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 t hree dimensional random binary mixture. The absorption coefficient, al ong any line-of-sight is a homogeneous Markov process, which is descri bed by a three-dimensional Kubo-Anderson process. The transfer equatio n is solved numerically by Monte-Carlo simulations on a massively para llel computer (a Connection Machine) by attaching one or several photo ns to each processor. The implementation of the simulations on the mac hine is discussed in detail, in particular the association between pho tons and processors and the storage of the data concerning the photons and the realizations of the statistics. With a CM-2 having 8000 proce ssors, it is possible, with an adequate strategy, to follow simultaneo usly millions of photons in hundreds of realizations and to reach opti cal thicknesses up to 100 with dispersions of order 10(-2) for the ref lection and transmission coefficients. The simulations are validated, in the case of the one-dimensional rod geometry, by comparison with th e exact analytical solution, constructed by averaging the solution of the non-stochastic problem (diffusion in a rod of given optical thickn ess) over the probability density of the optical thickness. The latter obeys a stochastic Liouville equation which is solved by a Green's fu nction method. The influence of the dimension of the Kubo-Anderson pro cess is studied for the case of a slab and it is shown that a slab con sisting in a pile of layers (ID process) is more transparent than one which consists in a stack of lumps (3D process). A strategy for improv ing the efficiency of Monte-Carlo simulations, based on the distributo n of the lengths of the individual steps of the photons, is presented and discussed.