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Article information
2021 , Volume 26, ¹ 5, p.52-64
Bautin S.P., Deryabin S.L.
Application of nonstationary self-similar variables for solving the three-dimensional problem of the decay of a special discontinuity
The aim of this study is to construct a solution to the problem of the decay of a special discontinuity in physical space. The problem reduces to finding of three-dimensional isentropic flows of a polytropic gas that occur after the instantaneous destruction of an impermeable wall separating an inhomogeneous moving gas from a vacuum at the initial moment of time. The problem takes into account the forces of gravity and Coriolis. Research methods. In the system of gas dynamics equations, a self-similar feature is introduced in a variable that outputs from the initial interface. For the resulting system, the Cauchy problem is formulated using conditions on the sound characteristic. The solution to this problem is constructed in the form of power series. The coefficients of the series are partly determined by solving algebraic equations, another part can be found as solutions of ordinary differential equations. The convergence of the constructed series is proved by the Majorant method. The results obtained in the work. In the form of a convergent power series, solutions to the problem of the decay of a special discontinuity in physical space are constructed. Conclusions. The solution constructed in physical space allows setting the initial conditions for the numerical simulation of this characteristic Cauchy problem using a difference scheme.
[full text]
Keywords: systemofgasdynamicsequations,non-stationaryself-similarvariables,soniccharacteristic,characteristicCauchyproblem,convergingseries
doi: 10.25743/ICT.2021.26.5.005
Author(s):
Bautin Sergey Petrovich
Dr. , Associate Professor
Position: Professor
Office: Snezhinsk Institute of Physics and Technology National Research Nuclear University MEPhI
Address: 456776, Russia, Snezhinsk, Komsomol str., 8
Phone Office: (343) 221 25 49
E-mail: SPBautin@mail.ru
SPIN-code: 4343-3821Deryabin Sergey Lvovich
Dr. , Professor
Position: Professor
Office: Ural state university of railway transport
Address: 620034, Russia, Ekaterinburg, Kolmogorov st., 66
Phone Office: (343)2-21-24-04
E-mail: SDeryabin@usurt.ru
References:
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Bibliography link:
Bautin S.P., Deryabin S.L. Application of nonstationary self-similar variables for solving the three-dimensional problem of the decay of a special discontinuity // Computational technologies. 2021. V. 26. ¹ 5. P. 52-64
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