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Author :
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (924 download)
Download or read book On Numerical Errors in the Boundary Conditions of the Euler Equations written by and published by . This book was released on 2000 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Boris Diskin
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (317 download)
Download or read book Analysis of Boundary Conditions for Factorizable Discretizations of the Euler Equations written by Boris Diskin and published by . This book was released on 2002 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, several sets of boundary conditions or factorizable schemes corresponding to the steady-state compressible Euler equations are evaluated. The analyzed model is a one-dimensional constant-coefficient problem. Numerical tests have been performed for a fully subsonic quasi-one-dimensional flow in a convergent/divergent channel. This paper focuses on the effect of boundary-condition equations on stability and accuracy of the discrete solutions. Explicit correspondence between solutions and boundary conditions is established through a boundary-condition-sensitivity (BCS) matrix. The following new findings are reported: (1) Examples of stable discrete problems contradicting a wide-spread belief that employment of a one-order-lower approximation schemes in an O(h)-small region does not affect the overall accuracy order of the solution have been found and explained. Such counterexamples can only be constructed for systems of differential equations. For scalar equations, the conventional wisdom is correct. (2) A negative effect of overspecified (although, exact) boundary conditions on accuracy and stability of the solution has been observed and explained. (3) Sets of practical boundary conditions for factorizable schemes providing stable second-order accurate solutions have been formulated. These schemes belong to a family of second-order schemes requiring second-order accuracy for some numerical-closure boundary conditions.
Author : Albrecht Eberle
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 3663068315
Total Pages : 456 pages
Book Rating : 4.6/5 (63 download)
Download or read book Numerical Solutions of the Euler Equations for Steady Flow Problems written by Albrecht Eberle and published by Vieweg+Teubner Verlag. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a dramatic increase of our abilities to solve numerically the governing equations of fluid mechanics. In design aerodynamics the classical potential-flow methods have been complemented by higher modelling-level methods. Euler solvers, and for special purposes, already Navier-Stokes solvers are in use. The authors of this book have been working on the solution of the Euler equations for quite some time. While the first two of us have worked mainly on algorithmic problems, the third has been concerned off and on with modelling and application problems of Euler methods. When we started to write this book we decided to put our own work at the center of it. This was done because we thought, and we leave this to the reader to decide, that our work has attained over the years enough substance in order to justify a book. The problem which we soon faced, was that the field still is moving at a fast pace, for instance because hyper sonic computation problems became more and more important.
Author : Ehteshamul Muhammed Hayder
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.F/5 ( download)
Download or read book Towards Perfectly Absorbing Boundary Conditions for Euler Equations written by Ehteshamul Muhammed Hayder and published by . This book was released on 1997 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Ehtesham Hayder
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (317 download)
Download or read book Towards Perfectly Absorbing Boundary Conditions for Euler Equations written by M. Ehtesham Hayder and published by . This book was released on 1997 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems - shock-vortex interactions, a plane free shear flow and an axisymmetric jet, with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.
Author : Timothy J. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 3662051893
Total Pages : 354 pages
Book Rating : 4.6/5 (62 download)
Download or read book Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Author : P. L. Roe
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.F/5 ( download)
Download or read book Error Estimates for Cell-vertex Solutions of the Compressible Euler Equations written by P. L. Roe and published by . This book was released on 1987 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : You-lan Zhu
Publisher : Springer
ISBN 13 : 3540481265
Total Pages : 255 pages
Book Rating : 4.5/5 (44 download)
Download or read book Numerical Methods for Partial Differential Equations written by You-lan Zhu and published by Springer. This book was released on 2006-11-15 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
ISBN 13 : 3322868591
Total Pages : 222 pages
Book Rating : 4.3/5 (228 download)
Download or read book Numerical Treatment of Coupled Systems written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The coupling considered in this volume may be of physical or numerical nature. Examples of the first kind are the solid-fluid interactions, microelectronic systems, and the coupled modelling in groundwater flow. Examples of the latter kind are the domain or subspace decomposition, the local defect correction method, and the very important FEM-BEM coupling.
Author : William F. Trench
Publisher : Thomson Brooks/Cole
ISBN 13 :
Total Pages : 764 pages
Book Rating : 4.:/5 (321 download)
Download or read book Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Author :
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.:/5 (317 download)
Download or read book Numerical Boundary Condition Procedures written by and published by . This book was released on 1981 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kendall Atkinson
Publisher : John Wiley & Sons
ISBN 13 : 1118164520
Total Pages : 272 pages
Book Rating : 4.1/5 (181 download)
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Author : Luigi Brugnano
Publisher : CRC Press
ISBN 13 : 1482263858
Total Pages : 239 pages
Book Rating : 4.4/5 (822 download)
Download or read book Line Integral Methods for Conservative Problems written by Luigi Brugnano and published by CRC Press. This book was released on 2016-03-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large
Author : Donald J. Estep
Publisher : American Mathematical Soc.
ISBN 13 : 0821820729
Total Pages : 125 pages
Book Rating : 4.8/5 (218 download)
Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
Author : L. Tourrette
Publisher : Nova Publishers
ISBN 13 : 9781560729402
Total Pages : 396 pages
Book Rating : 4.7/5 (294 download)
Download or read book Absorbing Boundaries and Layers, Domain Decomposition Methods written by L. Tourrette and published by Nova Publishers. This book was released on 2001 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM contains: Sections omitted from printing of text.
Author : Granville Sewell
Publisher : Academic Press
ISBN 13 : 1483259145
Total Pages : 284 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by Academic Press. This book was released on 2014-05-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.
Author : Robert M. Corless
Publisher : Springer Science & Business Media
ISBN 13 : 1461484537
Total Pages : 896 pages
Book Rating : 4.4/5 (614 download)
Download or read book A Graduate Introduction to Numerical Methods written by Robert M. Corless and published by Springer Science & Business Media. This book was released on 2013-12-12 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.
