VERIFICATION AND VALIDATION OF CFD SIMULATIONS

1 VERIFICATION AND VALIDATION OF CFD SIMULATIONSbyFred Stern, Robert V. Wilson, Hugh W. Coleman*, and Eric G. PatersonofIowa Institute of Hydraulic Researchand* Propulsion Research CenterMechanical and Aerospace Engineering DepartmentUniversity of Alabama in HuntsvilleHuntsville AL 35899 Sponsored byOffice of Naval ResearchGrant N00014-96-1-0018 Grant N00014-97-1-0014*Grant N00014-97-1-0151 IIHR Report No. 407 Iowa Institute of Hydraulic ResearchCollege of EngineeringThe University of IowaIowa City IA 52242 September 1999iiTable Of VERIFICATION and VALIDATION VERIFICATION and VALIDATION Concepts and Convergence Iterative Monotonic Convergence: Generalized Richardson Oscillatory Single CFD Comparison of Multiple Codes and/or Prediction of Corrected vs. Uncorrected Example for RANS CFD Geometry, Conditions, and Benchmark VERIFICATION and VALIDATION of Integral Variable: VERIFICATION and VALIDATION of Point Variable: Wave and A.

2 Derivation of simulation Error B. Generalized Richardson C. Analytical and VALIDATION methodology is presented for CFD simulation results froman already developed RANS CFD code applied for specified objectives, geometry,conditions, and available benchmark information. Concepts and definitions are providedfor errors and uncertainties and VERIFICATION and VALIDATION . The simulation error anduncertainty equations are derived with modeling and numerical errors being additive andmodeling and numerical uncertainties combining by root-sum-square. The concepts anddefinitions provide the mathematical framework for the VERIFICATION and is defined as a process for assessing numerical uncertainty and, whenconditions permit, estimating the sign and magnitude of the numerical error itself and theuncertainty in that error estimate.

3 Iterative and parameter convergence studies areconducted using multiple solutions with systematic parameter refinement to estimatenumerical errors and uncertainties. Three convergence conditions are possible: (i)monotonic convergence; (ii) oscillatory convergence; and (iii) divergence. For condition(i), generalized Richardson extrapolation for J input parameters and use of correctionfactors to account for the effects of higher-order terms and defining and estimating errorsand uncertainties is used. For condition (ii), the upper and lower bounds of the solutionoscillation are used to estimate uncertainties. For condition (iii), errors and uncertaintiescan not be is defined as a process for assessing modeling uncertainty by usingbenchmark experimental data and, when conditions permit, estimating the sign andmagnitude of the modeling error itself.

4 The comparison error (difference between data andsimulation values) and VALIDATION uncertainty (combination of uncertainties in data andportion of simulation uncertainties that can be estimated) are used in this example is provided for a RANS CFD code and results for steady flow for acargo/container research was sponsored by the Office of Naval Research under Grants N00014-96-1-0018, N00014-97-1-0014, and N00014-97-1-0151 under the administration of Rood. The authors gratefully acknowledge Dr. Rood and other colleagues, especiallyProf. Steele and Dr. H. Raven, who made significant contributions throughinsightful discussions and comments on early drafts. The recent Masters Theses ofMessrs. B. Chen and G. Dolphin and Thesis of Dr. Rhee all at The Universityof Iowa, Department of Mechanical Engineering were helpful both in the development andtesting of the present VERIFICATION and VALIDATION procedures and factorDbenchmark dataE, ECcomparison error, correctedpkorder of accuracyRkparameter refinement ratioS, SCsimulation result, correctedTtruthUuncertainty estimateDUdata uncertaintyEU,CEUcomparison error uncertainty, correctedIUiteration uncertaintyCPPUU,parameter uncertainty ( , grid size G and time step T), correctedreqdUprogrammatic VALIDATION requirementCSSUU, simulation uncertainty, correctedSMUsimulation modeling uncertaintySMAU simulation modeling assumption uncertaintySPDU simulation uncertainty due to use of previous dataNSSNCUU, simulation numerical uncertainty, correctedCVVUU, VALIDATION uncertainty, correctedkx increment in kth input parameter ( , grid size G and time step T)

5 Error error estimate with sign and magnitude II ,iteration error, estimate PP ,parameter error, estimateCSS , simulation error, correctedSN simulation numerical errorSMA simulation modeling assumption error solution changeSN error in 11. IntroductionDiscussion and methodology for estimating errors and uncertainties incomputational fluid dynamics (CFD) SIMULATIONS has reached a certain level of maturitywith increased attention and recent progress on common concepts and terminology(AIAA, 1998), advocacy and detailed methodology (Roache, 1998), and numerous casestudies ( , Mehta, 1998). Progress has been accelerated in response to the urgent needfor achieving consensus on concepts and terminology and useful methodology, as CFD isapplied to increasingly complex geometry and physics and integrated into the engineeringdesign process. Such consensus is required to realize the goals of simulation -based designand other uses of CFD such as simulating flows for which experiments are difficult ( ,full-scale Reynolds numbers, hypersonic flows, off-design conditions).

6 In spite of theprogress and urgency, the various viewpoints have not converged and currentmethodology falls short of providing practical procedures and methodology for estimatingerrors and uncertainties in CFD present work provides a pragmatic approach for estimating errors anduncertainties in CFD SIMULATIONS . Previous work on VERIFICATION (Stern et al., 1996) isextended and put on a more rigorous foundation and combined with subsequent work onvalidation (Coleman and Stern, 1997) [hereafter referred to as C&S] thereby providing theframework for overall procedures and methodology. The philosophy is stronglyinfluenced by experimental fluid dynamics (EFD) uncertainty analysis (Coleman andSteele, 1999), which has been standardized. Hopefully, CFD VERIFICATION and validationprocedures and methodology can reach a similar level of maturity and user variability canreach similar low levels, as for work is part of a larger program (Rood, 1996) for developing andimplementing a strategy for VERIFICATION and VALIDATION of Reynolds-averaged Navier-Stokes (RANS) ship hydrodynamics CFD codes.

7 The program includes complementaryCFD and EFD towing-tank investigations and considers errors and uncertainties in boththe SIMULATIONS and the data in assessing the success of the VERIFICATION and validationefforts. The work also benefited from collaboration with the 21st and 22nd InternationalTowing Tank Resistance Committees (ITTC, 1996 and 1999).The focus is on VERIFICATION and VALIDATION procedures and methodology for CFDsimulation results from an already developed CFD code applied for specified objectives,geometry, conditions, and available benchmark information. The procedures andmethodology were developed considering RANS CFD codes, but should be applicable toa fairly broad range of codes such as boundary-element methods and certain aspects oflarge-eddy and direct numerical present work differs in many respects from recent literature.

8 The presentationis relatively succinct with intention for use for practical applications ( , industrial CFD)for which numerical errors and uncertainties can not be considered negligible oroverlooked. The definitions of errors and uncertainties and VERIFICATION and VALIDATION thatare used in any approach need to be clearly stated. Table 1 summarizes the presentdefinitions along with those given by the AIAA (1998) and Roache (1998) forcomparison. The present and Roache (1998) definitions for errors and uncertainties areconsistent with those used for EFD. The AIAA (1998) definitions are from an information2theory perspective and differ from those used in EFD, but are not contradictory to thepresent definitions. The present definitions for VERIFICATION and VALIDATION are closely tiedto the present definitions of errors and uncertainties and equations derived for simulationerrors and uncertainties.

9 The Roache (1998) and AIAA (1998) definitions are broader,but not contradictory to the present definitions. The present approach includes both thesituations (1) of estimating errors and the uncertainty of those estimates and (2) ofestimating uncertainties only. Richardson extrapolation (RE) is used for VERIFICATION ,which is not new; however, the present generalizations for J input parameters and use ofcorrection factors to account for the effects of higher-order terms and in defining andestimating errors and uncertainties constitute a new approach. The use of quantitativeestimates for errors and the use of uncertainties for those estimates also constitute a newapproach in VERIFICATION and VERIFICATION and VALIDATION ProceduresThe overall CFD VERIFICATION and VALIDATION procedures can be conveniently grouped infour consecutive steps: (1) preparation; (2) VERIFICATION ; (3) VALIDATION ; and (4) The 1st step is preparation, which involves selection of the CFD codeand specification of objectives, geometry, conditions, and available benchmarkinformation.

10 The objectives might be prediction of certain variables at certain levels ofvalidation ( , programmatic VALIDATION requirements reqdU). The variables can either beintegral ( , resistance) or point ( , mean velocities and turbulent Reynolds stresses)values and the programmatic VALIDATION requirements may be different for each The 2nd step is VERIFICATION , which is defined as a process for assessingsimulation numerical uncertainty SNU and, when conditions permit, estimating the signand magnitude SN of the simulation numerical error itself and the uncertainty in thaterror estimate (referred to as the corrected simulation numerical uncertainty NSCU).Iterative and input parameter convergence studies are conducted using multiple solutionswith systematic parameter, as described in Section The 3rd step is VALIDATION , which is defined as a process for assessingsimulation modeling uncertainty SMU by using benchmark experimental data and, whenconditions permit, estimating the sign and magnitude of the simulation modeling error SM itself.