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Verification and Validation in Scientific Computing

Book Description

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.

Table of Contents

  1. Coverpage
  2. Verification and Validation in Scientific Computing
  3. Title page
  4. Copyright page
  5. Dedication
  6. Contents
  7. Preface
  8. Acknowledgments
  9. 1 Introduction
    1. 1.1 Historical and modern role of modeling and simulation
    2. 1.2 Credibility of scientific computing
    3. 1.3 Outline and use of the book
    4. 1.4 References
  10. Part I Fundamental concepts
    1. 2 Fundamental concepts and terminology
      1. 2.1 Development of concepts and terminology
      2. 2.2 Primary terms and concepts
      3. 2.3 Types and sources of uncertainties
      4. 2.4 Error in a quantity
      5. 2.5 Integration of verification, validation, and prediction
      6. 2.6 References
    2. 3 Modeling and computational simulation
      1. 3.1 Fundamentals of system specifications
      2. 3.2 Fundamentals of models and simulations
      3. 3.3 Risk and failure
      4. 3.4 Phases of computational simulation
      5. 3.5 Example problem: missile flight dynamics
      6. 3.6 References
  11. Part II Code verification
    1. 4 Software engineering
      1. 4.1 Software development
      2. 4.2 Version control
      3. 4.3 Software verification and validation
      4. 4.4 Software quality and reliability
      5. 4.5 Case study in reliability: the T experiments
      6. 4.6 Software engineering for large software projects
      7. 4.7 References
    2. 5 Code verification
      1. 5.1 Code verification criteria
      2. 5.2 Definitions
      3. 5.3 Order of accuracy
      4. 5.4 Systematic mesh refinement
      5. 5.5 Order verification procedures
      6. 5.6 Responsibility for code verification
      7. 5.7 References
    3. 6 Exact solutions
      1. 6.1 Introduction to differential equations
      2. 6.2 Traditional exact solutions
      3. 6.3 Method of manufactured solutions (MMS)
      4. 6.4 Physically realistic manufactured solutions
      5. 6.5 Approximate solution methods
      6. 6.6 References
  12. Part III Solution verification
    1. 7 Solution verification
      1. 7.1 Elements of solution verification
      2. 7.2 Round-off error
      3. 7.3 Statistical sampling error
      4. 7.4 Iterative error
      5. 7.5 Numerical error versus numerical uncertainty
      6. 7.6 References
    2. 8 Discretization error
      1. 8.1 Elements of the discretization process
      2. 8.2 Approaches for estimating discretization error
      3. 8.3 Richardson extrapolation
      4. 8.4 Reliability of discretization error estimators
      5. 8.5 Discretization error and uncertainty
      6. 8.6 Roache's grid convergence index (GCI)
      7. 8.7 Mesh refinement issues
      8. 8.8 Open research issues
      9. 8.9 References
    3. 9 Solution adaptation
      1. 9.1 Factors affecting the discretization error
      2. 9.2 Adaptation criteria
      3. 9.3 Adaptation approaches
      4. 9.4 Comparison of methods for driving mesh adaptation
      5. 9.5 References
  13. Part IV Model validation and prediction
    1. 10 Model validation fundamentals
      1. 10.1 Philosophy of validation experiments
      2. 10.2 Validation experiment hierarchy
      3. 10.3 Example problem: hypersonic cruise missile
      4. 10.4 Conceptual, technical, and practical difficulties of validation
      5. 10.5 References
    2. 11 Design and execution of validation experiments
      1. 11.1 Guidelines for validation experiments
      2. 11.2 Validation experiment example: Joint Computational/Experimental Aerodynamics Program (JCEAP)
      3. 11.3 Example of estimation of experimental measurement uncertainties in JCEAP
      4. 11.4 Example of further computational--experimental synergism in JCEAP
      5. 11.5 References
    3. 12 Model accuracy assessment
      1. 12.1 Elements of model accuracy assessment
      2. 12.2 Approaches to parameter estimation and validation metrics
      3. 12.3 Recommended features for validation metrics
      4. 12.4 Introduction to the approach for comparing means
      5. 12.5 Comparison of means using interpolation of experimental data
      6. 12.6 Comparison of means requiring linear regression of the experimental data
      7. 12.7 Comparison of means requiring nonlinear regression of the experimental data
      8. 12.8 Validation metric for comparing p-boxes
      9. 12.9 References
    4. 13 Predictive capability
      1. 13.1 Step 1: identify all relevant sources of uncertainty
      2. 13.2 Step 2: characterize each source of uncertainty
      3. 13.3 Step 3: estimate numerical solution error
      4. 13.4 Step 4: estimate output uncertainty
      5. 13.5 Step 5: conduct model updating
      6. 13.6 Step 6: conduct sensitivity analysis
      7. 13.7 Example problem: thermal heating of a safety component
      8. 13.8 Bayesian approach as opposed to PBA
      9. 13.9 References
  14. Part V Planning, management, and implementation issues
    1. 14 Planning and prioritization in modeling and simulation
      1. 14.1 Methodology for planning and prioritization
      2. 14.2 Phenomena identification and ranking table (PIRT)
      3. 14.3 Gap analysis process
      4. 14.4 Planning and prioritization with commercial codes
      5. 14.5 Example problem: aircraft fire spread during crash landing
      6. 14.6 References
    2. 15 Maturity assessment of modeling and simulation
      1. 15.1 Survey of maturity assessment procedures
      2. 15.2 Predictive capability maturity model
      3. 15.3 Additional uses of the PCMM
      4. 15.4 References
    3. 16 Development and responsibilities for verification, validation and uncertainty quantification
      1. 16.1 Needed technical developments
      2. 16.2 Staff responsibilities
      3. 16.3 Management actions and responsibilities
      4. 16.4 Development of databases
      5. 16.5 Development of standards
      6. 16.6 References
  15. Appendix: Programming practices
  16. Index