MONTE-CARLO SIMULATION OF A RADIATIVE-TRANSFER PROBLEM IN A RANDOM MEDIUM - APPLICATION TO A BINARY MIXTURE

This paper considers monochromatic radiative transfer in a diffusive three dimensional random binary mixture. The absorption coefficient, along any line-of-sight is a homogeneous Markov process, which is described by a three-dimensional Kubo-Anderson process. The transfer equation is solved numerically by Monte-Carlo simulations on a massively parallel computer (a Connection Machine) by attaching one or several photons to each processor. The implementation of the simulations on the machine is discussed in detail, in particular the association between photons and processors and the storage of the data concerning the photons and the realizations of the statistics. With a CM-2 having 8000 processors, it is possible, with an adequate strategy, to follow simultaneously millions of photons in hundreds of realizations and to reach optical thicknesses up to 100 with dispersions of order 10(-2) for the reflection and transmission coefficients. The simulations are validated, in the case of the one-dimensional rod geometry, by comparison with the exact analytical solution, constructed by averaging the solution of the non-stochastic problem (diffusion in a rod of given optical thickness) over the probability density of the optical thickness. The latter obeys a stochastic Liouville equation which is solved by a Green's function method. The influence of the dimension of the Kubo-Anderson process is studied for the case of a slab and it is shown that a slab consisting in a pile of layers (ID process) is more transparent than one which consists in a stack of lumps (3D process). A strategy for improving the efficiency of Monte-Carlo simulations, based on the distributon of the lengths of the individual steps of the photons, is presented and discussed.