Verification and validation (V&V) are the primary means to assess accuracy and reliability in computational simulations. This paper presents an extensive review of the literature in V&V in computational fluid dynamics (CFD), discusses methods and procedures for assessing V&V, and develops a number of extensions to existing ideas. The review of the development of V&V terminology and methodology points out the contributions from members of the operations research, statistics, and CFD communities. Fundamental issues in V&V are addressed, such as code verification versus solution verification, model validation versus solution validation, the distinction between error and uncertainty, conceptual sources of error and uncertainty, and the relationship between validation and prediction. The fundamental strategy of verification is the identification and quantification of errors in the computational model and its solution. In verification activities, the accuracy of a computational solution is primarily measured relative to two types of highly accurate solutions: analytical solutions and highly accurate numerical solutions. Methods for determining the accuracy of numerical solutions are presented and the importance of software testing during verification activities is emphasized. The fundamental strategy of 1 Accepted for publication in the review journal Progress in Aerospace Sciences.3 validation is to assess how accurately the computational results compare with the experimental data, with quantified error and uncertainty estimates for both. This strategy employs a hierarchical methodology that segregates and simplifies the physical and coupling phenomena involved in the complex engineering system of interest. A hypersonic cruise missile is used as an example of how this hierarchical structure is formulated. The discussion of validation assessment also encompasses a number of other important topics. A set of guidelines is proposed for designing and conducting validation experiments, supported by an explanation of how validation experiments are different from traditional experiments and testing. A description is given of a relatively new procedure for estimating experimental uncertainty that has proven more effective at estimating random and correlated bias errors in wind-tunnel experiments than traditional methods. Consistent with the authors' contention that nondeterministic simulations are needed in many validation comparisons, a three-step statistical approach is offered for incorporating experimental uncertainties into the computational analysis. The discussion of validation assessment ends with the topic of validation metrics, where two sample problems are used to demonstrate how such metrics should be constructed. In the spirit of advancing the state of the art in V&V, the paper concludes with recommendations of topics for future research and with suggestions for needed changes in the implementation of V&V in production and commercial software.4 Acknowledgements

Developers of computer codes, analysts who use the codes, and decision makers who rely on the results of the analyses face a critical question: How should confidence in modeling and simulation be critically assessed? Verification and validation (V&V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue.-3 -This paper presents our viewpoint of the state of the art in V&V in computational physics. (In this paper we refer to all fields of computational engineering and physics, e.g., computational fluid dynamics, computational solid mechanics, structural dynamics, shock wave physics, computational chemistry, etc., as computational physics.) We do not provide a comprehensive review of the multitudinous contributions to V&V, although we do reference a large number of previous works from many fields. We have attempted to bring together many different perspectives on V&V, highlight those perspectives that are effective from a practical engineering viewpoint, suggest future research topics, and discuss key implementation issues that are necessary to improve the effectiveness of V&V. We describe our view of the framework in which predictive capability relies on V&V, as well as other factors that affect predictive capability. Our opinions about the research needs and management issues in V&V are very practical: What methods and techniques need to be developed and what changes in the views of management need to occur to increase the usefulness, reliability, and impact of computational physics for decision making about engineering systems?We review the state of the art in V&V over a wide range of topics, for example, prioritization of V&V activities using the Phenomena Identification and Ranking Table (PIRT), code verification, software quality assurance (SQA), numerical error estimation, hierarchical experiments for validation, characteristics of validation experiments, the need to perform nondeterministic computational simulations in comparisons with experimental data, and validation metrics. We then provide an extensive discussion of V&V research and implementation issues that we believe must be addressed for V&V to be more effective in improving confidence in computational predictive capability. Some of the research topics addressed are development of improved procedures for the use of the PIRT for prioritizing V&V activities, the method of manufactured solutions for code verification, development and use of hierarchical validation diagrams, and the construction and use of validation metrics incorporating statistical measures. Some of the implementation topics address...

Verification and validation (V&V) are the primary means to assess accuracy and reliability in computational simulations. This paper presents an extensive review of the literature in V&V in computational fluid dynamics (CFD), discusses methods and procedures for assessing V&V, and develops a number of extensions to existing ideas. The review of the development of V&V terminology and methodology points out the contributions from members of the operations research, statistics, and CFD communities. Fundamental issues in V&V are addressed, such as code verification versus solution verification, model validation versus solution validation, the distinction between error and uncertainty, conceptual sources of error and uncertainty, and the relationship between validation and prediction. The fundamental strategy of verification is the identification and quantification of errors in the computational model and its solution. In verification activities, the accuracy of a computational solution is primarily measured relative to two types of highly accurate solutions: analytical solutions and highly accurate numerical solutions. Methods for determining the accuracy of numerical solutions are presented and the importance of software testing during verification activities is emphasized. The fundamental strategy of 1 Accepted for publication in the review journal Progress in Aerospace Sciences.3 validation is to assess how accurately the computational results compare with the experimental data, with quantified error and uncertainty estimates for both. This strategy employs a hierarchical methodology that segregates and simplifies the physical and coupling phenomena involved in the complex engineering system of interest. A hypersonic cruise missile is used as an example of how this hierarchical structure is formulated. The discussion of validation assessment also encompasses a number of other important topics. A set of guidelines is proposed for designing and conducting validation experiments, supported by an explanation of how validation experiments are different from traditional experiments and testing. A description is given of a relatively new procedure for estimating experimental uncertainty that has proven more effective at estimating random and correlated bias errors in wind-tunnel experiments than traditional methods. Consistent with the authors' contention that nondeterministic simulations are needed in many validation comparisons, a three-step statistical approach is offered for incorporating experimental uncertainties into the computational analysis. The discussion of validation assessment ends with the topic of validation metrics, where two sample problems are used to demonstrate how such metrics should be constructed. In the spirit of advancing the state of the art in V&V, the paper concludes with recommendations of topics for future research and with suggestions for needed changes in the implementation of V&V in production and commercial software.4 Acknowledgements

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The Predictive Capability Maturity Model (PCMM) is a new model that can be used to assess the level of maturity of computational modeling and simulation (M&S) efforts. The development of the model is based on both the authors' experience and their analysis of similar investigations in the past. The perspective taken in this report is one of judging the usefulness of a predictive capability that relies on the numerical solution to partial differential equations to better inform and improve decision making. The review of past investigations, such as the Software Engineering Institute's Capability Maturity Model Integration and the National Aeronautics and Space Administration and Department of Defense Technology Readiness Levels, indicates that a more restricted, more interpretable method is needed to assess the maturity of an M&S effort.