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ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 65M60

Application of discontinuous Galerkin method to modeling of two-dimensional flows of a multicomponent ideal gases mixture using local adaptive mesh refinement

R. V. Zhalnin1, V. F. Masyagin2, E. E. Peskova3, V. F. Tishkin4

AnnotationIn this article a numerical algorithm is developed for solving of gas dynamics equations for a mixture of ideal gases on adaptive locally refined grids. The algorithm is based on discontinuous Galerkin method. To avoid the appearance of non-physical oscillations near the discontinuities, the Barth-Jespersen limiter is used. The numerical algorithm is based on the data structure and algorithms of the p4est library. In present work the numerical simulation of one problem of Richtmyer-Meshkov instability development is considered and the triple point problem is solved using the developed numerical algorithm of high accuracy order. The obtained results are in good agreement with the well-known numerical solutions. The pictures plotted basing on the solution describe in detail the dynamics of the complex flows under consideration.
Keywordsdiscontinuous Galerkin method, gas dynamics equations, multicomponent gas mixture, parallel computing, adaptive mesh refinement, p4est

1Ruslan V. Zhalnin, Head of Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk, 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-1103-3321, zhrv@mrsu.ru

2Victor F. Masyagin, Senior Researcher, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk, 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6738-8183, masyaginvf@mrsu.ru

3Elizaveta E. Peskova, Junior Researcher, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk, 430005, Russia),Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0003-2618-1674, e.e.peskova@mail.ru

4Vladimir F. Tishkin, Department Head, Keldysh Institute of Applied Mathematics (4 Miusskaya sq., Moscow, 125047, Russia), D.Sc. (Physics and Mathematics), corresponding member of RAS, ORCID: http://orcid.org/0000-0001-7295-7002, v.f.tishkin@mail.ru

Citation: R. V. Zhalnin, V. F. Masyagin, E. E. Peskova, V. F. Tishkin, "[Application of discontinuous Galerkin method to modeling of two-dimensional flows of a multicomponent ideal gases mixture using local adaptive mesh refinement]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:2 (2019) 244–258 (In Russian)

DOI 10.15507/2079-6900.21.201902.244-258