Ensemble-type numerical uncertainty information from single model integrations

Rauser, Florian; Marotzke, Jochem; Korn, Peter

doi:10.1016/j.jcp.2015.02.043

Cited by 8 publications

(5 citation statements)

References 15 publications

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“…Существует ряд численных работ (например, [16]), которые основаны на том, что ошибка расчета (дискретизации)…”

Section: свойства погрешностей расчета и усеченияunclassified

“…Соответственно, два независимо выбранных вектора в пространстве большой размерности также "почти всегда" ортогональны. Таким образом, вполне детерминированные объекты приобретают некоторые статистические свойства, что образует параллель с результатами работ [14,16], касающихся статистических свойств ошибок усечения и аппроксимации.…”

Section: ортогональность в пространстве большой размерности и оценки unclassified

“…Оценки, полученные с помощью (16) и (17), достаточно близки даже для схем номинально высокого порядка. Это, вероятно, вызвано тем, что основная погрешность в данных тестах определяется скачками уплотнения и в соответствии с [38,39] имеет порядок, близкий к единице.…”

Section: численная оценка погрешности усеченияunclassified

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The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

Alekseev

Bondarev

2019

KIAM Prepr.

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Section: свойства погрешностей расчета и усеченияunclassified

Section: ортогональность в пространстве большой размерности и оценки unclassified

Section: численная оценка погрешности усеченияunclassified

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The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

Alekseev

Bondarev

2019

KIAM Prepr.

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“…A huge number of works are devoted to these studies. As an example, we can point to the works [1][2][3][4][5][6][7][8][9][10][11][12]. Verification of the obtained results and assessment of the accuracy of the applied numerical method was an obligatory part of research in the field of mathematical modeling of physical processes.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

On the construction of a generalized computational experiment in verification problems

Alekseev¹,

Bondarev²,

Галактионов³

et al. 2020

MathMon

View full text Add to dashboard Cite

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 applications of such approach in the presence of a reference solution and in its absence are discussed. An example of error surfaces constructing 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 problemthe Mach number and angle of attackare considered. In addition to the OpenFOAM solvers, the comparison included the WW method, which has a second order of accuracy in time and space and an adjustable artificial viscosity. 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.

show abstract

Ensemble-type numerical uncertainty information from single model integrations

Cited by 8 publications

References 15 publications

The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

On Applying of Generalized Computational Experiment to Numerical Methods Verification

On the construction of a generalized computational experiment in verification problems

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