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Generalized Computational Experiment and Verification Problems

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Abstract

This paper considers the construction of a generalized computational experiment for solving verification problems. The problem of comparative accuracy assessment of numerical methods is currently acquiring special relevance due to the introduction of published standards and widespread use of software packages that include a large number of different solvers. A generalized computational experiment makes it possible to obtain a numerical solution for a class of problems determined by variation ranges of their governing parameters. Analysis of results represented as multidimensional arrays, where the number of measurements depends on the dimension of the space of governing parameters, requires the use of scientific visualization and visual analytics tools. Some approaches to the application of generalized computational experiments with and without a reference solution are discussed. An example of constructing error surfaces when comparing some solvers from the OpenFOAM software package is considered. The classical problem of an inviscid oblique shock wave is used as a basic problem. Certain variations of its main parameters—Mach number and angle of attack—are analyzed. In addition, we consider an example of the cone flow problem with variable Mach number, cone angle, and angle of attack. The concept of an error index is introduced as an integral characteristic of deviations from the exact solution for each solver in the class of problems under consideration.

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Correspondence to A. K. Alekseev, A. E. Bondarev, V. A. Galaktionov or A. E. Kuvshinnikov.

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Translated by Yu. Kornienko

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Alekseev, A.K., Bondarev, A.E., Galaktionov, V.A. et al. Generalized Computational Experiment and Verification Problems. Program Comput Soft 47, 177–184 (2021). https://doi.org/10.1134/S0361768821030026

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