Factors of Safety for Richardson Extrapolation
Abstract
A factor of safety (FS) method for quantitative estimates of grid/time uncertainties for CFD solutions is derived to remove the deficiencies of GCI, corrected GCI(sub C), and correction factor (CF) methods, i.e., unreasonably small uncertainty when CF > 1 (estimated order of accuracy greater than theoretical) and lack of statistical analysis to prove 95% confidence for the estimated uncertainties to bound the true error. The approach follows the CF method but reflects the uncertainty instead of FS for CF < 1 for CF > 1 (CF = 1 is asymptotic range). FS at CF = 0 and 1 are determined by reliability and lower band of the confidence interval of the true mean based on statistical analysis using a large sample of analytical/numerical benchmarks covering 17 studies, 96 variables and 304 individual grid triplets. Only the FS method provides 95% confidence that the actual factor of safety FS(sub A) > 1 for the 304 grid convergence studies: confidence intervals are 86.2%, 92.1%, 91.5%, and 95.7% for GCI, GCI(sub C), CF, and FS. For 20% of the data 1.1 smaller or equal CF < 2.0, GCI, GCI(sub C), and CF methods fail as only 47.4%, 71.2%, 72.9% confidence intervals are achieved, whereas 89.3% is achieved for the FS method. Only the FS method has 95% confidence the lower band of the confidence interval for FS(sub A) is larger than 1.2 for different studies, variables, ranges of CF, and single CF values where multiple FS(sub A) are available.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 2009
- Accession Number
- ADA498086
Entities
People
- Fred Stern
- Tao Xing
Organizations
- University of Iowa