Solutions of the converging and diverging shock problem in a medium with varying density

Itamar Giron, Shmuel Balberg, Menahem Krief*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider the solutions of the Guderley problem, consisting of a converging and diverging hydrodynamic shock wave in an ideal gas with a power law initial density profile. The self-similar solutions and specifically the reflected shock coefficient, which determines the path of the reflected shock, are studied in detail for cylindrical and spherical symmetries and for a wide range of values of the adiabatic index and the spatial density exponent. Finally, we perform a comprehensive comparison between the analytic solutions and Lagrangian hydrodynamic simulations by setting proper initial and boundary conditions. A very good agreement between the analytical solutions and the numerical simulations is obtained. This demonstrates the usefulness of the analytic solutions as a code verification test problem.

Original languageAmerican English
Article number066112
JournalPhysics of Fluids
Issue number6
StatePublished - 1 Jun 2023

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