Difference scheme stability investigation for model of barotropic viscous gas

S. K. Orazov, N. N. Tungatarov

Abstract


In this paper, the technique of convergence of research and the stability difference schemes for the equations of gas dynamics in the presence of an electric field. The work consists in the strict mathematical definition of the conditions of stability and convergence of difference schemes, which relate to the long posed problems of computational mathematics. The studies enable significant progress in the study of the convergence and stability of difference schemes for gas dynamic tasks. The results of the thesis could be used for a wide class of problems of mathematics and mechanics. In the proof of the stability and convergence of difference schemes used by well-known theorems and inequality. All results are formulated as theorems.

Keywords


difference scheme, stability investigation, gas dynamic, convergence, electric field, barotropic viscous gas

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References


Otmar Stuetzer O. Apparent viscosity of a charged fluid // The Physics of Fluids / Published by the American Institute of Physics. – December, 1961. – Vol. 4, No 4. – P. 1226 - 1237.

Shohet Y. Errors and Stability of the Entry Problem Equations in Laminar Magnetohydrodynamic Flow // The Physics of Fluids / Published by the American Institute of Physics. – June, 1963. – Vol. 6, No 6. – Р. 797 - 802.

Smith C. V., Melcher J. R. Electrohydrodynamicall induced spatially periodic celluar stokes – flow // The Physics of Fluids – November, 1967. – Vol. 10, No 11. – Р. 2315 - 2322.

Itaya N. The existence and uniqueness of the solutions of the equations describing compressible viscous fluid flow. // Proc. Japan. Acad. – 1970. – Vol. 46, No 4. – Р. 379 - 382.

Tani A. On the first initial boundary value problem of compressible viscous fluid motion // Publisher Res. Institute Mathematical Science. – 1977. – Vol. 13. No 1. – Р. 193 - 251.