Singularity fitting in hydrodynamical calculations II

This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self- similar solutions for $gamma$ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary- value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of $gamma$; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows. (auth