Verification and validation in computational fluid dynamics

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 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. (C) 2002 Published by Elsevier Science Ltd.