Accelerating ray convergence in incident heat flux calculations using Sobol sequences

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−1ln(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.