At present, numerical modeling is the main, and often the only, tool for a detailed description of some physical phenomena in the research of the processes of compression of substances by shock waves. Studying the behavior of shock waves and rarefaction waves on the simplest model tests helps in the analysis of more complex calculations on laser installations. This paper proposes test problems that simulate compression by shock waves of a spherical layered system consisting of several substances. The modes of compression are considered when the maximal density in the central region is reached after the passage of the second or third shock waves.
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