Solutions of the imploding shock problem in a medium with varying density
Fluid Dynamics
2021-07-07 v1 High Energy Astrophysical Phenomena
Mathematical Physics
math.MP
Computational Physics
Plasma Physics
Abstract
We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and specifically the similarity exponent which determines the behavior of the accelerating shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of the adiabatic index and the spatial density exponent. We then demonstrate how the analytic solutions can be reproduced in Lagrangian hydrodynamic codes, thus demonstrating their usefulness as a code validation and verification test problem.
Keywords
Cite
@article{arxiv.2106.04971,
title = {Solutions of the imploding shock problem in a medium with varying density},
author = {Itamar Giron and Shmuel Balberg and Menahem Krief},
journal= {arXiv preprint arXiv:2106.04971},
year = {2021}
}