Quantitative error assessment of radiative transfer approximations of acoustic wave energies in unbounded and bounded random media

Abstract

This paper reports a series of numerical experiments comparing solutions of the 3D acoustic wave equation in a (randomly-fluctuating) heterogeneous medium to solutions of the radiative transfer equation. Parameters of the two equations are first chosen such that the radiative transfer solution is expected to provide an accurate approximation of the energy of the wave (weak-coupling regime), and the comparisons are excellent. Further simulations indicate that radiative transfer provides accurate approximations not only in the expected regime, but also for a wide range of frequencies and fluctuation levels of the propagation medium parameters, as long as the background velocity is appropriately selected. A particular attention is devoted to comparing wave solutions and radiative transfer approximations close to boundaries, where the accuracy of the radiative transfer equation has not been evaluated before.