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 explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Finite Element Methods for Viscous Incompressible Flows examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.
This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?
Heat transfer is the area of engineering science which describes the energy transport between material bodies due to a difference in temperature. The three different modes of heat transport are conduction, convection and radiation. In most problems, these three modes exist simultaneously. However, the significance of these modes depends on the problems studied and often, insignificant modes are neglected. Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions. Problems with slow fluid motion and heat transfer can be difficult problems to handle. Therefore, the complexity of combined fluid flow and heat transfer problems should not be underestimated and should be dealt with carefully. This book: Is ideal for teaching senior undergraduates the fundamentals of how to use the Finite Element Method to solve heat transfer and fluid dynamics problems Explains how to solve various heat transfer problems with different types of boundary conditions Uses recent computational methods and codes to handle complex fluid motion and heat transfer problems Includes a large number of examples and exercises on heat transfer problems In an era of parallel computing, computational efficiency and easy to handle codes play a major part. Bearing all these points in mind, the topics covered on combined flow and heat transfer in this book will be an asset for practising engineers and postgraduate students. Other topics of interest for the heat transfer community, such as heat exchangers and radiation heat transfer, are also included.
This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. Several sections derive the Fluid Dynamics equations from first thermo-mechanics principles and develop this multi-dimensional and infinite-directional upstream procedure by combining a finite element discretization with an implicit non-linearly stable Runge-Kutta time integration for the numerical solution of the Euler and Navier Stokes equations.
This book is a follow-up to the introductory text written by the same authors. The primary emphasis on this book is linear and nonlinear partial differential equations with particular concentration on the equations of viscous fluid motion. Each chapter describes a particular application of the finite element method and illustrates the concepts through example problems. A comprehensive appendix lists computer codes for 2-D fluid flow and two 3-D transient codes.
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.
Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
