doi: 10.18698/2309-3684-2017-4-6072
The article introduces a dependency for the pressure distribution in the disturbed region near the sphere streamlined by the flow of the supersonic inviscid gas, obtained when modifying the Shepard’s Method. We use known ratios for the pressure on the body and the shockwave as well as data from the numerical experiments. We have compared the results with the data not used in the learning process of the dependency coefficients. This comparison proves high confidence of the model obtained.
[1] Kotenev V.P. Matematicheskoe Modelirovanie — Mathematical Models and Computer Simulations, 2014, vol. 26, no. 9, pp. 141–148.
[2] Abramovich G.N. Prikladnaya gazovaya dinamika. V 2 ch. Ch. 1 [Applied gas dynamics. In 2 parts. Part 1]. Moscow, Nauka, Gl. red. fiz-mat. lit Publ., 1991, 600 p.
[3] Lyubimov A.N., Rusanov V.V. Techeniya gaza okolo tupykh tel. V 2 t. T. 2. [Gas flow near the stub bodies. In 2 vols. Vol. 2]. Moscow, Nauka Publ., 1970, pp. 30–49.
[4] Draper N.R., Smith H. Applied regression analysis (Wiley series in probability and statistics). Wiley-Interscience Publ., 1998, 736 p. [In Russ.: Draper N., Smith H. Prikladnoy regressionnyy analiz. Moscow, Dialektika Publ., 2007, 912 p.].
[5] Ferster E., Renc B. Methoden der Korrelation — und Regressiolynsanalyse. [In Russ.: Ferster E., Renc B. Metody korreliatsionnogo i regressionnogo analiza [The methods of correlation and regression analysis]. Moscow, Finansy i statistika Publ., 1981, 302 p.].
[6] Masyukov A.V. Vestnik Tverskogo gosudarstvennogo universiteta. Seriya: Prikladnaya matematika — Herald of Tver State University. Series: Applied Mathematics, 2007, no. 4, pp. 99–112.
[7] Shepard D. A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 1968 23rd ACM National Conference, 1968, pp. 517–524.
[8] Tonkikh E.G., Sapozhnikov D.A. Molodezhnyy nauchno-tekhnicheskiy vestnik (Youth scientific and technical bulletin), 2017, no. 5. Available at: http://sntbul.bmstu.ru/doc/859353.html (аccessed January 11, 2017).
[9] Vapnik V.N. Vosstanovlenie zavisimostey po empiricheskim dannym [Restoring dependencies using the empirical data]. Moscow, Nauka Publ., 1979, 448 p.
[10] Kotenev V.P., Sysenko V.A. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2015, no. 7, pp. 58–67.
[11] Flach P. Machine Learning: The art and science of algorithms that make sense of data. Cambridge, 2012, 349 p. [In Russ.: Flach P. Mashinnoe obuchenie. Nauka i iskusstvo postroeniya algoritmov, kotorye izvlekayut znaniya iz dannykh. Uchebnik. Moscow, DMK Press Publ., 2015, 400 p.].
[12] Witten I.H., Frank E. Data mining. Practical machine learning tools and techniques. Morgan Kaufmann Publishers, 2005, 525 p.
[13] Bazzhin A.P., Blagosklonov V.I., Minaylos A.N., Pirogova S.V. Uchenye zapiski TsAGI — TsAGI Science Journal, 1971, vol. 2, no. 3, pp. 95–100.
[14] Dimitrienko Yu.I., Kotenev V.P., Zakharov A.A. Metod lentochnykh adaptivnykh setok dlya chislennogo modelirovaniya v gazovoy dinamike [The method of belt adaptive grids for computational modelling in gas dynamics]. Moscow, FIZMATLIT Publ., 2011, 280 p.
[15] Bazilevskiy M.P. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2016, no. 10, pp. 104–116.
[16] Kotenev V.P., Ratslav R.A., Sapozhnikov D.A., Chernyshev I.V. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2017, no. 3, pp. 83–104.
[17] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2015, no. 8, pp. 75–91.В.П. Котенев, А.С. Пучков, Д.А. Сапожников, Е.Г. Тонких 72
[18] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A., Stroganov A.S. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 3, pp. 3–24.
[19] Dimitrienko Y., Koryakov M., Zakharov A. Finite Difference Methods, Theory and Applications, 2014, pp. 161–168.
Kotenev V.P., Puchkov A.S., Sapozhnikov D.A., Tonkikh E.G. Simulation of the pressure distribution in the disturbed region near the sphere streamlined by the inviscid flotation by means of the machine learning methods. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 60-72
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