Accession Number : AD0652591

Title :   NUMERICAL STUDIES OF STRONG SHOCK WAVES. PART VIII: PROPERTIES OF A SHOCK WAVE FOR A MACH NUMBER OF 2.5,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : Hicks,B. L. ; Smith,M. A.

Report Date : APR 1967

Pagination or Media Count : 40

Abstract : The report describes a study of the structure of a shock wave in a gas of hard spheres for a Mach number M1 = 2.5. The characteristics of the velocity distribution function f, of the collision integral, and of moments of these functions are discussed in detail for nine stations within the shock wave. The structure was calculated by solving the (non-linear) Boltzmann difference equation by an iterative numerical method that includes Monte Carlo evaluation of the collision integral and a number of other new techniques. The 12th iterate is taken to be the solution of the difference equation. The average convergence error of this iterate is estimated to be not more than 0.5% of f. It is found that although departures of the calculated solution from the Mott-Smith shock are generally small they are the smallest on the upstream side of the shock. The most important specific results are the following: The largest deviation of the calculated velocity distribution functions from the Mott-Smith functions occurs near the hot side of the shock and near the 'cold peak' in velocity space and amounts to 21% of f. The rms deviations at any given station in the shock are from four to ten times larger than the likely error at that station and eleven times larger than the estimated convergence error of the iteration method. (Author)

Descriptors :   (*SHOCK WAVES, *MATHEMATICAL ANALYSIS), MACH NUMBER, MONTE CARLO METHOD, CONVERGENCE, INTEGRALS, SPECIAL FUNCTIONS(MATHEMATICAL)

Subject Categories : Numerical Mathematics
      Radiofrequency Wave Propagation

Distribution Statement : APPROVED FOR PUBLIC RELEASE