Geodesic
Effective solving of three-dimensional gas dynamics problems with the Runge-Kutta discontinuous Galerkin method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 465-475

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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. 
@article{ZVMMF_2016_56_3_a13,
     author = {B. A. Korneev and V. D. Levchenko},
     title = {Effective solving of three-dimensional gas dynamics problems with the {Runge-Kutta} discontinuous {Galerkin} method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {465--475},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a13/}
}
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B. A. Korneev; V. D. Levchenko. Effective solving of three-dimensional gas dynamics problems with the Runge-Kutta discontinuous Galerkin method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 465-475. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a13/