Abstract
A numerical method is developed for calculating the non-steady-state motions of a compressible liquid, with application to problems of the impact type. A homogeneous, completely conservative difference scheme of the first order of exactness is used. For isolation of the discontinuities and “smoothing” of the solution, use is made of the introduction of an artificial viscosity, based on an analysis of the provisional properties of the solution. An investigation is made of the scheme stability and the necessary stability criteria are obtained. The article gives the detailed results of a calculation of the impact interaction between a spherical drop and a rigid surface. It is shown that the maximal pressure arising with the impact of a drop of liquid on a solid surface exceeds by several times the pressurecalculated using the one-dimensional theory; under these circumstances, the rate of expansion of the drop along the surface exceeds the initial velocity of the collision by an order of magnitude.
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–43, January–February, 1978.
In conclusion, the authors thank G. G. Chernyi for his continuing interest and his valuable evaluation of the results of the work, and L. F. Shaikhatarov, who participated in making the calculations.
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Gonor, A.L., Yakovlev, V.Y. Dynamics of the impact of a drop on a solid surface. Fluid Dyn 13, 25–31 (1978). https://doi.org/10.1007/BF01094455
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DOI: https://doi.org/10.1007/BF01094455