Strong convergent shock waves near the center of convergence - a power series solution

A Lagrangian formulation of the self-similar convergent shock problem is presented for a quiescent perfect gas of zero pressure. The initial density is either constant or decreasing towards the center according to a power law. One-dimensional plane, cylindrical, or spherical geometry is assumed. The paper is based on a power series representation of the nondimensional flow velocity f (Tau). Density, pressure, and particle trajectories are expressed analytically by f. Similarity parameters alpha, introduced as the near-center limit of a function describing the motion of the shock front, are determined by requiring the power series of f to converge. (INT)