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


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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.

About the authors

B. A. Korneev

Moscow Institute of Physics and Technology

Author for correspondence.
Email: boris.korneev@phystech.edu
Russian Federation, 9 Institutsky l., Dolgoprudny, Moscow region, 141700

V. D. Levchenko

Keldysh Institute of Applied Mathematics

Email: boris.korneev@phystech.edu
Russian Federation, 4 Miusskaya sq., Moscow, 125047

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