Comparison of Finite-Difference Schemes for the Burgers Problem

Murodil Erkinjon Ugli  Madaliev; Salimzhan Azamdzhanovich  Rakhmankulov; Mukhsinjon Musajon Ugli  Tursunaliev

doi:10.47494/mesb.2021.18.847

(1) Murodil Erkinjon Ugli Madaliev Fergana Polytechnic Institute, Fergana, Uzbekistan
Uzbekistan
(2) Salimzhan Azamdzhanovich Rakhmankulov Fergana Polytechnic Institute, Fergana, Uzbekistan
Uzbekistan
(3) Mukhsinjon Musajon Ugli Tursunaliev Fergana Polytechnic Institute, Fergana, Uzbekistan
Uzbekistan
(*) Corresponding Author

DOI:

https://doi.org/10.47494/mesb.2021.18.847

Keywords:

Lax method, Lax-Wendroff method, McCormack method, Warming, Cutler, Lomax method

Abstract

A large number of problems in physics and engineering leads to boundary value or initial boundary value problems for linear and nonlinear partial differential equations. At the same time, the number of tasks with analytical solutions is limited. These are problems in canonical domains, such as, for example, a rectangle, a circle, or a ball, and usually for equations with constant coefficients. In practice, it is often necessary to solve problems in very complex areas and for equations with variable coefficients, often nonlinear. This leads to the need to search for approximate solutions using various numerical methods.

Downloads

Download data is not yet available.

References

Ковеня В. М. Разностные методы решения многомерных задач: Курс лекций // Новосиб. гос. ун-т. Новосибирск, 2004. 146 с.

Ковеня В. М, Чирков Д. В. Методы конечных разностей и конечных объемов для решения задач математической физики. Учебное пособие Новосибирск – 2013.

Андерсон Д., Таннехилл Дж., Плетчер Р. Вычислительная гидромеханика и теплообмен: В 2-х т. Т. 1: Пер. с англ. —М.: Мир, 1990. – 384 с.

Burgers J. M. A948). A Mathematical Model Illustrating the Theory of Turbulence.— Adv. Appl. Mech., v. 1, p. 171—199. [Имеется перевод: Бюргере И. М. Об одной математической модели, иллюстрирующей теорию турбулентности. — В сб.: Проблемы механики. — М.: ИЛ, 1955, с. 422— 445.]

Lax P. D. (1954). Weak Solutions of Nonlinear Hyperbolic Equations and their Numerical Computatien. — Comms. Pure and Appl. Math., v. 7, p. 159—193.

Lax P. D., Wendroff B. (1960). Systems of Conservation Laws.— Comms. Pure and Appl. Math., v. 13, p. 217—237.

MacCormack R. W. (1969). The Effect of Viscosity in Hypervelocity Impact Cratering. — AIAA Paper 69—354, Cincinnati, Ohie.

Warming R. F., Kutler P., Lomax H. (1973). Second- and Third-Order Noncen tered Difference Schemes for Nonlinear Hyperbolic Equations. — AIAA Jour- Journal, v. 11, p. 189—196.

Годунов С. К., Забродин А. В., Иванов М. Я., Крайко А. Н., Прокопов Г. П. Численное решение многомерных задач газовой динамики.—М.: Наука, 1976. —400 с.

Malikov Z.M., Madaliev M.E. (2021) Mathematical modeling of a turbulent flow in a centrifugal separator. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika [Tomsk State University Journal of Mathematics and Mechanics]. 71.pp. 121–138

Malikov Z.M, Madaliev M.E. (2020) Numerical Simulation of Two-Phase Flow in a Centrifugal Separator. Fluid Dynamics. 55(8). pp. 1012–1028.

Malikov Z.M., Madaliev M.E. New two-fluid turbulence model-based numerical simulation of flow in a flat suddenly expanding channel. Herald of the Bauman Moscow State Technical University, Series Natural Sciences 4(97). 24–39. (2021). DOI: https://doi.org/10.18698/1812-3368-2021-4-24-39.

Madaliev, E., Madaliev, M., Adilov, K., Pulatov, T. Comparison of turbulence models for two-phase flow in a centrifugal separator. E3S Web of Conferences, 2021, 264, 01009.

Mirzoev, A.A., Madaliev, M., Sultanbayevich, D.Y., Habibullo Ugli, A.U. Numerical modeling of non-stationary turbulent flow with double barrier based on two liquid turbulence model. 2020 International Conference on Information Science and Communications Technologies, ICISCT 2020, 2020, 9351403.

Abdukarimov B. A., O’tbosarov S. R., Tursunaliyev M. M. Increasing Performance Efficiency by Investigating the Surface of the Solar Air Heater Collector //NM Safarov and A. Alinazarov. Use of environmentally friendly energy sources. – 2021

Abdukarimov, B. A., Sh R. O’tbosarov, and M. M. Tursunaliyev. "Increasing Performance Efficiency by Investigating the Surface of the Solar Air Heater Collector." NM Safarov and A. Alinazarov. Use of environmentally friendly energy sources (2014).

Мадхадимов, М. М., Абдулхаев, З. Э., & Сатторов, А. Х. (2018). Регулирования работы центробежных насосов с изменением частота вращения. Актуальные научные исследования в современном мире, (12-1), 83-88.

Abdulkhaev, Zokhidjon Erkinjonovich, Mamadali Mamadaliyevich Madraximov, Salimjon Azamdjanovich Rahmankulov, and Abdusalom Mutalipovich Sattorov. "INCREASING THE EFFICIENCY OF SOLAR COLLECTORS INSTALLED IN THE BUILDING." In " ONLINE-CONFERENCES" PLATFORM, pp. 174-177. 2021.

Abbasov, E. S., B. A. Abdukarimov, and A. M. Abdurazaqov. "Use of passive solar heaters in combination with local small boilers in building heating systems." Scientific-technical journal 3, no. 3 (2021): 32-35.

Абдукаримов, Б. А., О. А. Муминов, and Ш. Р. Утбосаров. "Оптимизация рабочих параметров плоского солнечного воздушного обогревателя." In Приоритетные направления инновационной деятельности в промышленности, pp. 8-11. 2020.

Toyirov, A. Kh, Sh M. Yuldashev, and B. P. Abdullayev. "Numerical modeling the equations of heat conductivity and burgers by the spectral-grid method." In НАУКА 2020. ТЕОРИЯ И ПРАКТИКА, pp. 30-31. 2020.

Abdulkhaev, Z. E., M. M. Madraximov, and M. A. O. Shoyev. "Reducing the Level of Groundwater In The City of Fergana." Int. J. Adv. Res. Sci. Commun. Technol 2, no. 2 (2021): 67-72.

Usarov, M., G. Mamatisaev, J. Yarashov, and E. Toshmatov. "Non-stationary oscillations of a box-like structure of a building." In Journal of Physics: Conference Series, vol. 1425, no. 1, p. 012003. IOP Publishing, 2019.

Erkinjonovich, Abdulkhaev Zokhidjon, and Madraximov Mamadali Mamadaliyevich. "WATER CONSUMPTION CONTROL CALCULATION IN HYDRAULIC RAM DEVICE." In E-Conference Globe, pp. 119-122. 2021.

Madaliev, E. U., T. Z. Musaev, R. M. Mat'yakubov, M. A. Akhmadaliev, G. D. Varlamov, S. K. Madaliev, and P. CURTIS. "DETERMINATION OF ACCELERATED CONDITIONS FOR THE CURING OF FURAN-PHENOL BINDERS." International polymer science and technology 24, no. 4 (1997): 85-88.

Abobakirovich, Abdukarimov Bekzod, O’Gli Mo’Minov Oybek Alisher, and Shoyev Mardonjon Ahmadjon O’G’Li. "Calculation of the thermal performance of a flat solar air heater." Достижения науки и образования 12 (53) (2019).

Abdikarimov, R., D. Usarov, S. Khamidov, O. Koraboshev, I. Nasirov, and A. Nosirov. "Free oscillations of three-layered plates." In IOP Conference Series: Materials Science and Engineering, vol. 883, no. 1, p. 012058. IOP Publishing, 2020.

Sodikovich, Abbasov Erkin, Nasretdinova Feruza Nabievna, Uzbekov Mirsoli Odiljanovich, and Ismoilov Ibroximjon Keldiboyevich. "Technique-economic analysis of the use of solar air collector in the conditions of the Fergana region of the Republic of Uzbekistan." European science review 1, no. 1-2 (2019).

Abdukarimov, Bekzod, Shuhratjon O'tbosarov, and Axmadullo Abdurazakov. "Investigation of the use of new solar air heaters for drying agricultural products." In E3S Web of Conferences, vol. 264, p. 01031. EDP Sciences, 2021.

Rashidov, Yu K., K. Yu Rashidov, I. I. Mukhin, Kh T. Suratov, J. T. Orzimatov, and Sh Sh Karshiev. "Main reserves for increasing the efficiency of solar thermal energy in heat supply systems." Applied Solar Energy 55, no. 2 (2019): 91-100.

Абдукаримов, Бекзод Абобакирович, Ахрор Адхамжон Угли Акрамов, and Шахноза Бахтиёрбек Кизи Абдухалилова. "Исследование повышения коэффициента полезного действия солнечных воздухонагревателей." Достижения науки и образования 2 (43) (2019).

Мадрахимов, М. М., and З. Э. Абдулҳаев. "Насос агрегатини ишга туширишда босимли сув узатгичлардаги ўтиш жараёнларини ҳисоблаш усуллари." Фарғона Политехника Институти Илмий–Техника Журнали 23, no. 3 (2019): 56-60.

Abdulkhaev, Zokhidjon, Mamadali Madraximov, Axmadullo Abdurazaqov, and Mardon Shoyev. "Heat Calculations of Water Cooling Tower." Uzbekistan Journal of Engineering and Technology (2021).