K. A. Zhukov, A. A. Kornev, M. A. Lozhnikov, A. V. Popov, “Acceleration of transition to stationary mode for solutions to a system of viscous gas dynamics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, Number 2,Pages <nobr>14

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Mathematics

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

K. A. Zhukov^a, A. A. Kornev^b, M. A. Lozhnikov^b, A. V. Popov^b

^a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: finite-difference approximation, numerical stabilization by initial data, equations of dynamics of viscous one-dimensional gas.

UDC: 519.6

Received: 25.10.2018