Acceleration of transition to stationary mode for solutions to a system of viscous gas dynamics

For the semi-implicit difference scheme approximating a system of equations for the dynamics of a one-dimensional viscous barotropic gas, explicit formulas for the initial data stabilization algorithm for the stationary solution by the zero approximation method are obtained. The spectrum of the corresponding linearized system on the stationary solution is studied and theoretical estimates of convergence are obtained. Numerical experiments for the nonlinear problem are carried out to confirm the efficiency of the method, and to reflect the dependence of the stabilization rate on the parameters of the original problem and the algorithm parameters.