Finite-difference method for computation of the 3-D gas dynamics equations with artificial viscosity

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.