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

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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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     author = {M. S. Zharylkanova and N. L. Klinacheva and A. P. Yalovets},
     title = {Semianalytic method for solving gas dynamics equations in {Euler} variables},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {32--40},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a4/}
}
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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/