Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures

TLDR

The paper establishes a mathematical framework for CFD simulation errors and uncertainties, defining verification as the assessment of numerical uncertainty and potential error magnitude, and validation as the assessment of modeling uncertainty using benchmark experimental data. It aims to present a comprehensive verification and validation methodology for CFD simulations that can be applied to existing codes without source‑code access, and to illustrate the approach with a RANS example for a cargo/container ship. The methodology estimates errors by treating numerical error as deterministic or stochastic, applying generalized Richardson extrapolation to input parameters, and using correction factors from analytical benchmarks, while also incorporating uncertainties from both simulation and experimental data into the validation assessment. The study discusses how validation results differ when numerical error is treated deterministically versus stochastically, highlighting interpretation strategies for each case.

Abstract

Part 1 of this two-part paper presents a comprehensive approach to verification and validation methodology and procedures for CFD simulations from an already developed CFD code applied without requiring availability of the source code for specified objectives, geometry, conditions, and available benchmark information. Concepts, definitions, and equations derived for simulation errors and uncertainties provide the overall mathematical framework. Verification is defined as a process for assessing simulation numerical uncertainty and, when conditions permit, estimating the sign and magnitude of the numerical error itself and the uncertainty in that error estimate. The approach for estimating errors and uncertainties includes (1) the option of treating the numerical error as deterministic or stochastic, (2) the use of generalized Richardson extrapolation for J input parameters, and (3) the concept of correction factors based on analytical benchmarks, which provides a quantitative metric to determine proximity of the solutions to the asymptotic range, accounts for the effects of higher-order terms, and are used for defining and estimating errors and uncertainties. Validation is defined as a process for assessing simulation modeling uncertainty by using benchmark experimental data and, when conditions permit, estimating the sign and magnitude of the modeling error itself. The approach properly takes into account the uncertainties in both the simulation and experimental data in assessing the level of validation. Interpretation of results of validation efforts both where the numerical error is treated as deterministic and stochastic are discussed. Part 2 provides an example for RANS simulations for a cargo/container ship where issues with regard to practical application of the methodology and procedures and interpretation of verification and validation results are discussed.