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Author: Martin Stynes Publisher: ISBN: 9781470450212 Category : MATHEMATICS Languages : en Pages :
Book Description
Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.
Author: Martin Stynes Publisher: ISBN: 9781470450212 Category : MATHEMATICS Languages : en Pages :
Book Description
Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.
Author: Willem Hundsdorfer Publisher: Springer Science & Business Media ISBN: 3662090171 Category : Technology & Engineering Languages : en Pages : 479
Book Description
Unique book on Reaction-Advection-Diffusion problems
Author: Hans-Görg Roos Publisher: Springer Science & Business Media ISBN: 3540344675 Category : Mathematics Languages : en Pages : 599
Book Description
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Author: John J H Miller Publisher: World Scientific ISBN: 9814452777 Category : Mathematics Languages : en Pages : 191
Book Description
Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Author: Hans Petter Langtangen Publisher: Springer ISBN: 3319554565 Category : Computers Languages : en Pages : 522
Book Description
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Author: John Crank Publisher: Oxford University Press ISBN: 9780198534112 Category : Mathematics Languages : en Pages : 428
Book Description
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author: D. Srinivasacharya Publisher: Springer ISBN: 9811319030 Category : Technology & Engineering Languages : en Pages : 638
Book Description
This book comprises selected papers from the International Conference on Numerical Heat Transfer and Fluid Flow (NHTFF 2018), and presents the latest developments in computational methods in heat and mass transfer. It also discusses numerical methods such as finite element, finite difference, and finite volume applied to fluid flow problems. Providing a good balance between computational methods and analytical results applied to a wide variety of problems in heat transfer, transport and fluid mechanics, the book is a valuable resource for students and researchers working in the field of heat transfer and fluid dynamics.
Author: Ronald E Mickens Publisher: World Scientific ISBN: 981122255X Category : Mathematics Languages : en Pages : 332
Book Description
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Author: Zhen Mei Publisher: Springer Science & Business Media ISBN: 3662041774 Category : Mathematics Languages : en Pages : 422
Book Description
This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.
Author: Maurizio Bottoni Publisher: Springer Nature ISBN: 3030797171 Category : Technology & Engineering Languages : en Pages : 541
Book Description
This book on computational techniques for thermal and fluid-dynamic problems arose from seminars given by the author at the Institute of Nuclear Energy Technology of Tsinghua University in Beijing, China. The book is composed of eight chapters-- some of which are characterized by a scholastic approach, others are devoted to numerical solution of ordinary differential equations of first order, and of partial differential equations of first and second order, respectively. In Chapter IV, basic concepts of consistency, stability and convergence of discretization algorithms are covered in some detail. Other parts of the book follow a less conventional approach, mainly informed by the author’s experience in teaching and development of computer programs. Among these is Chapter III, where the residual method of Orthogonal Collocations is presented in several variants, ranging from the classical Galerkin method to Point and Domain Collocations, applied to numerical solution of partial differential equations of first order. In most cases solutions of fluid dynamic problems are led through the discretization process, to the numerical solutions of large linear systems. Intended to impart a basic understanding of numerical techniques that would enable readers to deal with problems of Computational Fluid Dynamics at research level, the book is ideal as a reference for graduate students, researchers, and practitioners.
Author: Martin Stynes
Author: Martin Stynes
Author: Willem Hundsdorfer
Author: Hans-Görg Roos
Author: John J H Miller
Author: Hans Petter Langtangen
Author: John Crank
Author: D. Srinivasacharya
Author: Ronald E Mickens
Author: Zhen Mei
Author: Maurizio Bottoni