A numerical technique for solving the coupled radiative transfer and heat equations in a random medium with plane geometry

摘要

A Monte Carlo based numerical method is presented which generates statistical information equivalent to the unknown Aux density solution of the radiative transfer equation within a plane geometry, for a useful class of problems. This method scores all vectorial intersections of randomly generated light paths with a set of internal data surfaces spanning the random medium. This approach has not been previously considered, but can be implemented on a simple and compact computer code that is straightforward to utilize and adapt. The method is presented as an alternative or complement to standard numerical methods and is tested with diffusion theory. Many useful computations can be performed within several minutes. It is particularly well suited to modelling laser-generated heat sources within finite, artificial or biological random media. A numerical solution of the heat equation is then possible on the same set of data surfaces used in the optical model. Illustrative calculations are presented. [References: 23]