Fluid mechanics is a branch of classical physics that has a rich tradition in applied mathematics and numerical methods. It is at work virtually everywhere, from nature to technology. This broad and fundamental coverage of computational fluid dynamics (CFD) begins with a presentation of basic numerical methods and flows into a rigorous introduction to the subject. A heavy emphasis is placed on the exploration of fluid mechanical physics through CFD, making this book an ideal text for any new course that simultaneously covers intermediate fluid mechanics and computation. Ample examples, problems and computer exercises are provided to allow students to test their understanding of a variety of numerical methods for solving flow physics problems, including the point-vortex method, numerical methods for hydrodynamic stability analysis, spectral methods and traditional CFD topics.
The book is an introduction to the subject of fluid mechanics, essential for students and researchers in many branches of science. It illustrates its fundamental principles with a variety of examples
This advanced-level text describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow
Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-
Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-
This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical flui
Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided back
Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method,
Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method,
Motion is manifest in the atmosphere in an almost infinite variety of ways. In Dynamics in Atmospheric Physics, Dr Richard Lindzen describes the nature of motion in the atmosphere, develops fluid dynamics relevant to the atmosphere, and explores the role of motion in determining climate and atmospheric composition. The author presents the material in a lecture note style, and the emphasis throughout is on describing phenomena that are at the frontiers of current research, but due attention is given to the methodology of research and to the historical background of these topics. The author's treatment and choice of topics is didactic. Problems at the end of each chapter will help students assimilate the material. In general the discussions emphasize physical concepts, and throughout Dr Lindzen makes a concerted effort to avoid the notion that dynamic meteorology is simply the derivation of equations and their subsequent solution. His desire is that interested students will delve further
Motion is manifest in the atmosphere in an almost infinite variety of ways. In Dynamics in Atmospheric Physics, Dr Richard Lindzen describes the nature of motion in the atmosphere, develops fluid dynamics relevant to the atmosphere, and explores the role of motion in determining climate and atmospheric composition. The author presents the material in a lecture note style, and the emphasis throughout is on describing phenomena that are at the frontiers of current research, but due attention is given to the methodology of research and to the historical background of these topics. The author's treatment and choice of topics is didactic. Problems at the end of each chapter will help students assimilate the material. In general the discussions emphasize physical concepts, and throughout Dr Lindzen makes a concerted effort to avoid the notion that dynamic meteorology is simply the derivation of equations and their subsequent solution. His desire is that interested students will delve further
The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time,
The simulation of physical systems requires a simplified, hierarchical approach which models each level from the atomistic to the macroscopic scale. From quantum mechanics to fluid dynamics, this book systematically treats the broad scope of computer modeling and simulations, describing the fundamental theory behind each level of approximation. Berendsen evaluates each stage in relation to its applications giving the reader insight into the possibilities and limitations of the models. Practical guidance for applications and sample programs in Python are provided. With a strong emphasis on molecular models in chemistry and biochemistry, this 2007 book will be suitable for advanced undergraduate and graduate courses on molecular modeling and simulation within physics, biophysics, physical chemistry and materials science. It will also be a useful reference to all those working in the field. Additional resources for this title including solutions for instructors and programs are available
This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)–based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle–based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuu
Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable
This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The quantitative study of complexity is a rapidly developing subject with special impact in the fields of physics, mathematics, information science, and biology. Because of the variety of the approaches, no comprehensive discussion has previously been attempted. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular automata, stochastic processes, statistical mechanics and thermodynamics), mathematics (dynamical systems, ergodic and probability theory), information and computer science (coding, information theory and algorithmic complexity), electrical engi
The characterisation of fluid transport properties of rocks is one of the most important, yet difficult, challenges of reservoir geophysics, but is essential for optimal development of hydrocarbon and geothermal reservoirs. This book provides a quantitative introduction to the underlying physics, application, interpretation, and hazard aspects of fluid-induced seismicity with a particular focus on its spatio-temporal dynamics. It presents many real data examples of microseismic monitoring of hydraulic fracturing at hydrocarbon fields and of stimulations of enhanced geothermal systems. The author also covers introductory aspects of linear elasticity and poroelasticity theory, as well as elements of seismic rock physics and mechanics of earthquakes, enabling readers to develop a comprehensive understanding of the field. Fluid-Induced Seismicity is a valuable reference for researchers and graduate students working in the fields of geophysics, geology, geomechanics and petrophysics, and a
Mantle Dynamics provides an in-depth overview of the field of mantle dynamics in its present state. It surveys the physics and fluid dynamics of mantle convection, with theoretical, laboratory and com
