Geodesic
Finite-difference method for computation of the 3-D gas dynamics equations with artificial viscosity
Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 89-100

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In this paper present a new numerical method for the solution of the gas dynamics problems for 3-D systems in Eulerian variables. The proposed method uses the approximation $O(\tau^2+h^2_x+h^2_y+h^2_z)$ in the areas of the solution's smoothness and beyond the compression waves, $\tau$ for the time step, $h_x$, $h_y$, $h_z$ for the space variables steps. In the proposed difference scheme in addition to the Lax–Wendroff corrections, artificial viscosity $\mu$ monotonizing the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of computation of three-dimensional test problem for Euler equation are presented.
Keywords: numerical method, difference scheme, gas dynamics, adaptive artificial viscosity. 
@article{MM_2011_23_3_a7,
     author = {I. V. Popov and I. V. Fryazinov},
     title = {Finite-difference method for computation of the {3-D} gas dynamics equations with artificial viscosity},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--100},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_3_a7/}
}
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I. V. Popov; I. V. Fryazinov. Finite-difference method for computation of the 3-D gas dynamics equations with artificial viscosity. Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 89-100. http://geodesic.mathdoc.fr/item/MM_2011_23_3_a7/