...Tao Xing; Frederick Stern convergence extrapolation The Technical Brief by Roache [( 1 )] presents ten items of discussion of our factor of safety (FS) method for solution verification [( 2 )]. Our responses are listed below item-by-item using the same numbering as Roache...

...Patrick J. Roache 19 10 2010 28 07 2011 24 10 2011 24 10 2011 convergence of numerical methods extrapolation grid computing hydrodynamics physics computing ships A recent paper by Xing and Stern [( 1 )] provides additional performance data of interest...

... the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy and lack of statistical evidence that the interval of uncertainty at the 95% confidence level bounds the comparison error. Different error estimates are evaluated using the effectivity...

... as a basis for the assessment of the two corrections. After a physical-consistency analysis, the Richardson extrapolation is applied to quantify the numerical errors involved in all the calculations. Finally, experimental data are used to perform validation for both global and local predictions...

... (SGS) model contribution and numerical discretization errors are functions of the grid resolution. In this study, various indexes of quality measures, hereafter referred to as LES̱IQ, are proposed. The recommended LES̱IQ is based on the Richardson extrapolation concept. This method has been applied...

... of several methods of extrapolation. Alternative extrapolation schemes, such as the deferred extrapolation to limit technique, to calculate the coefficients in the Taylor series expansion of the error function are also considered. A new method is proposed that is based on the extrapolation of approximate...

... Extrapolation acting on multiple solutions. Sample test cases of both LES solutions and direct numerical simulations as well as published experimental data show excellent agreement between the integrated matched spectra and the respective turbulent statistics. Thus, the resultant uncertainties themselves...