**Singularity Fitting in Hydrodynamical Calculations II**

**Local PDF:** ADA385366.pdf

AD Number: ADA385366

Subject Categories: EXPLOSIONS
NUMERICAL MATHEMATICS

Corporate Author: LOS ALAMOS NATIONAL LAB NM

Title: Singularity Fitting in Hydrodynamical Calculations II

Personal Authors: Richtmyer, R. D.; Lazarus, R. B.

Report Date: DEC 1975

Pages: 19 PAGES

Report Number: LA-6108-MS, UC-32

Contract Number: W-7405-ENG-36

Monitor Acronym: XD

Monitor Series: XD

Descriptors: *SHOCK WAVES, *HYDRODYNAMIC CODES, BOUNDARY VALUE PROBLEMS,
ASYMPTOTIC SERIES, TWO DIMENSIONAL FLOW, DISCONTINUITIES, RAREFACTION, CURVE
FITTING.

Identifiers: SELF SIMILAR CALCULATIONS

Abstract: 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: (1) 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; (2) 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; (3) 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; (4) the
similarity theory for the outgoing shock, which takes into account the entropy
increase; (5) **a** "zooming" method for the study of the asymptotic behavior of
solutions of the full initial boundary-value problem; (6) 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 (l,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.

Limitation Code: APPROVED FOR PUBLIC RELEASE

Source Code: 211350

Citation Creation Date: 24 JAN 2001