Download Free Convection Diffusion Problems Book in PDF and EPUB Free Download. You can read online Convection Diffusion Problems and write the review.

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.
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 class of problems. At first they examine finite-difference methods for two-point boundary value problems, as their analysis requires little theoretical background. Upwinding, artificial diffusion, uniformly convergent methods, and Shishkin meshes are some of the topics presented. Throughout, the authors are concerned with the accuracy of solutions when the diffusion coefficient is close to zero. Later in the book they concentrate on finite element methods for problems posed in one and two dimensions. This lucid yet thorough account of convection-dominated convection-diffusion problems and how to solve them numerically is meant for beginning graduate students, and it includes a large number of exercises. An up-to-date bibliography provides the reader with further reading.
Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.
This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
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.
Accurate modeling of the interaction between convective and diffusive processes is one of the most common challenges in the numerical approximation of partial differential equations. This is partly due to the fact that numerical algorithms, and the techniques used for their analysis, tend to be very different in the two limiting cases of elliptic and hyperbolic equations. Many different ideas and approaches have been proposed in widely differing contexts to resolve the difficulties of exponential fitting, compact differencing, number upwinding, artificial viscosity, streamline diffusion, Petrov-Galerkin and evolution Galerkin being some examples from the main fields of finite difference and finite element methods. The main aim of this volume is to draw together all these ideas and see how they overlap and differ. The reader is provided with a useful and wide ranging source of algorithmic concepts and techniques of analysis. The material presented has been drawn both from theoretically oriented literature on finite differences, finite volume and finite element methods and also from accounts of practical, large-scale computing, particularly in the field of computational fluid dynamics.
Unique book on Reaction-Advection-Diffusion problems
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
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.