Assessment of randomized Quasi-Monte Carlo method efficiency in radiative heat transfer simulations

Abstract Radiation can play a central role in turbulent reactive flows where heat transfer is enhanced in applications with high temperature and pressure. The Monte Carlo method is a successful technique to solve the radiative transfer equation accurately with relative ease while retaining detailed properties. However, its drawback is associated to a slow convergence rate. One strategy to improve the efficiency of Monte Carlo method consists in replacing the pseudo-random sequences with an alternative sampling: the low-discrepancy sequences. The introduction of such sequences in Monte Carlo leads to Quasi-Monte Carlo methods. Their advantage lies in a higher convergence rate compared to MC methods which have however not been assessed in 3D participating media. Additionally, in order to get an error estimation which is necessary in practical applications, a randomization of Quasi-Monte Carlo is needed (Randomized-QMC). Such Randomized-QMC methods have not been considered for simulations of radiative heat transfer in participating media before. In the present study, Monte Carlo and Randomized Quasi-Monte Carlo methods are assessed in terms of efficiency and computational cost in radiative heat transfer simulations of three practical 3D configurations. Comparisons in terms of local standard deviation, convergence rate, and final computational cost show that Randomized Quasi-Monte Carlo outperforms Monte Carlo in all the investigated cases.

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