Geodesic
Semianalytic method for solving gas dynamics equations in Euler variables
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 2, pp. 32-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper presents a semi-analytical method for solving a system of equations of gas dynamics in Eulerian coordinates. Since only spatial derivatives are replaced by finite differences, the system of gas dynamic equations is reduced to a system of ordinary differential equations on a spatial grid. An approximate analytical solution of this system of differential equations for a small time-interval is used to describe the dynamics of a gas in the entire required time interval. Verification was carried out on one-dimensional test problems on the decay of an arbitrary discontinuity and the propagation of stationary shock waves of various intensities. To compare one-dimensional problems, the solution of test problems is given by the simple-to-implement basic particle-in-cell method. It is shown that the semi-analytical method has high accuracy of calculations, and is also the most universal method for calculating applied problems.
Keywords: semi-analytical method, particle-in-cell method, shock wave, decay of an arbitrary discontinuity. 
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M. S. Zharylkanova; N. L. Klinacheva; A. P. Yalovets. Semianalytic method for solving gas dynamics equations in Euler variables. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 2, pp. 32-40. http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a4/

[1] Yalovets A.P., “Calculation of Medium Flows under the Influence of Intense Flows of Charged Particles”, Prikladnaya mekhanika i tekhnicheskaya fizika, 38:1 (1997), 151-166 (in Russ.) | Zbl

[2] Belotserkovskiy O.M., Numerical Modeling in Continuum Mechanics, Fizmatlit Publ, M., 1994, 27–39 (in Russ.)

[3] E.S. Shestakovskaya, Ya.E. Starikov, “On one Method of Calculating Moving Boundaries in Euler Coordinates”, Journal of Computational and Engineering Mathematics, 6:4 (2019), 44–56 | DOI | MR | Zbl

[4] Belyaev P.E., Klinacheva N.L., “Impact of Gas Suspension Shielding Layer on the Force Effect of Shock Waves on a Rigid Wall”, Bulletin of the South Ural State University. Series of “Mathematics. Mechanics. Physics”, 8:4 (2016), 49–55 (in Russ.) | DOI | Zbl

[5] Landau L.D., Lifshits E.M., Hydrodynamics, Nauka Publ, M., 1988 (in Russ.)

[6] Kuropatenko V.F., Shestakovskaya E.S., Fundamentals of Numerical Methods of Continuum Mechanics, Monograph, Izdat. tsentr Yuzhno-Ural'skogo gosudarstvennogo universiteta Publ, Chelyabinsk, 2017, 253 pp. (in Russ.)

[7] Sadin D.V., “A Modification of the Large-Particle Method to a Scheme Having the Second Order of Accuracy in Space and Time for Shockwave Flows in a Gas Suspension”, Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming and Computer Software”, 12:2 (2019), 112–122 | DOI | Zbl