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Mathematical Approaches In Hydrodynamics
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Book Synopsis Mathematical Approaches in Hydrodynamics by : Touvia Miloh
Download or read book Mathematical Approaches in Hydrodynamics written by Touvia Miloh and published by SIAM. This book was released on 1991-01-01 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: To honor Professor Marshall P. Tulin on his 65th birthday (March 14, 1991), fluid mechanicians and applied mathematicians who have had close association and collaborated with Tulin during his career contribute papers in various areas related to his main interest naval hydrodynamics. No index. Annota
Book Synopsis Mathematical Methods for Hydrodynamic Limits by : Anna DeMasi
Download or read book Mathematical Methods for Hydrodynamic Limits written by Anna DeMasi and published by Springer. This book was released on 2006-11-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.
Book Synopsis Topological Methods in Hydrodynamics by : Vladimir I. Arnold
Download or read book Topological Methods in Hydrodynamics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Book Synopsis Applications of Group-Theoretical Methods in Hydrodynamics by : V.K. Andreev
Download or read book Applications of Group-Theoretical Methods in Hydrodynamics written by V.K. Andreev and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in variant and partially invariant solutions to the equations of hydrodynamics.
Book Synopsis Mathematical Methods in Fluid Dynamics by : Miloslav Feistauer
Download or read book Mathematical Methods in Fluid Dynamics written by Miloslav Feistauer and published by Chapman and Hall/CRC. This book was released on 1993-07-05 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the "Pitman Monographs and Surveys in Pure and Applied Mathematics" series, this text examines mathematical methods in fluid dynamics.
Book Synopsis Numerical Methods for Fluid Dynamics by : Dale R. Durran
Download or read book Numerical Methods for Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
Author :Division on Engineering and Physical Sciences Publisher :National Academies Press ISBN 13 :0309053838 Total Pages :304 pages Book Rating :4.3/5 (9 download)
Book Synopsis Simulated Voyages by : Division on Engineering and Physical Sciences
Download or read book Simulated Voyages written by Division on Engineering and Physical Sciences and published by National Academies Press. This book was released on 1996-04-21 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book assesses the state of practice and use of ship-bridge simulators in the professional development and licensing of deck officers and marine pilots. It focuses on full-mission computer-based simulators and manned models. It analyzes their use in instruction, evaluation and licensing and gives information and practical guidance on the establishment of training and licensing program standards, and on simulator and simulation validation.
Book Synopsis Mathematical Methods in Fluid Dynamics by : M. Feistauer
Download or read book Mathematical Methods in Fluid Dynamics written by M. Feistauer and published by Halsted Press. This book was released on 1993-08-01 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Fluid Dynamics by : Dia Zeidan
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.
Book Synopsis Nontraditional methods in mathematical hydrodynamics by : O. V. Troshkin
Download or read book Nontraditional methods in mathematical hydrodynamics written by O. V. Troshkin and published by American Mathematical Soc.. This book was released on 1995-03-16 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary Navier-Stokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair one-point velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.
Book Synopsis Spectral/hp Element Methods for Computational Fluid Dynamics by : George Karniadakis
Download or read book Spectral/hp Element Methods for Computational Fluid Dynamics written by George Karniadakis and published by OUP Oxford. This book was released on 2005-06-02 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretisation procedures on unstructured meshes, which are also recognised as more efficient for solution of time-dependent oscillatory solutions over long time periods. Here Karniadakis and Sherwin present a much-updated and expanded version of their successful first edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application, and is aimed at students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.
Book Synopsis Fundamentals of Geophysical Hydrodynamics by : Felix V. Dolzhansky
Download or read book Fundamentals of Geophysical Hydrodynamics written by Felix V. Dolzhansky and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold's approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation. This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author's highly acclaimed work in Moscow's Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.
Book Synopsis Challenges in Fluid Dynamics by : R.Kh. Zeytounian
Download or read book Challenges in Fluid Dynamics written by R.Kh. Zeytounian and published by Springer. This book was released on 2017-12-21 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field. The interested reader will also benefit from the general historical context in which the material is presented in the book. The book covers a wide range of relevant topics of the field, and the main tool being rational asymptotic modelling (RAM) approach. The target audience primarily comprises experts in the field of fluid dynamics, but the book may also be beneficial for graduate students.
Book Synopsis Introduction to Hydrodynamic Stability by : P. G. Drazin
Download or read book Introduction to Hydrodynamic Stability written by P. G. Drazin and published by Cambridge University Press. This book was released on 2002-09-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Author :Constantine Pozrikidis Publisher :Springer Science & Business Media ISBN 13 :0387958711 Total Pages :791 pages Book Rating :4.3/5 (879 download)
Book Synopsis Fluid Dynamics by : Constantine Pozrikidis
Download or read book Fluid Dynamics written by Constantine Pozrikidis and published by Springer Science & Business Media. This book was released on 2009-06-16 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ready access to computers has de?ned a new era in teaching and learning. The opportunity to extend the subject matter of traditional science and engineering curricula into the realm of scienti?c computing has become not only desirable, but also necessary. Thanks to portability and low overhead and operating cost, experimentation by numerical simulation has become a viable substitute, and occasionally the only alternative, to physical experimentation. The new framework has necessitated the writing of texts and monographs from a modern perspective that incorporates numerical and computer progr- ming aspects as an integral part of the discourse. Under this modern directive, methods, concepts, and ideas are presented in a uni?ed fashion that motivates and underlines the urgency of the new elements, but neither compromises nor oversimpli?es the rigor of the classical approach. Interfacing fundamental concepts and practical methods of scienti?c c- puting can be implemented on di?erent levels. In one approach, theory and implementation are kept complementary and presented in a sequential fashion. In another approach, the coupling involves deriving computational methods and simulation algorithms, and translating equations into computer code - structions immediately following problem formulations. Seamlessly interjecting methods of scienti?c computing in the traditional discourse o?ers a powerful venue for developing analytical skills and obtaining physical insight.
Book Synopsis Mathematical Fluid Mechanics by : B. Mahanthesh
Download or read book Mathematical Fluid Mechanics written by B. Mahanthesh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-06-08 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to include various significant research topics of mathematical fluid mechanics having relevance or applications in engineering and applied sciences, covering the tools and techniques used for developing mathematical methods and modelling related to real-life situations.
Book Synopsis Operator Approach to Linear Problems of Hydrodynamics by : Nikolay D. Kopachevskii
Download or read book Operator Approach to Linear Problems of Hydrodynamics written by Nikolay D. Kopachevskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume "Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems" by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30-40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.
