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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2016 Volume 56, Number 3, Pages 465–475 (Mi zvmmf10361)

This article is cited in 3 papers

Effective solving of three-dimensional gas dynamics problems with the Runge-Kutta discontinuous Galerkin method

B. A. Korneeva, V. D. Levchenkob

a Moscow Institute of Physics and Technology, 9 Institutsky l., Dolgoprudny, 141700, Moscow region, Russia
b Keldysh Institute of Applied Mathematics, 4 Miusskaya sq., 125047, Moscow, Russia

Abstract: In this paper we present the Runge–Kutta discontinuous Galerkin method (RKDG method) for the numerical solution of the Euler equations of gas dynamics. The method is being tested on a series of Riemann problems in the one-dimensional case. For the implementation of the method in the three-dimensional case, a DiamondTorre algorithm is proposed. It belongs to the class of the locally recursive non-locally asynchronous algorithms (LRnLA). With the help of this algorithm a significant increase of speed of calculations is achieved. As an example of the three-dimensional computing, a problem of the interaction of a bubble with a shock wave is considered.

Key words: gas dynamics, Euler equations, RKDG method, LRnLA algorithms, high-performance computing, bubble-shock interaction.

UDC: 519.634

Received: 15.05.2014
Revised: 20.07.2015

DOI: 10.7868/S0044466916030121


 English version:
Computational Mathematics and Mathematical Physics, 2016, 56:3, 460–469

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