On the construction of a generalized computational experiment in verification problems

Alekseev, A. K.; Bondarev, A. E.; Галактионов, В. А.; Kuvshinnikov, Artem E.

doi:10.20948/mathmontis-2020-48-3

Cited by 4 publications

(6 citation statements)

References 28 publications

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“…Explicit schemes are schemes in which the future distribution of matter is completely calculated based on the existing distribution of matter and known velocities of movement [3,6,19]. The most common calculation schemes are directional difference schemes [5,6,8,18,20].…”

Section: Resultsmentioning

confidence: 99%

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An improved finite-difference scheme for the conservation equations of matter

et al. 2023

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The finite-difference scheme of directed differences (the Courant-Isaacson-Ries scheme), which is widely used in the practice of aerohydrodynamic calculations, is studied theoretically and on the example of test problems. We applied the commonly used in practice Courant-Isakson-Ries directional difference scheme that allowed us to find and show distributions of velocities where the laws of the matter conservation are violated in the calculations in solving the matter conservation equations or the correspondence of the obtained solutions to the most general practical understandings on the essence of the matter transfer. A scheme free from the shortcomings of the Courant-Isaacson-Ries scheme has been constructed, tested, and proposed for use in aerohydrodynamic calculations by the finite difference method. Moreover, all the valuable properties of this well-known scheme are preserved. Among the maintained properties: are transportability, conservatism, stability in calculations, invariance, and adequacy of the essence of the physical phenomenon of the transfer of matter in space. The disadvantages of the new finite-difference scheme proposed for solving the equations of conservation of matter should be considered: an increase in the required RAM for storing electronic means of calculating information about the velocity field in memory and an increase in the number of calculations needed.

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Section: Resultsmentioning

confidence: 99%

“…This happened due to Courant, Isaacson, Rees, Levy [3]. They developed and researched a finite-difference scheme that makes it possible to calculate the effect of both inertial terms in the equations of motion and convection terms in the equations of conservation of the mass of a moving medium.…”

Section: Introductionmentioning

confidence: 99%

An improved finite-difference scheme for the conservation equations of matter

et al. 2023

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“…A large number of different applications of a generalized computational experiment are described in detail in [16][17][18][19][20][21][22][23][28][29][30]. The concept of a generalized computational experiment was applied to a wide range of both model and practical problems.…”

Section: Generalized Computational Experimentsmentioning

confidence: 99%

“…This section provides two examples of constructing a generalized computational experiment for a comparative assessment of numerical methods accuracy. As examples, we use the numerical results described in detail in the authors' works [20,23,29,30]. In these papers, two classes of computational gas dynamics problems were considered.…”

Section: Comparative Accuracy Estimation Using Reference Solutionmentioning

confidence: 99%

“…The concept, basic methods and approaches of a generalized computational experiment, as well as a number of software tools for its implementation were developed in Keldysh Institute of Applied Mathematics RAS. The main aspects of constructing a generalized computational experiment and examples of its implementation are described in detail in [16][17][18][19][20][21][22][23][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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On Applying of Generalized Computational Experiment to Numerical Methods Verification

Alekseev

Bondarev

Галактионов

et al. 2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

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This work is devoted to the application of a generalized computational experiment for a comparative assessment of numerical methods accuracy. A generalized computational experiment allows one to obtain a numerical solution for a class of problems determined by the ranges of defining parameters variation. The approaches to the application of a generalized computational experiment in the presence of a reference solution and in its absence are dis-cussed. An example of constructing error surfaces is given when the solvers of the OpenFOAM software package are compared. The classic inviscid problem of oblique shock wave is used as a basic task. Variations of the key parameters of the problem — the Mach number and angle of attack — are considered. An example of the problem of flow around a cone at an angle of attack with varying Mach number, cone angle and angle of attack is also considered. 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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Processing and visualization of the results of parametric numerical calculations

Bondarev

Kuvshinnikov

2021

J. Phys.: Conf. Ser.

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In modern problems of mathematical modeling in computational gas dynamics, it is increasingly necessary to implement parametric studies. In these cases, the key factors of the problem under consideration vary with the chosen step within the given ranges. Calculations of this kind can be effectively carried out by constructing 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 a generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the number of key factors. Processing and visual presentation of such arrays requires solving a number of separate tasks. The processing and visual presentation of the results are carried out for target functionals represented as a function of many variables. The report presents an examples of solving specific processing and visualization problems based on the implemented generalized computational experiment for 3D cone in supersonic flow.

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On the construction of a generalized computational experiment in verification problems

Cited by 4 publications

References 28 publications

An improved finite-difference scheme for the conservation equations of matter

An improved finite-difference scheme for the conservation equations of matter

On Applying of Generalized Computational Experiment to Numerical Methods Verification

Processing and visualization of the results of parametric numerical calculations

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