A quasi-Monte Carlo solver for thermal radiation in participating media. (February 2020) - Farmer, Joseph; Roy, Somesh
Highlights: A quasi-Monte Carlo (QMC) method using low-discrepancy sequences for thermal radiation transport is proposed. Three low-discrepancy sequences - Sobol, Halton, and Niederreiter - were tested and found to have comparable accuracy. The accuracy of QMC method was systematically evaluated in a series of one-dimensional and three-dimensional combustion-relevant configurations. The QMC method was found to have lower error and faster convergence rate than conventional Monte Carlo method for thermal radiation. A figure of merit defined from combination of computational cost and accuracy showed QMC to be significantly more advantageous than conventional Monte Carlo method for thermal radiation. Abstract: The Monte Carlo (MC) method is the most accurate method for resolving radiative heat transfer in participating media. However, it is also computationally prohibitive in large-scale simulations. To alleviate this, this study proposes a quasi-Monte Carlo (QMC) method for thermal radiation in participating media with a focus on combustion-related problems. The QMC method employs low-discrepancy sequences (LDS) in place of the traditional random numbers. Three different low-discrepancy sequences – Sobol, Halton, and Niederreiter – were examined as part of this work. The developed QMC method was first validated against analytical solutions of radiative heat transfer in several one-dimensional configurations. Then it was extended to three-dimensional practical combustion configurations. The results from QMC and traditional Monte Carlo are compared against benchmark solutions for each cases. It is shown that the error of the predicted radiation field from QMC is lower than an equivalent MC simulation. The computational cost of QMC was also found lower than MC due to the avoidance of requirement of several statistical runs for traditional Monte Carlo methods alongside achieving the reduction in error. In conclusion, significant improvements in computational costs and accuracy seen in the QMC method makes it an attractive alternative to traditional Monte Carlo methods in high-fidelity simulations.