the basis for optimizing design and operating conditions in CST systems.

This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings.The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, amongst others.This book is highly suitable for students in the subject area, but may also be a useful reference text for more advanced scientists and engineers.

This book introduces novel design techniques developed to increase the safety of aircraft engines. The authors demonstrate how the application of uncertainty methods can overcome problems in the accurate prediction of engine lift, caused by manufacturing error. This in turn ameliorates the difficulty of achieving required safety margins imposed by limits in current design and manufacturing methods. This text shows that even state-of-the-art computational fluid dynamics (CFD) are not able to predict the same performance measured in experiments; CFD methods assume idealised geometries but ideal geometries do not exist, cannot be manufactured and their performance differs from real-world ones. By applying geometrical variations of a few microns, the agreement with experiments improves dramatically, but unfortunately the manufacturing errors in engines or in experiments are unknown. In order to overcome this limitation, uncertainty quantification considers the probability density functions of manufacturing errors. It is then possible to predict the overall variation of the jet engine performance using stochastic techniques. Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines demonstrates that some geometries are not affected by manufacturing errors, meaning that it is possible to design safer engines. Instead of trying to improve the manufacturing accuracy, uncertainty quantification when applied to CFD is able to indicate an improved design direction. This book will be of interest to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students may also find it of use.

Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.

This book presents a new computational methodology called Computational Mass Transfer (CMT). It offers an approach to rigorously simulating the mass, heat and momentum transfer under turbulent flow conditions with the help of two newly published models, namely the C'2—εC'model and the Reynolds mass flux model, especially with regard to predictions of concentration, temperature and velocity distributions in chemical and related processes. The book will also allow readers to understand the interfacial phenomena accompanying the mass transfer process and methods for modeling the interfacial effect, such as the influences of Marangoni convection and Rayleigh convection. The CMT methodology is demonstrated by means of its applications to typical separation and chemical reaction processes and equipment, including distillation, absorption, adsorption and chemical reactors. Professor Kuo-Tsong Yu is a Member of the Chinese Academy of Sciences. Dr. Xigang Yuan is a Professor at the School of Chemical Engineering and Technology, Tianjin University, China.

The field of computational fluid dynamics (CFD) has matured since the au­ thor was first introduced to electronic computation in the mid-sixties. The progress of numerical methods has paralleled that of computer technology and software. Simulations are used routinely in all branches of engineering as a very powerful means for understanding complex systems and, ultimately, improve their design for better efficiency. Today's engineers must be capable of using the large simulation codes available in industry, and apply them to their specific problem by implemen­ ting new boundary conditions or modifying existing ones. The objective of this book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of phy­ sical phenomena, governed by equations that are related, yet simpler, than the equations they need to solve. The model problems presented here are linear, in most cases, and represent the propagation of waves in a medium, the diffusion of heat in a slab, and the equilibrium of a membrane under distributed loads. Yet, regardless of the origin of the problem, the partial differential equations (PDE's) reflect the physical phenomena to be modeled and can be classified as being of hyperbolic, parabolic or elliptic type. The numerical treatment depends on the equation type that can represent several physical situations as diverse as heat conduction and viscous fluid flow. Non­ linear model problems are also presented and solved, such as the transonic small disturbance equation and the equations of gas dynamics.

This volume reports results from the German research initiative MUNA (Management and Minimization of Errors and Uncertainties in Numerical Aerodynamics), which combined development activities of the German Aerospace Center (DLR), German universities and German aircraft industry. The main objective of this five year project was the development of methods and procedures aiming at reducing various types of uncertainties that are typical of numerical flow simulations. The activities were focused on methods for grid manipulation, techniques for increasing the simulation accuracy, sensors for turbulence modelling, methods for handling uncertainties of the geometry and grid deformation as well as stochastic methods for quantifying aleatoric uncertainties.

The field of computational fluid dynamics (CFD) has already had a significant impact on the science and engineering of fluid dynamics, ranging from a role in aircraft design to enhancing our understanding of turbulent flows. It is thus not surprising that there exist several excellent books on the subject. We do not attempt to duplicate material which is thoroughly covered in these books. In particular, our book does not describe the most recent developments in algorithms, nor does it give any instruction with respect to programming. Neither turbulence modelling nor grid generation are covered. This book is intended for a reader who seeks a deep understanding of the fundamental principles which provide the foundation for the algorithms used in CFD. As a result of this focus, the book is suitable for a first course in CFD, presumably at the graduate level. The underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provide a mathematical framework to describe and unify most numerical methods in common use for solving the partial differential equations governing the physics of fluid flow. This approach originated with the first author during his long and distinguished career as Chief of the CFD Branch at the NASA Ames Research Center.

High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.

Computational Fluid Dynamics (CFD) has been applied extensively to great benefit in the food processing sector. Its numerous applications include: predicting the gas flow pattern and particle histories, such as temperature, velocity, residence time, and impact position during spray drying; modeling of ovens to provide information about temperature and airflow pattern throughout the baking chamber to enhance heat transfer and in turn final product quality; designing hybrid heating ovens, such as microwave-infrared, infrared-electrical or microwave-electrical ovens for rapid baking; model the dynamics of gastrointestinal contents during digestion based on the motor response of the GI tract and the physicochemical properties of luminal contents; retort processing of canned solid and liquid foods for understanding and optimization of the heat transfer processes. This Brief will recapitulate the various applications of CFD modeling, discuss the recent developments in this field, and identify the strengths and weaknesses of CFD when applied in the food industry. ​

'Computational Fluid Dynamics Based on the Unified Coordinates'reviews the relative advantages and drawbacks of Eulerian and Lagrangian coordinates as well as the Arbitrary Lagrangian-Eulerian (ALE) and various moving mesh methods in Computational Fluid Dynamics (CFD) for one- and multi-dimensional flows. It then systematically introduces the unified coordinate approach to CFD, illustrated with numerous examples and comparisons to clarify its relation with existing approaches. The book is intended for researchers, graduate students and practitioners in the field of Computational Fluid Dynamics. Emeritus Professor Wai-Hou Hui and Professor Kun Xu both work at the Department of Mathematics of the Hong Kong University of Science & Technology, Hong Kong, China.

A SPECTER is haunting the scientific world-the specter of com­ puters. All the powers of traditional science have entered into a holy alliance to exorcise this specter: puristic theoreticians and tradition­ alistic experimentalists, editors and referees of prestigious journals, philosophers of science and mathematicians. Where is a pioneering computer simulation that has not been decried as unreliable by its opponents in power? The Computer Manifesto As a result of the enormous progress in computer technology made during the last few decades, computer simulations have become a very powerful and widely applicable tool in science and engineering. The main purpose of this. book is a comprehensive description of the background and possibilities for the application of computer simulation techniques in polymer fluid dynamics. Mod­ eling and understanding the flow behavior of polymeric liquids on the kinetic theory level is not merely a great intellectual challenge but rather a matter of immense practical importance, for example, in connection with plastics manu­ facture, processing of foods, and movement of biological fluids. The classical computer simulation technique for static problems in statis­ tical mechanics is the Monte Carlo method developed in the early 1950s. The name of this method underlines how unusual and strange the idea of using ran­ dom numbers in the exact sciences is at first glance. However, the Monte Carlo method is a rigorous and efficient means for evaluating moments and static spa­ tial correlation functions for given probability distributions.

This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics. A solutions manual to the exercises is in preparation.

This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engineers to get useful information on CFD for their activities. The procedural details are given with respect to particular tasks from the authors'field of research, for example simulations of liquid propellant rocket engine subsystems, turbo-pumps and the blood circulations in the human brain as well as the design of artificial heart devices. However, those examples serve as illustrations of computational and physical challenges relevant to many other fields. Unlike other books on incompressible flow simulations, no abstract mathematics are used in this book. Assuming some basic CFD knowledge, readers can easily transfer the insights gained from specific CFD applications in engineering to their area of interest.

High resolution upwind and centred methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Direct applicability of the methods include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition the book was thoroughly revised and contains substantially more, and new material both in its fundamental as well as in its applied parts.

This is a softcover reprint of a very popular hardcover edition, published in 1999. An account is given of the state of the art of numerical methods employed in computational fluid dynamics. Numerical principles are treated in detail, using elementary methods. Attention is given to difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed, as well as the shallow-water equations. A basic introduction is given to efficient iterative solution methods.'This book is a well-written graduate level text in computational fluid dynamics, with a good introduction to the two numerical methods, finite volume and finite difference. The material is well-organized, starting with simple one-dimensional equations and moving to numerical methods for two-dimensional and three-dimensional problems. There is a good mixture of theoretical and computational topics. This text should be of value to all researchers interested in computational fluid dynamics.'Mathematical Reviews

In 1917, the British scientist L. F. Richardson made the first reported attempt to predict the weather by solving partial differential equations numerically, by hand! It is generally accepted that Richardson's work, though unsuccess­ ful, marked the beginning of Computational Fluid Dynamics (CFD), a large branch of Scientific Computing today. His work had the four distinguishing characteristics of CFD: a PRACTICAL PROBLEM to solve, a MATHEMATICAL MODEL to represent the problem in the form of a set of partial differen­ tial equations, a NUMERICAL METHOD and a COMPUTER, human beings in Richardson's case. Eighty years on and these four elements remain the pillars of modern CFD. It is therefore not surprising that the generally accepted definition of CFD as the science of computing numerical solutions to Partial Differential or Integral Equations that are models for fluid flow phenomena, closely embodies Richardson's work. COMPUTERS have, since Richardson's era, developed to unprecedented levels and at an ever decreasing cost. PRACTICAL PROBLEMS to solved nu­ merically have increased dramatically. In addition to the traditional demands from Meteorology, Oceanography, some branches of Physics and from a range of Engineering Disciplines, there are at present fresh demands from a dynamic and fast-moving manufacturing industry, whose traditional build-test-fix approach is rapidly being replaced by the use of quantitative methods, at all levels. The need for new materials and for decision-making under envi­ ronmental constraints are increasing sources of demands for mathematical modelling, numerical algorithms and high-performance computing.