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The Importance Of Boundary Conditions In The Numerical Treatment Of Hyperbolic Equations
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Book Synopsis Handbook of Numerical Methods for Hyperbolic Problems by : Remi Abgrall
Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications - Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
Book Synopsis The Treatment of Lateral Boundary Conditions in Limited-area Models by : Ralph Shapiro
Download or read book The Treatment of Lateral Boundary Conditions in Limited-area Models written by Ralph Shapiro and published by . This book was released on 1977 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models used to simulate or predict atmospheric behavior are limited in scope because of insufficient knowledge of the initial conditions and forcing functions. But these limitations are generally dwarfed by the limited capacity and power of even the largest and most powerful computers. Thus, where a solution is required with high resolution for some limited area of interest, it is often impractical to solve the model throughout the entire domain with the same uniformly high resolution. A pragmatic approach is proposed here which overspecifies the artificial lateral boundaries of a fine-mesh, limited-area, nested region and depends upon a high-order phase and amplitude restoring interpolation along with a high-order, but weak, smoothing operator to control noise and ensure versimilitude. The dynamic tests are carried out in the framework of a multilevel primitive equation model and show unequivocally the importance of correct phase information for the lateral boundaries of the fine-mesh region. The results obtained indicate that the simple procedure proposed here should yield satisfactory results in operational fine-mesh, limited-area models.
Book Synopsis Shallow Water Hydrodynamics by : W.Y. Tan
Download or read book Shallow Water Hydrodynamics written by W.Y. Tan and published by Elsevier. This book was released on 1992-08-17 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within this monograph a comprehensive and systematic knowledge on shallow-water hydrodynamics is presented. A two-dimensional system of shallow-water equations is analyzed, including the mathematical and mechanical backgrounds, the properties of the system and its solution. Also featured is a new mathematical simulation of shallow-water flows by compressible plane flows of a special virtual perfect gas, as well as practical algorithms such as FDM, FEM, and FVM. Some of these algorithms have been utilized in solving the system, while others have been utilized in various applied fields. An emphasis has been placed on several classes of high-performance difference schemes and boundary procedures which have found wide uses recently for solving the Euler equations of gas dynamics in aeronautical and aerospatial engineering. This book is constructed so that it may serve as a handbook for practicians. It will be of interest to scientists, designers, teachers, postgraduates and professionals in hydraulic, marine, and environmental engineering; especially those involved in the mathematical modelling of shallow-water bodies.
Book Synopsis Computational Gasdynamics by : Culbert B. Laney
Download or read book Computational Gasdynamics written by Culbert B. Laney and published by Cambridge University Press. This book was released on 1998-06-13 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.
Book Synopsis Numerical Treatment of Partial Differential Equations by : Christian Grossmann
Download or read book Numerical Treatment of Partial Differential Equations written by Christian Grossmann and published by Springer Science & Business Media. This book was released on 2007-08-11 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.
Book Synopsis Numerical Boundary Condition Procedures by :
Download or read book Numerical Boundary Condition Procedures written by and published by . This book was released on 1982 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods in Fluid Dynamics by : Gary A. Sod
Download or read book Numerical Methods in Fluid Dynamics written by Gary A. Sod and published by Cambridge University Press. This book was released on 1985-10-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.
Book Synopsis Mathematical Aspects of Numerical Solution of Hyperbolic Systems by : A.G. Kulikovskii
Download or read book Mathematical Aspects of Numerical Solution of Hyperbolic Systems written by A.G. Kulikovskii and published by CRC Press. This book was released on 2000-12-21 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundary Parametric Control of Oscillations in Heat and Fluid Flows by : Ivan Kazachkov
Download or read book Boundary Parametric Control of Oscillations in Heat and Fluid Flows written by Ivan Kazachkov and published by Cambridge Scholars Publishing. This book was released on 2024-09-11 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on modeling and control of fluid movement and heat transfer in relation to the development and implementation of new highly effective technologies. It develops a new theory of parametric control of film flows and the production of amorphous granules for the creation of new unique materials. The book also explores the new challenges introduced by the influence of vibrations and electromagnetic fields on the flow of various liquids, including metals. The book details the discovery of three new hydrodynamic phenomena, and demonstrates their importance for the creation of unique devices and technologies. It also covers thermohydraulic processes in granular layers, and anomalous heat transfer in complex environments. This book will be of interest to mechanical engineers, electromagnetic experts, metallurgists, material scientists and all science lovers.
Book Synopsis Peridynamic Differential Operator for Numerical Analysis by : Erdogan Madenci
Download or read book Peridynamic Differential Operator for Numerical Analysis written by Erdogan Madenci and published by Springer. This book was released on 2019-01-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization. Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
Book Synopsis Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics by : Charles Hirsch
Download or read book Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics written by Charles Hirsch and published by Elsevier. This book was released on 2007-07-18 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book is a self-contained introduction to computational fluid dynamics (CFD). It covers the fundamentals of the subject and is ideal as a text or a comprehensive reference to CFD theory and practice. - New approach takes readers seamlessly from first principles to more advanced and applied topics. - Presents the essential components of a simulation system at a level suitable for those coming into contact with CFD for the first time, and is ideal for those who need a comprehensive refresher on the fundamentals of CFD. - Enhanced pedagogy features chapter objectives, hands-on practice examples and end of chapter exercises. - Extended coverage of finite difference, finite volume and finite element methods. - New chapters include an introduction to grid properties and the use of grids in practice. - Includes material on 2-D inviscid, potential and Euler flows, 2-D viscous flows and Navier-Stokes flows to enable the reader to develop basic CFD simulations. - Includes best practice guidelines for applying existing commercial or shareware CFD tools.
Book Synopsis The Numerical Treatment of Differential Equations by : Lothar Collatz
Download or read book The Numerical Treatment of Differential Equations written by Lothar Collatz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal.
Book Synopsis Computational Fluid Mechanics and Heat Transfer by : Dale Anderson
Download or read book Computational Fluid Mechanics and Heat Transfer written by Dale Anderson and published by CRC Press. This book was released on 2020-12-17 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Mechanics and Heat Transfer, Fourth Edition is a fully updated version of the classic text on finite-difference and finite-volume computational methods. Divided into two parts, the text covers essential concepts in the first part, and then moves on to fluids equations in the second. Designed as a valuable resource for practitioners and students, new examples and homework problems have been added to further enhance the student’s understanding of the fundamentals and applications. Provides a thoroughly updated presentation of CFD and computational heat transfer Covers more material than other texts, organized for classroom instruction and self-study Presents a wide range of computation strategies for fluid flow and heat transfer Includes new sections on finite element methods, computational heat transfer, and multiphase flows Features a full Solutions Manual and Figure Slides for classroom projection Written as an introductory text for advanced undergraduates and first-year graduate students, the new edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer.
Book Synopsis Initial-boundary Value Problems and the Navier-Stokes Equations by : Heinz-Otto Kreiss
Download or read book Initial-boundary Value Problems and the Navier-Stokes Equations written by Heinz-Otto Kreiss and published by SIAM. This book was released on 1989-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Download or read book Monthly Weather Review written by and published by . This book was released on 1983 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Flux-Corrected Transport by : Dmitri Kuzmin
Download or read book Flux-Corrected Transport written by Dmitri Kuzmin and published by Springer Science & Business Media. This book was released on 2012-04-02 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.
