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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 90–96 (Mi zvmmf10765)  

Mathematical modeling of high-speed interaction of metallic plates within the two-fluid Euler approach

P. S. Utkinab, S. V. Fortovab

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
b Institute for Computer Aided Design, Russian Academy of Sciences, Moscow, Russia

Abstract: A multifluid mathematical model for the computation of a high speed collision of metallic plates is constructed. Each material—steel, of which the first plate is made; lead, of which the second plate is made; and the surrounding air—is assumed to be a compressible fluid. The Baer-Nunziato equations are solved. The determining system of equations is hyperbolic, and it is numerically solved using the HLL method. The problem statement corresponds to the full-scale experiment. A lead plate is thrown in the direction of a steel plate at a velocity of 500 m/s. Both plates have free boundaries. The main characteristics of the process—formation of shock waves, their propagation to the free boundaries of the plates, reflection in the form of rarefaction waves, and interaction of the rarefaction waves with the interface between the metals—are obtained in the computations. The relative error of the parameters of the shock waves compared with the known computational and experimental data does not exceed 7%. An estimate of the acceleration of the interface between the plates due to the passage of the rarefaction wave propagating from the free boundary of the steel plate is obtained.

Key words: high speed collision, shock wave, rarefaction wave, three-fluid model, mathematical modeling, hyperbolic system of equations, HLL method.

Funding Agency Grant Number
Russian Science Foundation 17-11-01293


DOI: https://doi.org/10.31857/S004446690002011-3

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1377–1383

Bibliographic databases:

UDC: 519.63
Received: 05.03.2018

Citation: P. S. Utkin, S. V. Fortova, “Mathematical modeling of high-speed interaction of metallic plates within the two-fluid Euler approach”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 90–96; Comput. Math. Math. Phys., 58:8 (2018), 1377–1383

Citation in format AMSBIB
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