Monte Carlo functional expansion calculation of free molecular flows

Authors:
A. G. Petschek, R. E. Williamson, W. J. Krauser and P. C. White

Journal:
Math. Comp. **33** (1979), 765-777

MSC:
Primary 82A70; Secondary 65C05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521290-8

MathSciNet review:
521290

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Abstract | References | Similar Articles | Additional Information

Abstract: A Monte Carlo technique for Knudsen flow, light transmission in tubes, the flow of cold neutrons, phonon transmission, heat transfer calculations and other problems involving free streaming in cylindrical enclosures is described. The coefficients of a functional expansion of the view factors are estimated by Monte Carlo, are then perturbed in a least squares minimum sense to satisfy some consistency conditions, and finally are used to calculate the collision density on the boundary and the transmission of the enclosure. Without importance sampling or other variance reduction techniques, the calculational work required for a given accuracy is reduced by a factor frequently near 10 when compared to a simple calculation in which particles are followed from entrance to exit.

**[1]**D. H. Davis,*Monte Carlo calculation of molecular flow rates through a cylinder elbow and pipes of other shapes*, J. Appl. Phys.**31**(1960), 1169–1176. MR**0113274****[2]**A. G. PETSCHEK, R. E. WILLIAMSON & W. J. KRAUSER, "A novel Monte Carlo binning technique,"*Trans. Amer. Nuclear Soc.*, v. 27, 1977, pp. 377-378.**[3]**E. GARELIS & T. E. WAINWRIGHT, "Free molecular flow in a right circular cylinder,"*Phys. Fluids*, v. 16, 1973, pp. 476-481.**[4]**J. A. FLECK, JR., "Effective fluorescent lifetimes in ruby laser rods,"*J. Appl. Phys.*, v. 36, 1965, pp. 1301-1306.**[5]**D. BLECHSCHMIDT, "Monte Carlo study of light transmission through a cylindrical tube,"*J. Vac. Sci. T.*, v. 11, 1974, pp. 570-574.**[6]**I. BERCEANU & V. K. IGNATOVICH, "Molecular flow of ultracold neutrons through long tubes,"*Vacuum*, v. 23, 1973, pp. 441-445.**[7]**R. SIEGEL & J. R. HOWELL,*Thermal Radiation Heat Transfer*, McGraw-Hill, New York, 1972.**[8]**J. M. HAMMERSLY & D. C. HANDSCOMB,*Monte Carlo Methods*, Methuen, London, 1964.**[9]**T. M. JORDON, "Advanced Monte Carlo concepts in radiation shielding calculations: Methods and applications,"*Nuclear Engin. Design*, v. 13, 1970, pp. 415-422.**[10]**B. L. BEERS & V. W. PINE, "Functional expansion Monte Carlo electron transport calculations,"*IEEE Trans. Nuclear Sci.*, v. NS-23, 1976, pp. 1850-1856.**[11]**A. S. BERMAN, "Free molecule transmission probabilities,"*J. Appl. Phys.*, v. 36, 1965, p. 3356.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521290-8

Article copyright:
© Copyright 1979
American Mathematical Society