Accuracy of transport models for waves in random media

This paper addresses the validity of radiative transfer equations as a model for the energy density of waves propagating in highly heterogeneous media. Comparisons between acoustic wave simulations over domains of size comparable to 500 wavelengths in two space dimensions and Monte Carlo simulations of radiative transfer equations are performed. In the so-called weak coupling regime, the agreement between the energy densities obtained by solving the wave equations and those predicted by solving the radiative transfer equations is remarkable. The domain of validity of the radiative transfer equations is assessed by looking at the fluctuations in the energy density they predict in the presence of small-volume defects in the underlying media.