×

zbMATH — the first resource for mathematics

Acceleration of the process of entering stationary mode for solutions of a linearized system of viscous gas dynamics. II. (English. Russian original) Zbl 1397.35236
Mosc. Univ. Math. Bull. 73, No. 3, 85-89 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 3, 3-8 (2018).
Summary: For finite-difference approximation of the linearized system of differential equations of viscous gas dynamics, the governing Dirichlet boundary conditions are constructed to guarantee the acceleration of the process of reaching the steady state solution. Necessary estimates are presented for the rate of convergence in the case of zero boundary conditions as well as the calculation results for stabilization in the case of initial conditions with jumps of pressure arid/or density.
For Part I, see [the authors, ibid. 73, No. 1, 24–29 (2018; Zbl 1393.35191); translation from Vestn. Mosk. Univ., Ser. I 73, No. 1, 26–32 (2018)].

MSC:
35Q35 PDEs in connection with fluid mechanics
76N15 Gas dynamics (general theory)
Citations:
Zbl 1393.35191
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zhukov, K. A.; Kornev, A. A.; Popov, A. V., Acceleration of the process of entering stationary mode for solutions of a linearized system of viscous gas dynamics. I, Vestn. Mosk. Univ., Matem. Mekhan., 1, 26, (2018) · Zbl 1393.35191
[2] Lebedev, V. I., Difference analogues of orthogonal expansions of basic differential operators and some boundary value problems of mathematical physics, I, II, Zh. Vychisl. Matem Matem. Fiz., 3, 449, (1964)
[3] A. A. Samarskii and E. S. Nikolaev, Solution Methods for Grid Equations (Nauka, Moscow, 1978) [in Russian].
[4] N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods (BINOM, Moscow, 2012) [in Russian]. · Zbl 0638.65001
[5] Fursikov, A. V., Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback, Matem. Sborn., 192, 115, (2001) · Zbl 1019.93047
[6] Fursikov, A. V., Stabilizability of two-dimensional navier—stokes equations with help of boundary feedback control, J. Math. Fluid Mech., 3, 259, (2001) · Zbl 0983.93021
[7] Fursikov, A. V., Real processes arid realizability of stabilization method for navier—stokes system by means of control with feedback from domain boundary, Nonlinear Problems of Mathematical Physics and Related Issues, In Honor of Acad, O, A, Ladyzhenskaya, Int. Math, Series, 2, 127-164, (2002)
[8] Chizhonkov, E. V., Numerical aspects of one stabilization method, Russ. J. Numer. Anal. Math. Modelling, 18, 363, (2003) · Zbl 1058.65095
[9] Chizhonkov, E. V., Projection operators for numerical stabilization, Vychisl. Metody Programm., 5, 161, (2004)
[10] Vedernikova, E. Yu.; Kornev, A. A., To the problem of rod heating, Vestn. Mosk. Univ. Matem. Mekhan., 6, 10, (2014) · Zbl 1358.93141
[11] Kornev, A. A., Modeling the stabilization process on the boundary conditions for the quasi-two-dimensional flow with the four vortex structure, Matem. Mod., 29, 99, (2017) · Zbl 06966947
[12] Kornev, A. A., The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type, Russ. J. Numer. Anal. Math. Modelling, 32, 245, (2017) · Zbl 06760709
[13] Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V., A new approach to solution of asymptotic stabilization problems, Zh. Vychisl. Matem. Matem. Fiz., 49, 2167, (2009)
[14] Kornev, A. A., Numerical aspects of a problem of asymptotic stabilization by the right-hand side, Russ. J. Numer. Anal. Math. Modelling, 23, 407, (2008) · Zbl 1152.65064
[15] Zhukov, K. A.; Popov, A. V., The study of economical difference scheme for unstationary motion of weakly compressible gas, Zh. Vychisl. Matem. Matem. Fiz., 45, 677, (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.