Compressible Navier Stokes Equations

Author : Pavel Plotnikov,Jan Sokołowski
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 48,5 Mb
Release : 2012-08-04
Category : Mathematics
ISBN : 9783034803670

Get Book

Compressible Navier-Stokes Equations by Pavel Plotnikov,Jan Sokołowski Pdf

The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Author : A. Novotný,Raphaël Danchin,Misha Perepelitsa
Publisher : Unknown
Page : 0 pages
File Size : 52,7 Mb
Release : 2016
Category : Navier-Stokes equations
ISBN : 2856298478

Get Book

Topics on Compressible Navier-Stokes Equations by A. Novotný,Raphaël Danchin,Misha Perepelitsa Pdf

This issue includes contributions from the session Etats de la Recherche: Topics on Compressible Navier-Stokes Equations that was held from May 21-25, 2012 at the Laboratoire de Mathematiques in Le Bourget du Lac, France. This national training session provided the opportunity to gather four internationally renowned specialists (D. Bresch, A. Novotny, R. Danchin, and M. Perepetlisa) and allow them to present the major actual mathematical developments related to the well-posedness character problem for the compressible Navier-Stokes equations to non-subject specialists. For the sake of unity, this special issue includes only the contributions dedicated to the non-degenerate viscosities case, aiming to present a self-contained contribution on the subject: global weak-solutions a la Leray, intermediate solutions a la Hoff and strong solutions in critical spaces a la Fujita-Kato.

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642597213

Get Book

Discontinuous Galerkin Methods by Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu Pdf

A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Author : Marie Odile Bristeau
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 44,6 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9783322878731

Get Book

Numerical Simulation of Compressible Navier-Stokes Flows by Marie Odile Bristeau Pdf

With the advent of super computers during the last ten years, the numerical simulation of viscous fluid flows modeled by the Navier-Stokes equations is becoming a most useful tool in Aircraft and Engine Design. In fact, compressible Navier-Stokes solvers tend to constitute the basic tools for many industrial applications occuring in the simulation of very complex turbulent and combustion phenomena. In Aerospace Engineering, as an exemple, their mathematical modelization requires reliable and robust methods for solving very stiff non linear partial differential equations. For the above reasons, it was clear that a workshop on this topic would be of interest for the CFD community in order to compare accuracy and efficiency of Navier-Stokes solvers on selected external and internal flow problems using different numerical approaches. The workshop was held on 4-6 December 1985 at Nice, France and organized by INRIA with the sponsorship of the GAMM Committee on Numerical Methods in Fluid Mechanics.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 48,8 Mb
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 9783663111719

Get Book

Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations by Anonim Pdf

Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor

Author : Antonín Novotny,Ivan Straskraba
Publisher : Oxford University Press on Demand
Page : 527 pages
File Size : 53,9 Mb
Release : 2004-06-17
Category : Mathematics
ISBN : 9780198530848

Get Book

Introduction to the Mathematical Theory of Compressible Flow by Antonín Novotny,Ivan Straskraba Pdf

These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes an index and bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow."--Jacket.

Author : Eduard Feireisl
Publisher : Oxford University Press
Page : 228 pages
File Size : 47,9 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198528388

Get Book

Dynamics of Viscous Compressible Fluids by Eduard Feireisl Pdf

This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.

Author : Heinz-Otto Kreiss,Jens Lorenz
Publisher : SIAM
Page : 408 pages
File Size : 44,8 Mb
Release : 1989-01-01
Category : Science
ISBN : 9780898719130

Get Book

Initial-boundary Value Problems and the Navier-Stokes Equations by Heinz-Otto Kreiss,Jens Lorenz Pdf

Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

Author : Anonim
Publisher : Unknown
Page : 62 pages
File Size : 43,7 Mb
Release : 1974
Category : Electronic
ISBN : NASA:31769000530439

Get Book

Numerical Solution of the Time-dependent Compressible Navier-Stokes Equations in Inlet Regions by Anonim Pdf

Author : Pierre-Louis Lions
Publisher : Oxford University Press
Page : 370 pages
File Size : 45,8 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 0198514883

Get Book

Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models by Pierre-Louis Lions Pdf

Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

Author : John Groves Heywood
Publisher : World Scientific
Page : 256 pages
File Size : 54,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9810233000

Get Book

Theory of the Navier-Stokes Equations by John Groves Heywood Pdf

This volume collects the articles presented at the Third International Conference on ?The Navier-Stokes Equations: Theory and Numerical Methods?, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.

Author : Roger Temam
Publisher : American Mathematical Society
Page : 426 pages
File Size : 45,8 Mb
Release : 2024-05-24
Category : Mathematics
ISBN : 9781470477868

Get Book

Navier–Stokes Equations by Roger Temam Pdf

Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.

Author : Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Publisher : Birkhäuser
Page : 186 pages
File Size : 48,7 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9783319448350

Get Book

Mathematical Theory of Compressible Viscous Fluids by Eduard Feireisl,Trygve G. Karper,Milan Pokorný Pdf

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 : Josef Malek,Jindrich Necas,Mirko Rokyta
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642573088

Get Book

Advances in Mathematical Fluid Mechanics by Josef Malek,Jindrich Necas,Mirko Rokyta Pdf

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Author : Alvin Bayliss,Institute for Computer Applications in Science and Engineering
Publisher : Unknown
Page : 32 pages
File Size : 46,9 Mb
Release : 1985
Category : Electronic
ISBN : NASA:31769000673874

Get Book

A Fourth-order Scheme for the Unsteady Compressible Navier-Stokes Equations by Alvin Bayliss,Institute for Computer Applications in Science and Engineering Pdf