519.6:533.6 Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids

Dimitrienko Y. I. (Bauman Moscow State Technical University), Koryakov M. N. (Bauman Moscow State Technical University), Zakharov A. A. (Bauman Moscow State Technical University)

GAS DYNAMICS, IDEAL GAS, NUMERICAL METHODS, RKDG, TVD


doi: 10.18698/2309-3684-2015-4-7591


This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.


[1] Anderson J.D. Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics, Reston, Virginia, 2nd ed., 2006, 232 p.
[2] McNamara J.J., Friedmann P.P. Aeroelastic and Aerothermoelastic Analysis of Hypersonic Vehicles: Current Status and Future Trends. 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 23–26 April 2007, Honolulu, Hawaii. Available at: http://www.mecheng.osu.edu/lab/cael/sites/default/files/AIAA-2007-2013
[3] Bratchev A.V., Zabarko D.A., Vatolina E.G., Korobkov A.A., Sakharov V.I. Izvestiya Instituta inzhenernoy fiziki — Proceedings of the Engineering Physics Institute, 2009, vol. 2, no. 12, pp. 42−49.
[4] Dimitrienko Yu.I., Zakharov A.A., Koryakov M.N., Syzdykov E.K. Izvestiya vuzov. Seriya Mashinostroenie — Proceedings of Higher Educational Institutions. Series Machine Building, 2014, no. 3, pp. 23–34.
[5] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A., Stroganov A.S. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, no. 3, 2014, pp. 3–24.
[6] Dimitrienko Yu.I., Zakharov A.A., Koryakov M.N., Syzdykov E.K., Minin V.V. Inzhenernyi zhurnal: nauka i innivatsii — Engineering Journal: Science and Innovation, 2013., issue 9. Available at: http://engjournal.ru/catalog/ mathmodel/aero/1114.html
[7] Dimitrienko Yu.I., Zakharov A.A., Abbakumov A.S., Koryakov M.N., Syzdykov E.K. Vestnic MGTU im. N.E. Baumana. Seriya Estestvennye nauki — Herald of Bauman Moscow State Technical University. Series: Natural Sciences, 2011, no. 4, pp. 44–54.
[8] Galanin M.P., Grishchenko E.V., Savenkov E.B., Tokareva S.A. Preprint IPM im. M.V. Keldisha RAN — Keldish's Preprint RAS, 2006, no. 52, 30 p.
[9] Tokareva S.A. Matematicheskoe modelirovanie techeniy zhidkosti i gaza na osnove razryvnogo metoda Galerkina [Mathematical modeling of fluid and gas on the basis of Galerkin's discontinuous method]. Moscow, BMSTU Publ., 2010, 141 p.
[10] Dimitrienko Yu.I., Kotenev V.P., Zakharov A.A. Metod lentochnykh adaptivnykh setok dlya chislennogo modelirovaniya v gazovoy dinamike [The adaptive banded grid method for numerical simulation in gas dynamics]. Moscow, Fizmatlit Publ., 2011, 280 p.
[11] Cockburn B., Shu C.-W. Journal of Scientific Computing, 2001, vol. 16, no. 3.
[12] Zienkiewicz O.C., Taylor R.L. The basis, 2000, vol. 1, 708 p.
[13] Petrov I.B., Lobanov A.I. Lektsii po vychislitelnoy matematike [Lectures on numerical mathematics]. Moscow, Internet-universitet informatsionnych technologiy; BINOM; Laboratoriya znaniy; 2006, 523 p.
[14] Eleuterio F. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics. Berlin, Springer, 2009, 749 p.
[15] Godunov S.K., ed. Chislennoe reshenie mnogomernyh zadach gazovoy dinamiki [Numerical solution of gas dynamics multidimensional problem]. Moscow, Nauka Publ., 1976, 401 p.
[16] Kulikovskiy A.G., Pogorelov N.V., Semenov A.Yu. Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravneniy [Mathematical problems on numerical solution of hyperbolic equation systems]. Moscow, Fizmatlit Publ., 2012, 656 p.
[17] Rohde А.А. Computational Study of Flow around a Rotating Disc in Flight. Florida, 2000, 169 p.
[18] Harten A. High Resolution Schemes for Hyperbolic Conservation Laws. J. Comp. Phys., 1983, vol. 49, рр. 357−393.
[19] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A., Syzdykov E.K. Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of Bauman Moscow State Technical University. Series: Natural Sciences, 2011, no. 2, pp. 87–97.
[20] Lubimov A.N., Rusanov V.V. Techeniya gaza okolo tupykh tel [Gas flows about blunt body]. Moscow, Nauka Publ., 1970, vol. 2, 380 p.
[21] Salnikov V.D. Ogarev-online. Razdel “Fiziko-matematicheskie nauki” — Ogarev-online. Section Physical and Mathematical Sciences, 2014, no. 19.
Available at: http://journal.mrsu.ru/arts/razrabotka-neyavnojj-skhemy-dlyamodelirovaniya-techenijj-szhimaemogo-gaza


Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91



Download article

Количество скачиваний: 1036