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Verification Of Transport Codes By The Method Of Manufactured Solutions
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Book Synopsis VERIFICATION OF TRANSPORT CODES BY THE METHOD OF MANUFACTURED SOLUTIONS by :
Download or read book VERIFICATION OF TRANSPORT CODES BY THE METHOD OF MANUFACTURED SOLUTIONS written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the Method of Manufactured Solutions (MMS) to the verification of transport codes. We derive analytic fixed sources required by the MMS procedure for several types of transport problems and apply the method to the Attila transport code. By means of this method we discover and correct several coding mistakes in Attila and ultimately verify its correct implementation for the problems studied. Our studies reveal that the MMS procedure is a useful tool for transport code development.
Book Synopsis Computer Simulation Validation by : Claus Beisbart
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.
Book Synopsis Code Verification by the Method of Manufactured Solutions by :
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.
Book Synopsis Verification of Computer Codes in Computational Science and Engineering by : Patrick Knupp
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.
Book Synopsis Code Verification Using the Method of Manufactured Solutions by : Vasanth Kumar Murali
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.
Book Synopsis Advances in Computers by : Marvin Zelkowitz
Download or read book Advances in Computers written by Marvin Zelkowitz and published by Elsevier. This book was released on 2006-04-25 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of Advances in Computers is number 66 in the series that began back in 1960. This series presents the ever changing landscape in the continuing evolution of the development of the computer and the field of information processing. Each year three volumes are produced presenting approximately 20 chapters that describe the latest technology in the use of computers today. Volume 66, subtitled "Quality software development," is concerned about the current need to create quality software. It describes the current emphasis in techniques for creating such software and in methods to demonstrate that the software indeed meets the expectations of the designers and purchasers of that software. - In-depth surveys and tutorials on software development approaches - Well-known authors and researchers in the field - Extensive bibliographies with most chapters - All chapters focus on software development issues - Discussion of high end computing applications, a topic generally not understood by most software professionals
Book Synopsis Verification of 2D Navier-stokes Codes by the Method of Manufactured Solutions by : Vasanth Kumar Murali
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:
Book Synopsis Handbook of Numerical Simulation of In-Flight Icing by : Wagdi George Habashi
Download or read book Handbook of Numerical Simulation of In-Flight Icing written by Wagdi George Habashi and published by Springer Nature. This book was released on 2024-01-12 with total page 1278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook of Numerical Simulation of In-Flight Icing covers an array of methodologies and technologies on numerical simulation of in-flight icing and its applications. Comprised of contributions from internationally recognized experts from the Americas, Asia, and the EU, this authoritative, self-contained reference includes best practices and specification data spanning the gamut of simulation tools available internationally that can be used to speed up the certification of aircraft and make them safer to fly into known icing. The collection features nine sections concentrating on aircraft, rotorcraft, jet engines, UAVs; ice protection systems, including hot-air, electrothermal, and others; sensors and probes, CFD in the aid of testing, flight simulators, and certification process acceleration methods. Incorporating perspectives from academia, commercial, government R&D, the book is ideal for a range of engineers and scientists concerned with in-flight icing applications.
Book Synopsis Verification of Computer Codes in Computational Science and Engineering by : Patrick Knupp
Download or read book Verification of Computer Codes in Computational Science and Engineering written by Patrick Knupp and published by Chapman and Hall/CRC. This book was released on 2002-10-29 with total page 160 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.
Book Synopsis Numerical Mathematics and Advanced Applications ENUMATH 2019 by : Fred J. Vermolen
Download or read book Numerical Mathematics and Advanced Applications ENUMATH 2019 written by Fred J. Vermolen and published by Springer Nature. This book was released on 2021-04-30 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).
Book Synopsis 32nd AIAA Fluid Dynamics Conference and Exhibit by :
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:
Book Synopsis GPU Solutions to Multi-scale Problems in Science and Engineering by : David A. Yuen
Download or read book GPU Solutions to Multi-scale Problems in Science and Engineering written by David A. Yuen and published by Springer Science & Business Media. This book was released on 2013-01-09 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the new topic of GPU computing with many applications involved, taken from diverse fields such as networking, seismology, fluid mechanics, nano-materials, data-mining , earthquakes ,mantle convection, visualization. It will show the public why GPU computing is important and easy to use. It will offer a reason why GPU computing is useful and how to implement codes in an everyday situation.
Book Synopsis Finite Difference Methods in Heat Transfer by : M. Necati Özişik
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
Book Synopsis AIAA Journal by : American Institute of Aeronautics and Astronautics
Download or read book AIAA Journal written by American Institute of Aeronautics and Astronautics and published by . This book was released on 2007 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis DNA Techniques to Verify Food Authenticity by : Malcolm Burns
Download or read book DNA Techniques to Verify Food Authenticity written by Malcolm Burns and published by Royal Society of Chemistry. This book was released on 2019-10-14 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The food supply chain needs to reassure consumers and businesses about the safety and standards of food. Global estimates of the cost of food fraud to economies run into billions of dollars hence a huge surge in interest in food authenticity and means of detecting and preventing food fraud and food crime. Approaches targeting DNA markers have assumed a pre-eminence. This book is the most comprehensive and timely collection of material from those working at the forefront of DNA techniques applied to food authenticity. Addressing the new field of analytical molecular biology as it combines the quality assurance rigour of analytical chemistry with DNA techniques, it introduces the science behind DNA as a target analyte, its extraction, amplification, detection and quantitation as applied to the detection of food fraud and food crime. Making the link with traditional forensic DNA profiling and describing emerging and cutting-edge techniques such as next generation sequencing, this book presents real-world case studies from a wide perspective including from analytical service providers, industry, enforcement agencies and academics. It will appeal to food testing laboratories worldwide, who are just starting to use these techniques and students of molecular biology, food science and food integrity. Food policy professionals and regulatory organisations who will be using these techniques to back up legislation and regulation will find the text invaluable. Those in the food industry in regulatory and technical roles will want to have this book on their desks.
Book Synopsis The Dynamics of Partially Molten Rock by : Richard F. Katz
Download or read book The Dynamics of Partially Molten Rock written by Richard F. Katz and published by Princeton University Press. This book was released on 2022-01-18 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable synthesis of the physics of magmatism for students and scholars Magma genesis and segregation have shaped Earth since its formation more than 4.5 billion years ago. Now, for the first time, the mathematical theory describing the physics of magmatism is presented in a single volume. The Dynamics of Partially Molten Rock offers a detailed overview that emphasizes the fundamental physical insights gained through an analysis of simplified problems. This textbook brings together such topics as fluid dynamics, rock mechanics, thermodynamics and petrology, geochemical transport, plate tectonics, and numerical modeling. End-of-chapter exercises and solutions as well as online Python notebooks provide material for courses at the advanced undergraduate or graduate level. This book focuses on the partial melting of Earth’s asthenosphere, but the theory presented is also more broadly relevant to natural systems where partial melting occurs, including ice sheets and the deep crust, mantle, and core of Earth and other planetary bodies, as well as to rock-deformation experiments conducted in the laboratory. For students and researchers aiming to understand and advance the cutting edge, the work serves as an entrée into the field and a convenient means to access the research literature. Notes in each chapter reference both classic papers that shaped the field and newer ones that point the way forward. The Dynamics of Partially Molten Rock requires a working knowledge of fluid mechanics and calculus, and for some chapters, readers will benefit from prior exposure to thermodynamics and igneous petrology. The first book to bring together in a unified way the theory for partially molten rocks End-of-chapter exercises with solutions and an online supplement of Jupyter notebooks Coverage of the mechanics, thermodynamics, and chemistry of magmatism, and their coupling in the context of plate tectonics and mantle convection Notes at the end of each chapter highlight key papers for further reading
Download or read book Aerospace America written by and published by . This book was released on 2007 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
