Numerical Methods for Navier-Stokes Equations, Birken, Philipp
Автор: John G. Heywood; Kyuya Masuda; Reimund Rautmann; V Название: The Navier-Stokes Equations Theory and Numerical Methods ISBN: 3540527702 ISBN-13(EAN): 9783540527701 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Contains articles on a wide variety of aspects of Navier-Stokes equations. This book surveys the subject via open problems and deals with the interplay between theory and numerical analysis.
Описание: This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures.
Автор: John G. Heywood; Kyuya Masuda; Reimund Rautmann; V Название: The Navier-Stokes Equations II - Theory and Numerical Methods ISBN: 3540562613 ISBN-13(EAN): 9783540562610 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Tani: Evolution free boundary problemfor equations of motion of viscous compressible barotropicliquid.- W. Miyakawa:On some coerciveestimates for the Stokes problem in unbounded domains.- R. v.Wahl:Decomposition of solenoidal fields into poloidal fields,toroidal fields and the mean flow.
Описание: Presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. This book discusses the conditions required to satisfy the no-slip boundary conditions in the various formulations. For each formulation, it provides a statement of the mathematical problem.
Описание: The numerical treatment of the evolutionary incompressible Navier-Stokes equations, which determine many practicaIly relevant fluid flows, is an area of considerable interest for industrial as weIl as scientific applications. Im- portant for drawing furt her conclusions for the behavior of certain flows in diverse disciplines such as (astro-)physics, engineering, meteorology, oceanog- raphy, or biology is a reliable, robust and efficient numerical model. The goal of computing highly complex flows requires the development of sophisticated algorithms. In general, numerical schemes which do not cause high computa- tional cost, often suffer from stability or reliability problems and vice versa. So, it demands a numerical and physical a-priori knowledge from the user in order to select the "best fitting algorithm" for a particular problem under consideration. The use of knowledge about physical phenomena appearing in a specific problem aIlows the relaxation of some robustness-conditions that otherwise need to be imposed on the numerical scheme in order to ensure reliability with respect to the convergence behavior. To this end, this leads to permittance of numerical models simulating continuous flows which do not satisfy severe stability restrictions that lead to robust schemes, with the advantage of lower computational costs necessary to obtain the same accu- racy. A major part of this book is devoted to such schemes that are of great importance: classical projection methods 01 high er order and nonstationary quasi-compressibility methods.
Описание: The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics.
In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen- sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob- lems although the time-dependent problems are of fundamental importance.
This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view.
Also, we have neither discussed the implemen- tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Описание: In structure mechanics analysis, finite element methods are now well estab- lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap- proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require- ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977. (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients, l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Автор: Ad?lia Sequeira Название: Navier—Stokes Equations and Related Nonlinear Problems ISBN: 148991417X ISBN-13(EAN): 9781489914170 Издательство: Springer Рейтинг: Цена: 22203.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. In addition to the editor, the organizers were Carlos Albuquerque (FC, University of Lisbon), Casimiro Silva (University of Madeira) and Juha Videman (1ST, Technical University of Lisbon).
Описание: This is the second of four volumes on the Navier-Stokes equations, specifically on Nonlinear Stationary Problems. The work is an up-to-date and detailed investigation of these problems for motions in domains of different types: bounded, exterior and domain with noncompact boundaries.
Автор: Stenger Название: Navier–Stokes Equations on R3 ? [0, T] ISBN: 3319275240 ISBN-13(EAN): 9783319275246 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this monograph, leading researchers in the world ofnumerical analysis, partial differential equations, and hard computationalproblems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z,t) ? ?3 ? [0, T]. Initially converting the PDE to asystem of integral equations, the authors then describe spaces A of analytic functions that housesolutions of this equation, and show that these spaces of analytic functionsare dense in the spaces S of rapidlydecreasing and infinitely differentiable functions. This method benefits fromthe following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error boundsFollowing the proofs of denseness, the authors prove theexistence of a solution of the integral equations in the space of functions A ? ?3 ? [0, T], and provide an explicit novelalgorithm based on Sinc approximation and Picard–like iteration for computingthe solution. Additionally, the authors include appendices that provide acustom Mathematica program for computing solutions based on the explicitalgorithmic approximation procedure, and which supply explicit illustrations ofthese computed solutions.
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