Spectral Elements For Transport Dominated Equations
DOWNLOAD
Download Spectral Elements For Transport Dominated Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Spectral Elements For Transport Dominated Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Spectral Elements For Transport Dominated Equations
DOWNLOAD
Author : Daniele Funaro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Elements For Transport Dominated Equations written by Daniele Funaro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential model problems presenting multiscale solutions. This is the case, for instance, with functions displaying a smooth behavior, except in certain regions where sudden and sharp variations are localized. Typical examples are internal or boundary layers. When the number of degrees of freedom in the discretization process is not sufficient to ensure a fine resolution of the layers, some stabilization procedures are needed to avoid unpleasant oscillatory effects, without adding too much artificial viscosity to the scheme. In the field of finite elements, the streamline diffusion method, the Galerkin least-squares method, the bub ble function approach, and other recent similar techniques provide excellent treatments of transport equations of elliptic type with small diffusive terms, referred to in fluid dynamics as advection-diffusion (or convection-diffusion) equations. Goals This book is an attempt to guide the reader in the construction of a computa tional code based on the spectral collocation method, using algebraic polyno mials. The main topic is the approximation of elliptic type boundary-value par tial differential equations in 2-D, with special attention to transport-diffusion equations, where the second-order diffusive terms are strongly dominated by the first-order advective terms. Applications will be considered especially in the case where nonlinear systems of partial differential equations can be re duced to a sequence of transport-diffusion equations.
Spectral Methods
DOWNLOAD
Author : Claudio Canuto
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30
Spectral Methods written by Claudio Canuto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Mathematics categories.
Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Spectral Hp Element Methods For Computational Fluid Dynamics
DOWNLOAD
Author : George Karniadakis
language : en
Publisher: American Chemical Society
Release Date : 2013-01-10
Spectral Hp Element Methods For Computational Fluid Dynamics written by George Karniadakis and has been published by American Chemical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-10 with Mathematics categories.
Revision of: Spectral/hp element methods for CFD. 1999.
Variational Multiscale Stabilization Of Finite And Spectral Elements For Dry And Moist Atmospheric Problems
DOWNLOAD
Author : Simone Marras
language : en
Publisher:
Release Date : 2013
Variational Multiscale Stabilization Of Finite And Spectral Elements For Dry And Moist Atmospheric Problems written by Simone Marras and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
In this thesis the finite and spectral element methods (FEM and SEM, respectively) applied to problems in atmospheric simulations are explored through the common thread of Variational Multiscale Stabilization (VMS). This effort is justified by three main reasons. (i) the recognized need for new solvers that can efficiently execute on massively parallel architectures ¿a spreading framework in most fields of computational physics in which numerical weather prediction (NWP) occupies a prominent position. Element-based methods (e.g. FEM, SEM, discontinuous Galerkin) have important advantages in parallel code development; (ii) the inherent flexibility of these methods with respect to the geometry of the grid makes them a great candidate for dynamically adaptive atmospheric codes; and (iii) the localized diffusion provided by VMS represents an improvement in the accurate solution of multi-physics problems where artificial diffusion may fail. Its application to atmospheric simulations is a novel approach within a field of research that is still open. First, FEM and VMS are described and derived for the solution of stratified low Mach number flows in the context of dry atmospheric dynamics. The validity of the method to simulate stratified flows is assessed using standard two- and three-dimensional benchmarks accepted by NWP practitioners. The problems include thermal and gravity driven simulations. It will be shown that stability is retained in the regimes of interest and a numerical comparison against results from the the literature will be discussed. Second, the ability of VMS to stabilize the FEM solution of advection-dominated problems (i.e. Euler and transport equations) is taken further by the implementation of VMS as a stabilizing tool for high-order spectral elements with advection-diffusion problems. To the author¿s knowledge, this is an original contribution to the literature of high order spectral elements involved with transport in the atmosphere. The problem of monotonicity-preserving high order methods is addressed by combining VMS-stabilized SEM with a discontinuity capturing technique. This is an alternative to classical filters to treat the Gibbs oscillations that characterize high-order schemes. To conclude, a microphysics scheme is implemented within the finite element Euler solver, as a first step toward realistic atmospheric simulations. Kessler microphysics is used to simulate the formation of warm, precipitating clouds. This last part combines the solution of the Euler equations for stratified flows with the solution of a system of transport equations for three classes of water: water vapor, cloud water, and rain. The method is verified using idealized two- and three-dimensional storm simulations.
Chebyshev And Fourier Spectral Methods
DOWNLOAD
Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05
Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Numerical Analysis Of Partial Differential Equations
DOWNLOAD
Author : S. H, Lui
language : en
Publisher: John Wiley & Sons
Release Date : 2011-08-30
Numerical Analysis Of Partial Differential Equations written by S. H, Lui and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Mathematics categories.
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
Automated Solution Of Differential Equations By The Finite Element Method
DOWNLOAD
Author : Anders Logg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-24
Automated Solution Of Differential Equations By The Finite Element Method written by Anders Logg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-24 with Computers categories.
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Spectral Methods In Matlab
DOWNLOAD
Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2000-01-01
Spectral Methods In Matlab written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.
Spectral Methods For Incompressible Viscous Flow
DOWNLOAD
Author : Roger Peyret
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-03-28
Spectral Methods For Incompressible Viscous Flow written by Roger Peyret and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-28 with Mathematics categories.
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
Numerical Models For Differential Problems
DOWNLOAD
Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-22
Numerical Models For Differential Problems written by Alfio Quarteroni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-22 with Mathematics categories.
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.