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Recent Developments of Mathematical Fluid Mechanics

Recent Developments of Mathematical Fluid Mechanics
Author: Herbert Amann
Publisher: Birkhäuser
Total Pages: 478
Release: 2016-03-17
Genre: Mathematics
ISBN: 3034809395

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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.


Recent Developments in Theoretical Fluid Mechanics

Recent Developments in Theoretical Fluid Mechanics
Author: G P Galdi
Publisher: CRC Press
Total Pages: 182
Release: 1993-08-23
Genre: Mathematics
ISBN: 9780582226845

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Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics.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.


A Mathematical Introduction to Fluid Mechanics

A Mathematical Introduction to Fluid Mechanics
Author: A. J. Chorin
Publisher: Springer Science & Business Media
Total Pages: 213
Release: 2012-12-06
Genre: Science
ISBN: 1468400827

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These notes are based on a one-quarter (i. e. very short) course in fluid mechanics taught in the Department of Mathematics of the University of California, Berkeley during the Spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima tion procedures. The goals were: (i) to present some of the basic ideas of fluid mechanics in a mathematically attractive manner (which does not mean "fully rigorous"); (ii) to present the physical back ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; (iil. ) 'to interest some of the students in this beautiful and difficult subject. The notes are divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented; it is hoped that it helps to clarify the ideas. The third chapter contains an analysis of one-dimensional gas iv flow, from a mildly modern point of view. Weak solutions, Riemann problems, Glimm's scheme, and combustion waves are discussed. The style is informal and no attempt was made to hide the authors' biases and interests.


Mathematical Fluid Mechanics

Mathematical Fluid Mechanics
Author: Jiri Neustupa
Publisher: Birkhäuser
Total Pages: 271
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034882432

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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.


Introduction to Mathematical Fluid Dynamics

Introduction to Mathematical Fluid Dynamics
Author: Richard E. Meyer
Publisher: Courier Corporation
Total Pages: 194
Release: 2012-03-08
Genre: Science
ISBN: 0486138941

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Geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences, this introductory text covers kinematics, momentum principle, Newtonian fluid, compressibility, and other subjects. 1971 edition.


Mathematical Methods in Engineering

Mathematical Methods in Engineering
Author: Nuno Miguel Fonseca Ferreira
Publisher: Springer
Total Pages: 311
Release: 2014-08-18
Genre: Technology & Engineering
ISBN: 9400771835

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This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.


Numerical Fluid Dynamics

Numerical Fluid Dynamics
Author: Dia Zeidan
Publisher: Springer Nature
Total Pages: 323
Release: 2022-05-18
Genre: Technology & Engineering
ISBN: 9811696659

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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.


Progress in Mathematical Fluid Dynamics

Progress in Mathematical Fluid Dynamics
Author: Tristan Buckmaster
Publisher: Springer Nature
Total Pages: 169
Release: 2020-09-28
Genre: Mathematics
ISBN: 3030548996

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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.


Recent Trends in Applied Mathematics

Recent Trends in Applied Mathematics
Author: S. R. Mishra
Publisher: Springer Nature
Total Pages: 460
Release: 2021-03-01
Genre: Technology & Engineering
ISBN: 9811598177

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This book presents select proceedings of the International Conference on Applied Mathematics in Science and Engineering (AMSE 2019). Various topics covered include computational fluid dynamics, applications of differential equations in engineering, numerical methods for ODEs and PDEs, mathematical modeling and analysis of biological systems, optimal control and controllability of differential equations, fractional calculus and its applications, nonlinear analysis, and functional analysis. This book will be of interest to researchers, academicians and students in the fields of applied sciences, mathematics and engineering.


Recent Advances in Computational Fluid Dynamics

Recent Advances in Computational Fluid Dynamics
Author: C.C. Chao
Publisher: Springer
Total Pages: 0
Release: 1989-05-26
Genre: Science
ISBN: 9783540508724

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From the preface: Fluid dynamics is an excellent example of how recent advances in computational tools and techniques permit the rapid advance of basic and applied science. The development of computational fluid dynamics (CFD) has opened new areas of research and has significantly supplemented information available from experimental measurements. Scientific computing is directly responsible for such recent developments as the secondary instability theory of transition to turbulence, dynamical systems analyses of routes to chaos, ideas on the geometry of turbulence, direct simulations of turbulence, three-dimensional full-aircraft flow analyses, and so on. We believe that CFD has already achieved a status in the tool-kit of fluid mechanicians equal to that of the classical scientific techniques of mathematical analysis and laboratory experiment.