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Matem. Mod., 2020, Volume 32, Number 10, Pages 34–46 (Mi mm4221)  

Modeling of Richtmyer–Meshkov instability development using the discontinuous Galerkin method and local-adaptive meshes

R. V. Zhalnina, V. F. Masyagina, E. E. Peskovaa, V. F. Tishkinb

a National Research Mordovia State University, Saransk
b Keldysh Institute of Applied Mathematics of RAS, Moscow

Abstract: The article presents a numerical algorithm for solving equations of multicomponent gas dynamics using the discontinuous Galerkin method on local-adaptive grids. The numerical algorithm uses a data structure and a dynamic local grid adaptation algorithm from the p4est library. We use Lax–Friedrichs–Rusanov numerical and HLLC flows. To get rid of non-physical oscillations, the Barth–Jespersen limiter is applied. As a result of the study, a numerical simulation of the development of the Richtmyer–Meshkov instability was carried out, the results obtained were compared with experimental results and known numerical solutions of this problem. It is concluded that the calculated and experimental data are in good agreement. In the future, it is expected to study this process using a model that takes into account the phenomena of viscosity and thermal conductivity.

Keywords: turbulent mixing, Richtmyer–Meshkov instability, discontinuous Galerkin method, parallel computing, local-adaptive meshes, p4est.

DOI: https://doi.org/10.20948/mm-2020-10-03

Full text: PDF file (417 kB)
First page: PDF file
References: PDF file   HTML file

Received: 06.11.2019
Revised: 06.11.2019
Accepted:23.12.2019

Citation: R. V. Zhalnin, V. F. Masyagin, E. E. Peskova, V. F. Tishkin, “Modeling of Richtmyer–Meshkov instability development using the discontinuous Galerkin method and local-adaptive meshes”, Matem. Mod., 32:10 (2020), 34–46

Citation in format AMSBIB
\Bibitem{ZhaMasPes20}
\by R.~V.~Zhalnin, V.~F.~Masyagin, E.~E.~Peskova, V.~F.~Tishkin
\paper Modeling of Richtmyer--Meshkov instability development using the discontinuous Galerkin method and local-adaptive meshes
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 10
\pages 34--46
\mathnet{http://mi.mathnet.ru/mm4221}
\crossref{https://doi.org/10.20948/mm-2020-10-03}


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