Verification of Computer Codes in Computational Science and Engineering

Author: Patrick Knupp,Kambiz Salari

Publisher: CRC Press

ISBN: 1420035428

Category: Mathematics

Page: 160

View: 4464


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.

Mechanisms of Vascular Disease

A Textbook for Vascular Specialists

Author: Robert Fitridge

Publisher: Springer Nature

ISBN: 3030436837

Category: Medical

Page: 733

View: 6907


This extensively revised third edition provides a practically applicable guide to the pathophysiology, assessment and management of vascular disorders encountered in vascular surgical practice. It features detailed information on the latest developments in the pathophysiology of conditions including atherosclerosis, multi-organ failure, limb compartment syndromes and Raynaud’s phenomenon in a clear easy to digest format. Disorders such as reperfusion injuries, vasculitides, and aortic dissection are covered. Furthermore, key topics in vascular and endovascular practice such as radiation biology and radiation safety are also detailed. Each chapter contains a set of learning objectives and key references, enabling the reader to quickly identify key points. Mechanisms of Vascular Disease: A Textbook for Vascular Specialists comprehensively covers a variety of common and unusual pathophysiologies encountered in vascular surgery, and is an ideal resource for both the trainee, and practicing clinical vascular surgeon seeking an up-to-date resource on the topic.

Multiscale Methods

Bridging the Scales in Science and Engineering

Author: Jacob Fish

Publisher: OUP Oxford

ISBN: 0191579734

Category: Mathematics

Page: 624

View: 1674


Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness? The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of error estimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biological systems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.

Verification and Validation in Scientific Computing

Author: William L. Oberkampf,Christopher J. Roy

Publisher: Cambridge University Press

ISBN: 1139491768

Category: Computers

Page: N.A

View: 4546


Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

Computational Methods in Transport: Verification and Validation

Author: Frank Graziani

Publisher: Springer Science & Business Media

ISBN: 3540773622

Category: Science

Page: 332

View: 8765


The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.

AIAA Guide for the Verification and Validation of Computational Fluid Dynamics Simulations

Author: American Institute of Aeronautics and Astronautics

Publisher: Amer Inst of Aeronautics &

ISBN: 9781563472855

Category: Mathematics

Page: 19

View: 1268


This document presents for guidelines for assessing the credibility of modeling and simulation in computational fluid dynamics. The two main principles that are necessary for assessing credibility are verification and validation. Verification is the process of determining if a computational simulation accurately represents the conceptual model, but no claim is made of the relationship of the simulation to the real world. Validation is the process of determining if a computational simulation represents the real world. This document defines a number of key terms, discusses fundamental concepts, and specifies general procedures for conducting verification and validation of computational fluid dynamics simulations. The document's goal is to provide a foundation for the major issues and concepts in verification and validation. However, this document does not recommend standards in these areas because a number of important issues are not yet resolved. It is hoped that the guidelines will aid in the research, development, and use of computational fluid dynamics simulations by establishing common terminology and methodology for verification and validation. The terminology and methodology should also be useful in other engineering and science disciplines.

Assessing the Reliability of Complex Models

Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification

Author: National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification

Publisher: National Academies Press

ISBN: 0309256348

Category: Mathematics

Page: 144

View: 2832


Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.

Experimentation, Validation, and Uncertainty Analysis for Engineers

Author: Hugh W. Coleman,W. Glenn Steele

Publisher: John Wiley & Sons

ISBN: 0470168889

Category: Technology & Engineering

Page: 336

View: 2257


This Third Edition helps you assess and manage uncertainty at all stages of experimentation and validation of simulations In this greatly expanded Third Edition, the acclaimed Experimentation, Validation, and Uncertainty Analysis for Engineers guides readers through the concepts of experimental uncertainty analysis and the applications in validating models and simulations, solving problems experimentally, and characterizing the behavior of systems. This Third Edition presents the current, internationally accepted methodology from ISO, ANSI, and ASME standards to cover the planning, design, debugging, and execution phases of experiments. Cases in which the experimental result is determined only once or when the result is determined multiple times in a test are addressed and illustrated with examples from the authors' experience. The important practical cases in which multiple measured variables share correlated errors are discussed in detail, and strategies to take advantage of such effects in calibrations and comparative testing situations are presented. The methodology for determining uncertainty by Monte Carlo analysis is described in detail. Knowledge of the material in this Third Edition is a must for those involved in executing or managing experimental programs or validating models, codes, and simulations. Professionals and students in disciplines spanning the full range of engineering and science will find this book an essential guide.