Geodesic
Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids
Matematičeskoe modelirovanie i čislennye metody, no. 8 (2015), pp. 75-91 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Gas dynamics, ideal gas, numerical methods, RKDG, TVD. 
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Yu. I. Dimitrienko; M. N. Koryakov; A. A. Zakharov. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Matematičeskoe modelirovanie i čislennye metody, no. 8 (2015), pp. 75-91. http://geodesic.mathdoc.fr/item/MMCM_2015_8_a4/

[1] Anderson J.D., Hypersonic and High-Temperature Gas Dynamics, American Institute of Aeronautics and Astronautics, Reston, Virginia, 2006, 232 pp.

[2] McNamara J.J., Friedmann P.P., Aeroelastic and Aerothermoelastic Analysis of Hypersonic Vehicles: Current Status and Future Trends, Structural Dynamics, 48th AIAA/ASME/ASCE/AHS/ASC Structures, and Materials Conference, 23–26 pp. 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., Proceedings of the Engineering Physics Institute, 2:12 (2009), 42–49

[4] Dimitrienko Yu.I., Zakharov A.A., Koryakov M.N., Syzdykov E.K., Proceedings of Higher Educational Institutions. Series Machine Building, 2014, no. 3, 23–34

[5] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A., Stroganov A.S., Mathematical Modeling and Computational Methods, 2014, no. 3, 3–24

[6] Dimitrienko Yu.I., Zakharov A.A., Koryakov M.N., Syzdykov E.K., Minin V.V., Engineering Journal: Science and Innovation, 2013, no. 9 href {http://engjournal.ru/catalog/mathmodel/aero/1114.html }{engjournal.ru/catalog/mathmodel/aero/1114.html}

[7] Dimitrienko Yu.I., Zakharov A.A., Abbakumov A.S., Koryakov M.N., Syzdykov E.K., Herald of Bauman Moscow State Technical University. Series: Natural Sciences, 2011, no. 4, 44–54

[8] Galanin M.P., Grishchenko E.V., Savenkov E.B., Tokareva S.A., Keldish's Preprint RAS No 52, 2006

[9] Tokareva S.A., Mathematical modeling of fluid and gas on the basis of Galerkin's discontinuous method, BMSTU Publ., Moscow, 2010, 141 pp.

[10] Dimitrienko Yu.I., Kotenev V.P., Zakharov A.A., The adaptive banded grid method for numerical simulation in gas dynamics, Fizmatlit Publ., Moscow, 2011, 280 pp.

[11] Cockburn V., Shu C.-W., “Runge — Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems”, Journal of Scientific Computing, 16:3 (2001)

[12] Zienkiewicz O.C., Taylor R.L., The finite element method. The basis, 1 (2000)

[13] Petrov I.B., Lobanov A.I., Lectures on numerical mathematics, Laboratoriya znaniy, Moscow, 2006, 523 pp.

[14] Eleuterio F., Toro Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin, 2009, 749 pp.

[15] Godunov S.K., Numerical solution of gas dynamics multidimensional problem, Nauka Publ., Moscow, 1976, 401 pp.

[16] Kulikovskiy A.G., Pogorelov N.V., Semenov A.Yu., Mathematical problems on numerical solution of hyperbolic equation systems, Fizmatlit Publ., Moscow, 2012, 656 pp.

[17] Rohde A.A., “Computational Study Of Flow Around A Rotating Disc In Flight”, Florida, 2000

[18] Harten A., “High Resolution Schemes for Hyperbolic Conservation Laws”, J. Comp. Phys., 49 (1983)

[19] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A., Syzdykov E.K., Herald of Bauman Moscow State Technical University. Series: Natural Sciences, 2011, no. 2, 87–97

[20] Lubimov A.N., Rusanov V.V., Gas flows about blunt body, Nauka Publ., Moscow, 1970, 380 pp.

[21] Salnikov V.D., “Section Physical and Mathematical Sciences”, Ogarev-online., 2014, no. 19