Numerical simulation of converging spherical shock waves with symmetry violation

Konyukhov A.V., Rostilov T.A.
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The study of the development of π-periodic perturbations of a converging spherical shock wave leading to cumulation limitation is performed. The study is based on 3D hydrodynamic calculations with the Carnahan – Starling equation of state for hard sphere fluid. The method of solving the Euler equations on moving (compressing) grids allows one to trace the evolution of the converging shock wave front with high accuracy in a wide range of its radius. The compression rate of the computational grid is adapted to the motion of the shock wave front, while the motion of the boundaries of the computational domain satisfy the condition of its supersonic velocity relative to the medium. This leads to the fact that the solution is determined only by the initial data at the grid compression stage. The second order TVD scheme is used to reconstruct the vector of conservative variables at the boundaries of the computational cells in combination with the Rusanov scheme for calculating the numerical vector of flows. The choice is due to a strong tendency for the manifestation of carbuncle-type numerical instability in the calculations, which is known for other classes of flows. In the three-dimensional case of the observed force, the carbuncle effect was obtained for the first time, which is explained by the specific nature of the flow: the concavity of the shock wave front in the direction of motion, the unlimited (in the symmetric case) growth of the Mach number, and the stationarity of the front on the computational grid. The applied numerical method made it possible to study the detailed flow pattern on the scale of cumulation termination, which is impossible within the framework of the Whitham method of geometric shock wave dynamics, which was previously used to calculate converging shock waves. The study showed that the limitation of cumulation is associated with the transition from the Mach interaction of converging shock wave segments to a regular one due to the progressive increase in the ratio of the azimuthal velocity at the shock wave front to the radial velocity with a decrease in its radius. It was found that this ratio is represented as a product of a limited oscillating function of the radius and a power function of the radius with an exponent depending on the initial packing density in the hard sphere model. It is shown that increasing the packing density parameter in the hard sphere model leads to a significant increase in the pressures achieved in a shock wave with broken symmetry. For the first time in the calculation, it is shown that at the scale of cumulation termination, the flow is accompanied by the formation of high-energy vortices, which involve the substance that has undergone the greatest shock-wave compression. Influencing heat and mass transfer in the region of greatest compression, this circumstance is important for current practical applications of converging shock waves for the purpose of initiating reactions (detonation, phase transitions, controlled thermonuclear fusion).

Keywords: numerical simulation, converging shock waves, symmetry violation, shock wave focusing, cumulation, hard sphere fluid
Citation in English: Konyukhov A.V., Rostilov T.A. Numerical simulation of converging spherical shock waves with symmetry violation // Computer Research and Modeling, 2025, vol. 17, no. 1, pp. 59-71
Citation in English: Konyukhov A.V., Rostilov T.A. Numerical simulation of converging spherical shock waves with symmetry violation // Computer Research and Modeling, 2025, vol. 17, no. 1, pp. 59-71
DOI: 10.20537/2076-7633-2025-17-1-59-71
URL: http://crm-en.ics.org.ru/journal/article/3576/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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