Geodesic
On a Lagrangian-Eulerian method calculation of unsteady flows compressible media
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 78-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, a numerical method for calculating two-dimensional flows in Eulerian coordinates is implemented, which is based on an explicit Lagrangian-Eulerian difference scheme. The calculation of each time step is carried out in two stages. At the Lagrangian stage, a difference scheme based on the Kuropatenko method is used, which has zero energy dissipation on smooth solutions and minimal distraction on strong discontinuities. At the Eulerian stage, the mesh is rebuilded and all the parameters of the substance are recalculated from the old mesh to the new one in accordance with the laws of conservation of mass, momentum and energy. The developed numerical algorithm has shown its operability when tested on tasks having an analytical or reference solution.
Keywords: Lagrangian-Eulerian method, shock wave calculation method, Kuropatenko method. 
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E. S. Shestakovskaya; Ya. E. Starikov; I. R. Makeeva. On a Lagrangian-Eulerian method calculation of unsteady flows compressible media. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 78-90. http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a7/

[1] J. Neumann, R. Richtmayer, “A Method for the Numerical Calculation of Hydrodynamical Shocks”, Journal of Applied Physics, 21:3 (1950), 232–237 | DOI | MR | Zbl

[2] P.D. Lax, “Weak Solution of Nonlinear Hyperbolic Equations and their Numerical Computations”, Communications on Pure and Applied Mathematics, 7:1 (1954), 159–193 | DOI | MR | Zbl

[3] Godunov S.K., “Difference Method for Calculating Shock Waves”, Russian Mathematical Surveys, 12:1 (1957), 176–177 (in Russian) | MR | Zbl

[4] Kuropatenko V.F., “Shockwave Calculation Method”, Academy of Sciences of USSR Reports, 3:4 (1960), 771–772 (in Russian) | MR

[5] Rozhdestvenskiy B.L., Systems of Quasi-Linear Equations and their Applications to Gas Dynamics, Nauka, M., 1978 (in Russian) | MR

[6] Harlow F.H., “Numerical Particle-in-Cell Method for Hydrodynamic Problems”, Computational Methods in Hydrodynamics, Mir, M., 1967, 316–342 (in Russian)

[7] Belotserkovskiy S.M., Davydov Ju.M., Method of Large Particles in Gas Dynamics, Nauka, M., 1982 (in Russian)

[8] 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

[9] 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: Mathematics, Mechanics, Physics, 8:4 (2016), 49–55 (in Russian) | DOI | MR | Zbl

[10] 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 (in Russian) | DOI | Zbl

[11] Voronin B.L., Skrypnik S.I., Sofronov I.D., “Euler-Lagrangian Method for the Numerical Solution of Three-Dimensional Problems of Gas Dynamics with Allowance for Heat Conduction”, Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes, 3 (1988), 3–8 (in Russian)

[12] Bahrah S.M., Bezrukov I.Ju., Spiridonov V.F., “Investigation of the Convergence of Lagrangian-Eulerian Difference Schemes on the Example of the Problem "Blast Waves\textquotedblright”, Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes, 2 (2005), 60–64 (in Russian)

[13] Darova N.S., Dibirov O.A., Zharova G.V., Shanin A.A., Janilkin Ju.V., “Complex of programs EGAK. Lagrangian-Eulerian Method for Calculating Two-Dimensional Gas-Dynamic Flows of a Multicomponent Medium”, Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes, 1994, no. 2, 51–58 (in Russian)

[14] Belyaev P.E., Makeeva I.R., Pigasov E.E., Mastyuk D.A., “Adaptation of Kuropatenko Method for Calculating Shock Waves in Euler Coordinates”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 14:1 (2021), 91–103 (in Russian) | DOI | Zbl

[15] Kuropatenko V.F., Kuznecova I.I., Makeeva I.R., “Investigation of the Effect of Pulsating Injection on the Flow Near a Streamlined Body”, Problems of Atomic Science and Technology. Series: Mathematical Modelling of Physical Processes, 3 (2001), 60–71 (in Russian)

[16] Kuropatenko V.F., Shestakovskaya E.S., Essentials of Numerical Methods in Continuum Mechanics, South Ural State University Publishing Centre, Chelyabinsk, 2017 (in Russian)

[17] P.R. Woodward, P. Colella, “The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks”, Journal of Computational Physics, 54:1 (1984), 115–173 | DOI | MR | Zbl

[18] C.W. Hirt, B.D. Nichols, “Volume Of Fluid (VOF) Method for the Dynamics of Free Boundaries”, Journal of Computational Physics, 39:1 (1981), 201–225 | DOI | Zbl