Accession Number : AD0661338

Title :   NUMERICAL STUDIES OF STRONG SHOCK WAVES. PART X. ON THE ACCURACY OF MONTE CARLO SOLUTIONS OF THE NON-LINEAR BOLTZMAN EQUATION,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : Hicks,Bruce L. ; Smith,Margaret A.

Report Date : SEP 1967

Pagination or Media Count : 42

Abstract : Nordsieck's Monte Carlo method of evaluating the Boltzmann collision integral made possible for the first time solutions of the non-linear Boltzmann equation for many kinetic theory problems of interest. The paper summarizes an extensive series of numerical calculations directed toward understanding and evaluating the various errors in these solutions. A generally useful method is described that permits estimation of the random or Monte Carlo part of the error in any quantity derivable from the computed values of the velocity distribution function or from the two parts of the Boltzmann collision integral. Some of the systematic errors can be evaluated. The errors in the velocity distribution function, in the collision integral and in moments of each of these function are discussed for two problems of physical interest for which the Boltzmann equation has been solved by the Monte Carlo method on the CDC 1604 computer, namely, for the pseudo-shock and the shock wave. In the solution of the shock problem for a Mach number of 2.5, the random errors in the velocity distribution function and the collision integral amount to 2% or less, and random errors in the moments of these functions range from 0.03 to 2.7%. (Author)

Descriptors :   (*SHOCK WAVES, NUMERICAL ANALYSIS), INTEGRALS, MONTE CARLO METHOD, ACCURACY, NONLINEAR SYSTEMS, MATHEMATICAL PREDICTION, ERRORS, DISTRIBUTION FUNCTIONS, STATISTICAL MECHANICS, KINETIC ENERGY, MOMENTS, CONVERGENCE

Subject Categories : Aerodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE