Numerical Analysis Of Compressible Fluid Flows
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| Author | : Eduard Feireisl |
| Publisher | : Springer Nature |
| Total Pages | : 530 |
| Release | : 2022-01-01 |
| Genre | : Mathematics |
| ISBN | : 3030737888 |
This book is devoted to the numerical analysis of compressible fluids in the spirit of the celebrated Lax equivalence theorem. The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists. The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions). The concept of a weak-strong uniqueness principle in the class of generalized solutions is used to prove the convergence of various numerical methods. The problem of oscillatory solutions is solved by an original adaptation of the method of K-convergence. An effective method of computing the Young measures is presented. Theoretical results are illustrated by a series of numerical experiments. Applications of these concepts are to be expected in other problems of fluid mechanics and related fields.
| Author | : William Layton |
| Publisher | : SIAM |
| Total Pages | : 220 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898718902 |
Introduction to the Numerical Analysis of Incompressible Viscous Flows treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. This book provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester. Audience: this unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations.
| Author | : Eduard Feireisl |
| Publisher | : Birkhäuser |
| Total Pages | : 189 |
| Release | : 2016-11-25 |
| Genre | : Mathematics |
| ISBN | : 3319448358 |
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.
| Author | : Philipp Birken |
| Publisher | : Chapman & Hall/CRC |
| Total Pages | : 234 |
| Release | : 2021 |
| Genre | : Mathematics |
| ISBN | : 9781003025214 |
Numerical Methods for Unsteady Compressible Flow Problems is written to give both mathematicians and engineers an overview of the state of the art in the field, as well as of new developments. The focus is on methods for the compressible Navier-Stokes equations, the solutions of which can exhibit shocks, boundary layers and turbulence. The idea of the text is to explain the important ideas to the reader, while giving enough detail and pointers to literature to facilitate implementation of methods and application of concepts. The book covers high order methods in space, such as Discontinuous Galerkin methods, and high order methods in time, in particular implicit ones. A large part of the text is reserved to discuss iterative methods for the arising large nonlinear and linear equation systems. Ample space is given to both state-of-the-art multigrid and preconditioned Newton-Krylov schemes. Features Applications to aerospace, high-speed vehicles, heat transfer, and more besides Suitable as a textbook for graduate-level courses in CFD, or as a reference for practitioners in the field
| Author | : Miloslav Feistauer |
| Publisher | : Oxford University Press |
| Total Pages | : 560 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780198505884 |
This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.
| Author | : Eleuterio F. Toro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 635 |
| Release | : 2013-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 366203915X |
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.
| Author | : Sven Gross |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2011-04-26 |
| Genre | : Mathematics |
| ISBN | : 3642196861 |
This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.
| Author | : Roger Peyret |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 364 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642859526 |
In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.
| Author | : Jiri Neustupa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2001-08-01 |
| Genre | : Mathematics |
| ISBN | : 9783764365936 |
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
| Author | : Francesca di Mare |
| Publisher | : Springer Nature |
| Total Pages | : 125 |
| Release | : 2020-07-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3030496260 |
This book reports on advanced theories and methods aimed at characterizing the dynamics of non-ideal compressible fluids. A special emphasis is given to research fostering the use of non-ideal compressible fluids for propulsion and power engineering. Both numerical and experimental studies, as well as simulations, are described in the book, which is based on selected contributions and keynote lectures presented at the 2nd International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power. Held on October 4-5 in Bochum, Germany, the seminar aimed at fostering collaborations between academics and professionals. The two perspectives have been gathered together in this book, which offers a timely guide to advanced fundamentals, innovative methods and current applications of non-ideal compressible fluids to developing turbomachines, and for propulsion and power generation.
