Explicit formulas for the initial data stabilization algorithm for the stationary solution are obtained by zero approximation method for the semi-implicit difference scheme approximating a system of equations for the dynamics of a one-dimensional viscous barotropic gas. The spectrum of the corresponding linearized system on the stationary solution is studied and theoretical convergence estimates 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.

中文翻译：

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粘性气体动力学系统解的加速过渡到平稳模式

通过近似于一维粘性正压气体动力学方程组的半隐式差分方案的零近似方法，获得了固定解初始数据稳定算法的显式公式。研究了相应线性化系统在平稳解上的谱，并获得了理论收敛估计。进行了非线性问题的数值实验，以确认该方法的有效性，并反映了稳定率对原始问题和算法参数的依赖性。