Modest, M. F. M., Sandip. "Chapter 20 - The Monte Carlo Method for Participating Media," Radiative Heat Transfer (Fourth Edition). Academic Press, 2022, pp. 737-773.
Abstract: This chapter extends the Monte Carlo (MC) method, introduced in Chapter 7 for surface transport, to participating media. Random number relationships for sampling emission locations, directions, and wavelengths within the medium (volume) are derived. Likewise, random number relationships for volumetric absorption and scattering are developed. Treatment of spectral lines in molecular gases using both narrow-band and line-by-line data is discussed. Media with discrete stochastic particle fields, droplets, and solid particles are also addressed in detail. A separate section is dedicated to the backward MC method, which is an important variation of the standard (forward) MC. Finally, several alternative MC formulations, dedicated toward either improving the statistical accuracy or the efficiency, are discussed. These include energy partitioning, direct exchange MC, reciprocity MC, and deviational MC.
Keywords: Monte Carlo (MC) method; participating media; particles; droplets; molecular gases; backward MC; energy partitioning; direct exchange MC; reciprocity MC; deviational MC