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Author : Vasanth Kumar Murali
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)
Download or read book Verification of 2D Navier-stokes Codes by the Method of Manufactured Solutions written by Vasanth Kumar Murali and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vasanth Kumar Murali
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (53 download)
Download or read book Code Verification Using the Method of Manufactured Solutions written by Vasanth Kumar Murali and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Implementations of numerical simulations for solving systems of partial differential equations are often not verified and are falsely assumed to work correctly. As a result, the implementations are prone to coding errors that could degrade the accuracy of the solution. In order to ensure that a code is written correctly, rigorous verification of all parts of the code is necessary. Code verification is the task of ascertaining whether a numerical algorithm is solving the governing equations of the problem correctly. If an exact solution existed for the governing equations then verification would be easier but these solutions are rare because of the non-linearity of common Computational Fluid Dynamics (CFD) problems. In the absence of exact solutions, grid refinement studies are the most commonly used methods to verify codes using simulations on a sequence of grids but even these studies have limitations. The Method of Manufactured Solutions (MMS) is a novel and a recently developed technique that verifies the observed order-of-accuracy of the implementation of a numerical algorithm. The method is more general and overcomes many of the limitations of the method of exact solutions and grid refinement studies. The central idea is to modify the governing equations and the boundary conditions by adding forcing functions or source terms in order to drive the discrete solution to a prescribed or 'manufactured' solution chosen a priori. A grid convergence study is performed subsequently to determine the observed orders. Two methods of accuracy assessment are presented here - solution accuracy analysis and residual error analysis. The method based on the error in the spatial residual is computationally less expensive and proved to be a valuable debugging tool. In the present work, the Method of Manufactured Solutions (MMS) is implemented on a compressible flow solver that solves the two-dimensional Euler equations on structured grids and an incompressible code that solves the two-dimensional Navier-Stokes equations on unstructured meshes. Exponential functions are used to 'manufacture' steady solutions to the governing equations. Solution and residual error analyses are presented. The influence of grid non-uniformity on the numerical accuracy is studied.
Author : Claus Beisbart
Publisher : Springer
ISBN 13 : 3319707663
Total Pages : 1056 pages
Book Rating : 4.3/5 (197 download)
Download or read book Computer Simulation Validation written by Claus Beisbart and published by Springer. This book was released on 2019-04-09 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume introduces and discusses the methods of validating computer simulations in scientific research. The core concepts, strategies, and techniques of validation are explained by an international team of pre-eminent authorities, drawing on expertise from various fields ranging from engineering and the physical sciences to the social sciences and history. The work also offers new and original philosophical perspectives on the validation of simulations. Topics and features: introduces the fundamental concepts and principles related to the validation of computer simulations, and examines philosophical frameworks for thinking about validation; provides an overview of the various strategies and techniques available for validating simulations, as well as the preparatory steps that have to be taken prior to validation; describes commonly used reference points and mathematical frameworks applicable to simulation validation; reviews the legal prescriptions, and the administrative and procedural activities related to simulation validation; presents examples of best practice that demonstrate how methods of validation are applied in various disciplines and with different types of simulation models; covers important practical challenges faced by simulation scientists when applying validation methods and techniques; offers a selection of general philosophical reflections that explore the significance of validation from a broader perspective. This truly interdisciplinary handbook will appeal to a broad audience, from professional scientists spanning all natural and social sciences, to young scholars new to research with computer simulations. Philosophers of science, and methodologists seeking to increase their understanding of simulation validation, will also find much to benefit from in the text.
Download or read book Code Verification Using The Method of Manufactured Solutions written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Implementations of numerical simulations for solving systems of partial differential equations are often not verified and are falsely assumed to work correctly. As a result, the implementations are prone to coding errors that could degrade the accuracy of the solution. In order to ensure that a code is written correctly, rigorous verification of all parts of the code is necessary. Code verification is the task of ascertaining whether a numerical algorithm is solving the governing equations of the problem correctly. If an exact solution existed for the governing equations then verification would be easier but these solutions are rare because of the non-linearity of common Computational Fluid Dynamics (CFD) problems. In the absence of exact solutions, grid refinement studies are the most commonly used methods to verify codes using simulations on a sequence of grids but even these studies have limitations. The Method of Manufactured Solutions (MMS) is a novel and a recently developed technique that verifies the observed order-of-accuracy of the implementation of a numerical algorithm. The method is more general and overcomes many of the limitations of the method of exact solutions and grid refinement studies. The central idea is to modify the governing equations and the boundary conditions by adding forcing functions or source terms in order to drive the discrete solution to a prescribed or ``manufactured' solution chosen a priori. A grid convergence study is performed subsequently to determine the observed orders. Two methods of accuracy assessment are presented here - solution accuracy analysis and residual error analysis. The method based on the error in the spatial residual is computationally less expensive and proved to be a valuable debugging tool. In the present work, the Method of Manufactured Solutions (MMS) is implemented on a compressible flow solver that solves the two-dimensional Euler equations on structured grids and an incompressible code that solves th.
Author :
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (684 download)
Download or read book Code Verification by the Method of Manufactured Solutions written by and published by . This book was released on 2000 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: A procedure for code Verification by the Method of Manufactured Solutions (MMS) is presented. Although the procedure requires a certain amount of creativity and skill, we show that MMS can be applied to a variety of engineering codes which numerically solve partial differential equations. This is illustrated by detailed examples from computational fluid dynamics. The strength of the MMS procedure is that it can identify any coding mistake that affects the order-of-accuracy of the numerical method. A set of examples which use a blind-test protocol demonstrates the kinds of coding mistakes that can (and cannot) be exposed via the MMS code Verification procedure. The principle advantage of the MMS procedure over traditional methods of code Verification is that code capabilities are tested in full generality. The procedure thus results in a high degree of confidence that all coding mistakes which prevent the equations from being solved correctly have been identified.
Author : Patrick Knupp
Publisher : CRC Press
ISBN 13 : 1420035428
Total Pages : 161 pages
Book Rating : 4.4/5 (2 download)
Download or read book Verification of Computer Codes in Computational Science and Engineering written by Patrick Knupp and published by CRC Press. This book was released on 2002-10-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed. Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness. Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.
Author :
Publisher :
ISBN 13 :
Total Pages : 564 pages
Book Rating : 4.0/5 ( download)
Download or read book 32nd AIAA Fluid Dynamics Conference and Exhibit written by and published by . This book was released on 2002 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mohammad Faghri
Publisher : WIT Press
ISBN 13 : 1845641604
Total Pages : 497 pages
Book Rating : 4.8/5 (456 download)
Download or read book Transport Phenomena in Fires written by Mohammad Faghri and published by WIT Press. This book was released on 2008 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Controlled fires are beneficial for the generation of heat and power while uncontrolled fires, like fire incidents and wildfires, are detrimental and can cause enormous material damage and human suffering. This edited book presents the state-of-the-art of modeling and numerical simulation of the important transport phenomena in fires. It describes how computational procedures can be used in analysis and design of fire protection and fire safety. Computational fluid dynamics, turbulence modeling, combustion, soot formation, thermal radiation modeling are demonstrated and applied to pool fires, flame spread, wildfires, fires in buildings and other examples.
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ISBN 13 :
Total Pages : 776 pages
Book Rating : 4.F/5 ( download)
Download or read book Aerospace America written by and published by . This book was released on 2004 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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Publisher : ScholarlyEditions
ISBN 13 : 1464963754
Total Pages : 2526 pages
Book Rating : 4.4/5 (649 download)
Download or read book Issues in Mechanical Engineering: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 2526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Mechanical Engineering / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Mechanical Engineering. The editors have built Issues in Mechanical Engineering: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mechanical Engineering in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Mechanical Engineering: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author : Gabriel Winter
Publisher : Elsevier
ISBN 13 : 0080460968
Total Pages : 415 pages
Book Rating : 4.0/5 (84 download)
Download or read book Parallel Computational Fluid Dynamics 2004 written by Gabriel Winter and published by Elsevier. This book was released on 2005-07-12 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel CFD 2004, the sixteenth international conference on Parallel Computational Fluid Dynamics and other modern scientific domains, has been held since May 24th till May 27th, 2004 in Las Palmas de Gran Canaria, Spain. The specialized, high-level Parallel CFD conferences are organised on travelling locations all over the world, yearly because of multidisciplinary subject of parallel CFD and its rapidly evolving nature.The conference featured 8 invited lectures, 3 Mini Symposia, contributed papers and one Tutorial & Short Course. More than 80 multi-disciplinary presentations of the Parallel CFD had been presented, with participants from 17 countries. The sessions involved contributed papers on many diverse subjects including turbulence, complex flows, unstructured and adaptive grids, industrial applications, developments in software tools and environments as parallel optimization tools. This Book presents an up-to-date overview of the state of the art in parallel computational fluid dynamics.- Report on current research in the field.- Researchers around the world are included.- Subject is important to all interested in solving large fluid dynamics problems.- It is of interest to researchers in computer science, engineering and physical sciences.- It is an interdisciplinary activity. Contributions include scientists with a variety of backgrounds.- It is an area which is rapidly changing.
Author : M. Necati Özişik
Publisher : CRC Press
ISBN 13 : 1482243466
Total Pages : 580 pages
Book Rating : 4.4/5 (822 download)
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-20 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering. Features Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analytical–numerical approaches
Author : Katate Masatsuka
Publisher : Lulu.com
ISBN 13 : 1304827933
Total Pages : 306 pages
Book Rating : 4.3/5 (48 download)
Download or read book I do like CFD, VOL.1, Second Edition written by Katate Masatsuka and published by Lulu.com. This book was released on 2009-02-11 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Version 2.9 (May. 2024): This is a unique and highly technical book on Computational Fluid Dynamics (CFD). The first half talks about mathematical foundations and governing equations ranging from simple model equations (advection/diffusion, Euler-Tricomi, Cauchy-Riemann, Burgers, etc.) used for algorithm development to the incompressible/compressible Euler and Navier-Stokes equations in various forms with complete Jacobians and eigen-structures in 1, 2, and 3 dimensions. The other half talks about general methods for deriving exact solutions (separation of variables, transformation, superposition, etc.) and numerous exact solutions that can be readily used for accuracy verification of a CFD code (Ringleb's flow, Fraenkel's flow, boundary layer, viscous shock structure, etc.). This book can be a very useful resource for students studying basics of CFD as well as researchers/practitioners in CFD. - PDF version is available at cfdbooks.com. [Note: PDF does not contain some contents of the Printed version.]
Author :
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (243 download)
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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ISBN 13 :
Total Pages : 602 pages
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Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author : Mass Per Pettersson
Publisher : Springer
ISBN 13 : 3319107143
Total Pages : 217 pages
Book Rating : 4.3/5 (191 download)
Download or read book Polynomial Chaos Methods for Hyperbolic Partial Differential Equations written by Mass Per Pettersson and published by Springer. This book was released on 2015-03-10 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.
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Publisher :
ISBN 13 :
Total Pages : 538 pages
Book Rating : 4.3/5 (91 download)
Download or read book Aeronautical Engineering written by and published by . This book was released on 1991 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
