Comparative Evaluation of the Accuracy of Numerical Methods on Reference Solutions

Abstract

When organizing a mass practical solution of computational problems of gas dynamics with the help of mathematical modeling, information on the comparative accuracy of the numerical methods used is now increasingly in demand. As a rule, calculators need information not only for a particular combination of the defining gas-dynamic parameters of the problem (characteristic Mach, Reynolds numbers, etc.), but also for the variation of these parameters in certain ranges. This work presents numerical studies devoted to a comparative assessment of the accuracy of numerical methods for a number of problems with reference solutions. The calculation of these problems is carried out for ranges of characteristic numbers using various numerical methods. The results obtained are compared with the reference solution and make it possible to estimate the error for each of the numerical methods. Calculations are carried out using the construction of a generalized computational experiment. A generalized computational experiment is a computational technology that combines the solution of mathematical modeling problems, parallel technologies and visual analytics technologies. The results of the generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the defining parameters. Analysis and visual representation of the obtained results provide information on the comparative accuracy of the numerical method for the selected class of problems.