On comparison of solutions at verification

The impact of a proximity measure on the comparison of the numerical and etalon solutions is addressed from the viewpoint of the verification of solutions and codes. The deterministic and stochastic options for the estimation of the discretization error are considered via the ensemble of numerical solutions obtained by different schemes if etalon solutions are not available. The relation of the solution error norm and the valuable functional errors is studied via Cauchy–Bunyakovsky–Schwarz inequality. The results of the numerical tests are provided for the two-dimensional Euler equations and demonstrate the impact of proximity measure on the error estimation by the ensemble of solutions and the efficiency of considered algorithms. The comparison of different proximity measure choice (norms and metrics) for the estimation of the discretization error and for the comparison of flowfields corresponding to both the small flow structure variations and qualitatively different flow patterns is the new element of the paper. The application the valuable functional error for treating the approximation errors is also novel. The feasibility for computationally cheap (single grid, in contrast to the Richardson extrapolation) quantitative verification of solutions and codes considered and demonstrated in the paper may be useful at application of the Russian Federation standards concerning CFD codes and solutions verification.