Proceedings of CHT 04 ICHMT International Symposium on Advances in Computational Heat Transfer April 19 24 2004 Norway CHT 04 V1 QUANTITATIVE V V OF CFD SIMULATIONS AND CERTIFICATION OF CFD CODES WITH EXAMPLES Fred Stern Robert Wilson Jun Shao IIHR Hydroscience Engineering The University of Iowa Iowa City IA 52246 Correspondence author Fax 319 335 5238 Email Frederick stern uiowa edu ABSTRACT Definitions and equations are provided for quantitative assessment of numerical verification and modeling validation errors and uncertainties for CFD simulations and of intervals of certification for CFD codes Verification validation and certification methodology and procedures are described Examples are presented of quantitative V V for RANS and DES simulations and certification of RANS codes for ship hydrodynamics applications Opportunities and challenges for achieving consensus and standard V V and certification methodology and procedures are discussed INTRODUCTION In spite of the ever increasing need and importance for standards for computational fluid dynamics CFD uncertainty analysis accuracy estimation there are currently many viewpoints covering all aspects from basic concepts and definitions to detailed methodology and procedures A similar situation existed for experimental fluid dynamics EFD uncertainty analysis ca 1960 for which currently standards are widely accepted and available although widespread use is still lacking Pioneering work was done by Roache 1 who proposed the grid convergence index GCI for estimating uncertainty due to grid and time step errors based on Richardson extrapolation RE using multiple solutions on systematically refined grids thereby providing a quantitative metric for verification Ref 2 expanded on this work through overall discussion of verification and validation V V including use of EFD definitions for errors and uncertainties phrases e g verification deals with equations solved correctly and validation with correct equations and verification deals with mathematics and validation with physics and activities e g method of manufactured solutions and benchmark solutions for verification and use of experimental data for validation defining V V discussion for V V of both codes and solutions many case studies demonstrating use of GCI single grid error estimation methods and broader issues such as code quality assurance and certification Such definitions for V V however in the authors viewpoint are inadequate Quantitative metrics are needed for both verification and validation and methodology is needed for combining errors and uncertainties The AIAA Committee on Standards for CFD 3 and Guide for V V of CFD Simulations 4 uses definitions from information theory for errors and uncertainties with emphasis on measurement of accuracy as opposed to estimation of errors and uncertainties follows Roache s phrases and expands considerably on his activities along with broad statements in defining V V discusses mostly code but also solution V V and additionally discusses policy statements on experimental and numerical accuracy Code verification activities measure accuracy in relation to benchmark analytical and ordinary and partial differential equation solutions for simplified problems along with software quality assurance identify quantify and reduce errors in the computational model and its numerical solution Model validation activities measure accuracy in relation to experimental data with emphasis on validation tiers based on unit problems benchmark cases subsystem cases and complete systems identify and quantify error and uncertainty in the conceptual and computational models quantify the numerical error in the computational solution estimate the experimental uncertainty and compare the computational and experimental results Solution verification largely follows Roache in using GCI along with consistency and iterative convergence checks Rigorous implementation is impressive 5 6 nonetheless these definitions are subject to same criticisms mentioned earlier Another problem with such definitions is lack of an overall mathematical framework for V V which is considered essential in the author s viewpoint similarly as it is an essential and integral part of EFD uncertainty analysis The literature also includes editorial policy statements 7 additional guidelines 8 and numerous case studies which mostly focus on verification procedures for 2D problems e g volume 36 of the AIAA Journal and volume 124 of the ASME Journal of Fluids Engineering In general this literature follows approaches similar to that described above The authors and colleagues 9 developed an alternative quantitative approach to solution V V specifically for already developed CFD codes for industrial applications geometry and domain models initial boundary and other conditions fluid properties and input parameters such as iteration numbers and grid and time step sizes which differs considerably from previous approaches It is assumed that code verification and quality assurance issues have already been dealt with during code development Similarly if appropriate it is assumed that model validation for simplified problems has also already been dealt with during model development The philosophy is strongly influenced by EFD uncertainty analysis 10 including use of EFD definitions for errors and uncertainties The methodology is based on concepts definitions and equations derived for simulation errors and uncertainties which provide the overall mathematical framework Verification procedures for estimating numerical errors and uncertainties include 1 the options of estimating the numerical uncertainty or the numerical error itself which is used to obtain a corrected solution and its uncertainty and 2 the concept of correction factors based on analytical benchmarks Previously developed validation methodology and procedures for estimating modeling errors and uncertainties 11 were extended to include the option of use of corrected solutions The V V approach 9 has been shown successful in establishing intervals of V V for RANS simulations for ship hydrodynamics by present authors and colleagues 12 18 and international colleagues through its use at recent Gothenburg 2000 Workshop on CFD in Ship Hydrodynamics 19 A shortcoming of this and other V V approaches is that the justification for uncertainty estimates at 95 confidence level is based on reasoning similar to that used for EFD bias uncertainties at the 0order
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