A statistical approach for computational fluid dynamics (CFD) state-of-the-art (SoA) assessment is presented for specified benchmark test cases and validation variables, based on the combination of solution and N-version verification and validation (V&V). Solution V&V estimates the systematic numerical and modeling errors/uncertainties. N-version verification estimates the random simulation uncertainty. N-version validation estimates the random absolute error uncertainty, which is combined with the experimental and systematic numerical uncertainties into the SoA uncertainties and then used to determine whether or not the individual codes/simulations and the mean code are N-version validated at the USoAi and USoA intervals, respectively. The scatter is due to differences in models and numerical methods, grid types, domains, boundary conditions, and other setup parameters. Differences between codes/simulations and implementations are due to myriad possibilities for modeling and numerical methods and their implementation as CFD codes and simulation applications. Industrial CFD codes are complex software with many user options such that even in solving the same application, different results may be obtained by different users, not necessarily due to user error but rather the variability arising from the selection of various models, numerical methods, and setup options. Examples are shown for ship hydrodynamics applications using results from the Seventh CFD Ship Hydrodynamics and Second Ship Maneuvering Prediction Workshops. The role and relationship of individual code solution V&V versus N-version V&V and SoA assessment are discussed.
MFIX-Exa: A path toward exascale CFD-DEM simulations
