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

A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O(τ² + h _x ² + h _y ² + h _z ²) in the areas of the solution’s smoothness and beyond the compression waves; τ is the time step; and h _x , h _y , and h _z are space variable steps. In the proposed difference scheme, in addition to Lax-Wendroff corrections, artificial viscosity μ that monotonizes the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of the computation of the 3D test problem for the Euler equation are presented.