Singularity fitting in hydrodynamical calculations II

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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 ... continued below

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16 p.

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Richtmyer, R.D. & Lazarus, R.B. September 1, 1975.

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Description

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)

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16 p.

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Dep. NTIS

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  • Other Information: Orig. Receipt Date: 30-JUN-76

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  • Report No.: LA--6108-MS
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/4048719 | External Link
  • Office of Scientific & Technical Information Report Number: 4048719
  • Archival Resource Key: ark:/67531/metadc870035

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • September 1, 1975

Added to The UNT Digital Library

  • Sept. 16, 2016, 12:32 a.m.

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  • Oct. 12, 2017, 2:10 p.m.

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Richtmyer, R.D. & Lazarus, R.B. Singularity fitting in hydrodynamical calculations II, report, September 1, 1975; New Mexico. (digital.library.unt.edu/ark:/67531/metadc870035/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.