Download or read book Contributions to Current Challenges in Mathematical Fluid Mechanics written by Giovanni P. Galdi and published by Birkhäuser. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct

Download or read book Recent Developments of Mathematical Fluid Mechanics written by Herbert Amann and published by Birkhäuser. This book was released on 2016-03-17 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

Download or read book Mathematical Fluid Dynamics Present and Future written by Yoshihiro Shibata and published by Springer. This book was released on 2016-12-01 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

Download or read book Progress in Mathematical Fluid Dynamics written by Tristan Buckmaster and published by Springer Nature. This book was released on 2020-09-28 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together four contributions to mathematical fluid mechanics, a classical but still highly active research field. The contributions cover not only the classical Navier-Stokes equations and Euler equations, but also some simplified models, and fluids interacting with elastic walls. The questions addressed in the lectures range from the basic problems of existence/blow-up of weak and more regular solutions, to modeling and aspects related to numerical methods. This book covers recent advances in several important areas of fluid mechanics. An output of the CIME Summer School "Progress in mathematical fluid mechanics" held in Cetraro in 2019, it offers a collection of lecture notes prepared by T. Buckmaster, (Princeton), S. Canic (UCB) P. Constantin (Princeton) and A. Kiselev (Duke). These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics.

Download or read book Advances in Mathematical Fluid Mechanics written by Rolf Rannacher and published by Springer Science & Business Media. This book was released on 2010-03-17 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the ?eld of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, re?ecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 21–25, 2007 and organized on the oc- sion of Professor Galdi’s 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian ?ow problems, with special emphasis on hydrodynamic stability and ?uid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down signi?cant milestones in these ?elds, with a great in?uence on interdis- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through int- lectual guidance and others indirectly by pairing them with well chosen senior c- laborators. A brief review of Professor Galdi’s activities and some impressions by colleagues and friends are included here.

Download or read book Mathematical Topics in Fluid Mechanics written by Jose Francisco Rodrigues and published by CRC Press. This book was released on 2020-10-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

Download or read book Fundamental Trends in Fluid structure Interaction written by Giovanni Paolo Galdi and published by World Scientific. This book was released on 2010 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction of a fluid with a solid body is a widespread phenomenon in nature, occurring at different scales and different applied disciplines. Interestingly enough, even though the mathematical theory of the motion of bodies in a liquid is one of the oldest and most classical problems in fluid mechanics, mathematicians have, only very recently, become interested in a systematic study of the basic problems related to fluid-structure interaction, from both analytical and numerical viewpoints. Fundamental Trends in Fluid-Structure Interaction is a unique collection of important papers written by world-renowned experts aimed at furnishing the highest level of development in several significant areas of fluid-structure interactions. The contributions cover several aspects of this discipline, from mathematical analysis, numerical simulation and modeling viewpoints, including motion of rigid and elastic bodies in a viscous liquid, particulate flow and hemodynamic.

Download or read book Advances in Fluid Mechanics written by Dia Zeidan and published by Springer Nature. This book was released on 2022-06-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book provides invited and reviewed contributions in mathematical, physical and experimental modelling and simulations in all fluid mechanics branches. Contributions explore the emerging and state-of-the-art tools in the field authored by well-established researchers to derive improved performance of modelling and simulations. Serving the multidisciplinary fluid mechanics community, this book aims to publish new research work that enhances the prediction and understanding of fluid mechanics and balances from academic theory to practical applications through modelling, numerical studies, algorithms and simulation. The book offers researchers, students and practitioners significant insights on modelling and simulations in fluid mechanics. It offers readers a range of academic contributions on fluid mechanics by researchers that have become leaders in their field. The research work presented in this book will add values to the existing literature in terms of what needs to be done better to direct modelling and simulations towards a growing and rapidly developing field.

Download or read book Recent Developments in Theoretical Fluid Mechanics written by G.P.. NECAS GALDI (J.) and published by CRC Press. This book was released on 2020-06-30 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics. The five papers appearing in this volume are centred around the mathematical theory of the Navier-Stokes equations (incompressible and compressible) and certain selected non-Newtonian modifications.

Download or read book Mathematical Fluid Mechanics written by Jiri Neustupa and published by Springer Science & Business Media. This book was released on 2001-08-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Five Decades of Tackling Models for Stiff Fluid Dynamics Problems written by Radyadour Kh. Zeytounian and published by Springer Science & Business Media. This book was released on 2013-12-03 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics.

Download or read book Mathematical Theory of Compressible Viscous Fluids written by Eduard Feireisl and published by Birkhäuser. This book was released on 2016-11-25 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book New Directions in Mathematical Fluid Mechanics written by Andrei V. Fursikov and published by Springer Science & Business Media. This book was released on 2010-01-11 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 3, 2005, Alexander Vasil’evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov’s contributions to science is provided in the following article “Scienti?c portrait of Alexander Vasil’evich Kazhikhov”. This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.

Download or read book Sir James Lighthill and Modern Fluid Mechanics written by Lokenath Debnath and published by World Scientific. This book was released on 2008 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is perhaps the first book containing biographical information of Sir James Lighthill and his major scientific contributions to the different areas of fluid mechanics, applied mathematics, aerodynamics, linear and nonlinear waves in fluids, geophysical fluid dynamics, biofluiddynamics, aeroelasticity, boundary layer theory, generalized functions, and Fourier series and integrals. Special efforts is made to present Lighthill's scientific work in a simple and concise manner, and generally intelligible to readers who have some introduction to fluid mechanics. The book also includes a list of Lighthill's significant papers.Written for the mathematically literate reader, this book also provides a glimpse of Sir James' serious attempt to stimulate interest in mathematics and its diverse applications among the general public of the world, his profound influence on teaching of mathematics and science with newer applications, and his deep and enduring concern on enormous loss of human lives, economic and marine resources by natural hazards. By providing detailed background information and knowledge, sufficient to start interdisciplinary research, it is intended to serve as a ready reference guide for readers interested in advanced study and research in modern fluid mechanics.

Download or read book Numerical Methods for Flows written by Harald van Brummelen and published by Springer Nature. This book was released on 2020-02-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

Download or read book Numerical Fluid Dynamics written by Dia Zeidan and published by Springer Nature. This book was released on 2022-05-18 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains select invited chapters on the latest research in numerical fluid dynamics and applications. The book aims at discussing the state-of-the-art developments and improvements in numerical fluid dynamics. All the chapters are presented for approximating and simulating how these methods and computations interact with different topics such as shock waves, non-equilibrium single and two-phase flows, elastic human-airway, and global climate. In addition to the fundamental research involving novel types of mathematical sciences, the book presents theoretical and numerical developments in fluid dynamics. The contributions by well-established global experts in fluid dynamics have brought different features of numerical fluid dynamics in a single book. The book serves as a useful resource for high-impact advances involving computational fluid dynamics, including recent developments in mathematical modelling, numerical methods such as finite volume, finite difference and finite element, symbolic computations, and open numerical programs such as OpenFOAM software. The book addresses interdisciplinary topics in industrial mathematics that lie at the forefront of research into new types of mathematical sciences, including theory and applications. This book will be beneficial to industrial and academic researchers, as well as graduate students, working in the fields of natural and engineering sciences. The book will provide the reader highly successful materials and necessary research in the field of fluid dynamics.

Download or read book Topics in Mathematical Fluid Mechanics written by Peter Constantin and published by Springer. This book was released on 2013-04-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.