Download or read book Quadratic Finite Element Method for 1D Deterministic Transport written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract not provided.
Download or read book Quadratic Finite Element Method for 1D Deterministic Neutron Transport written by J. M. Ferguson and published by . This book was released on 2004 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic Finite Element Method for 1D Deterministic Transport written by J. M. Ferguson and published by . This book was released on 2004 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r}, {und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r}, {und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
Download or read book Finite Element Methods for Particle Transport written by Ron Tunstall Ackroyd and published by Taylor & Francis Group. This book was released on 1997 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the transport of neutral particles, neutrons and photons, using the finite element method to address practical problems in nuclear power and mineral prospecting. Includes discussions of how the method began and has matured to become a practical tool complementing the stochastic Monte Carlo method, spatial finite elements, examples of calculations, equivalent forms of the Boltzmann equation, neutron streaming in voids, some aspects of discontinuous variational solutions, complementary principles and benchmarking, time-dependent transport, and modelling three-dimensional systems. Double spaced. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Computational Methods in Transport written by Frank Graziani and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
Download or read book Finite Element Modeling Of Multiscale Transport Phenomena written by Vahid Nassehi and published by World Scientific Publishing Company. This book was released on 2010-10-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex multiscale systems such as combined free or porous flow regimes and transport processes governed by combined diffusion, convection and reaction mechanisms, which cannot be readily modeled using traditional methods, can be solved by multiscale or stabilized finite element schemes.Due to the importance of the described multiscale processes in applications such as separation processes, reaction engineering and environmental systems analysis, a sound knowledge of such methods is essential for many researchers and design engineers who wish to develop reliable solutions for industrially relevant problems. The main scope of this book is to provide an authoritative description of recent developments in the field of finite element analysis, with a particular emphasis on the multiscale finite element modeling of transport phenomena and flow problem./a
Download or read book Development of a Quadratic Finite Element Solution of the Convective transport Equation written by David A. Dillard and published by . This book was released on 1978 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Method written by Gouri Dhatt and published by John Wiley & Sons. This book was released on 2012-12-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.
Download or read book The Finite Element Method written by Darrell W. Pepper and published by Taylor & Francis. This book was released on 2005-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This much-anticipated second edition introduces the fundamentals of the finite element method featuring clear-cut examples and an applications-oriented approach. Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications, including structural analysis and fluid flow. Much attention is given to the development of the discrete set of algebraic equations, beginning with simple one-dimensional problems that can be solved by inspection, continuing to two- and three-dimensional elements, and ending with three chapters describing applications. The increased number of example problems per chapter helps build an understanding of the method to define and organize required initial and boundary condition data for specific problems. In addition to exercises that can be worked out manually, this new edition refers to user-friendly computer codes for solving one-, two-, and three-dimensional problems. Among the first FEM textbooks to include finite element software, the book contains a website with access to an even more comprehensive list of finite element software written in FEMLAB, MAPLE, MathCad, MATLAB, FORTRAN, C++, and JAVA - the most popular programming languages. This textbook is valuable for senior level undergraduates in mechanical, aeronautical, electrical, chemical, and civil engineering. Useful for short courses and home-study learning, the book can also serve as an introduction for first-year graduate students new to finite element coursework and as a refresher for industry professionals. The book is a perfect lead-in to Intermediate Finite Element Method: Fluid Flow and Heat and Transfer Applications (Taylor & Francis, 1999, Hb 1560323094).
Download or read book Transactions of the American Nuclear Society written by American Nuclear Society and published by . This book was released on 1958 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Finite Element Method Theory Implementation and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Download or read book Finite element Method written by Pin Tong and published by MIT Press (MA). This book was released on 1977 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Method written by Sinan Muftu and published by Elsevier. This book was released on 2022-07-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Method: Physics and Solution Methods enables the reader to develop a sound understanding of physical systems so that they can get the most out of their use of the finite element method. Nearly all physical systems in the FEM realm are represented by partial differential equations. This book focuses on 1D and 2D elasticity, and 1D and 2D heat transfer problems, with a detailed derivation of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. After a chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing PDE is defined over a sub-segment (element) of the solution domain. As well as being an invaluable guide to thorough and effective use of the finite element method, this book also functions as an authoritative reference on theory of elasticity, heat transfer and mechanics of beams and plates.
Download or read book Continuously Deforming Finite Element Methods for Transport Problems written by Alan Craig Mueller and published by . This book was released on 1983 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Finite Element Method written by Darrell W. Pepper and published by CRC Press. This book was released on 2017-04-11 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-explanatory guide introduces the basic fundamentals of the Finite Element Method in a clear manner using comprehensive examples. Beginning with the concept of one-dimensional heat transfer, the first chapters include one-dimensional problems that can be solved by inspection. The book progresses through more detailed two-dimensional elements to three-dimensional elements, including discussions on various applications, and ending with introductory chapters on the boundary element and meshless methods, where more input data must be provided to solve problems. Emphasis is placed on the development of the discrete set of algebraic equations. The example problems and exercises in each chapter explain the procedure for defining and organizing the required initial and boundary condition data for a specific problem, and computer code listings in MATLAB and MAPLE are included for setting up the examples within the text, including COMSOL files. Widely used as an introductory Finite Element Method text since 1992 and used in past ASME short courses and AIAA home study courses, this text is intended for undergraduate and graduate students taking Finite Element Methodology courses, engineers working in the industry that need to become familiar with the FEM, and engineers working in the field of heat transfer. It can also be used for distance education courses that can be conducted on the web. Highlights of the new edition include: - Inclusion of MATLAB, MAPLE code listings, along with several COMSOL files, for the example problems within the text. Power point presentations per chapter and a solution manual are also available from the web. - Additional introductory chapters on the boundary element method and the meshless method. - Revised and updated content. -Simple and easy to follow guidelines for understanding and applying the Finite Element Method.
Download or read book The Finite Element Method written by Patrick Ciarlet and published by John Wiley & Sons. This book was released on 2023-08-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities. This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.
Download or read book The Finite Element Method for Initial Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2017-10-17 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathematical details as well as applications of space-time coupled and space-time decoupled finite element methods for IVPs. Space-time operator classification, space-time methods of approximation, and space-time calculus of variations are used to establish unconditional stability of space-time methods during the evolution. Space-time decoupled methods are also presented with the same rigor. Stability of space-time decoupled methods, time integration of ODEs including the finite element method in time are presented in detail with applications. Modal basis, normal mode synthesis techniques, error estimation, and a posteriori error computations for space-time coupled as well as space-time decoupled methods are presented. This book is aimed at a second-semester graduate level course in FEM.
