Accelerating ray convergence in incident heat flux calculations using Sobol sequences

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Abstract

In this paper an improved quadrature scheme based on the reverse Monte Carlo method implemented using Sobol sequences to generate ray orientations is presented. This has the property that a more uniform pattern of rays on the unit hemisphere is produced compared to the usual implementation of the reverse Monte Carlo method. The use of Sobol sequences gives a ray convergence rate for the incident heat flux that is asymptotically equivalent to O (NRay- 1). The generation of ray directions using Sobol sequences means that the Central Limit Theorem no longer holds. In its place a Gaussian variable is formulated from the incident intensity distributions calculated using Sobol sequences. This makes it possible to calculate confidence limits for a prediction of incident heat flux and the confidence limits contract with ray number at a rate of O (NRay- 1 l n (NRay)). An extension to the Monte Carlo method combined with Sobol sequences is also presented that exploits the shape of the incident intensity distribution to a receiver. The new methodology is relatively simple to implement and shows some promising improvements in computational efficiency. © 2008 Elsevier Masson SAS. All rights reserved.

Original languageEnglish
Pages (from-to)1338-1347
Number of pages10
JournalInternational Journal of Thermal Sciences
Volume48
Issue number7
DOIs
Publication statusPublished - Jul 2009

Keywords

  • Jet fires
  • Monte-Carlo method
  • Ray effect
  • Sobol sequences
  • Thermal radiation modelling

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