In the following, we shall present the formulation for tracing particles from surfaces to surfaces inside an enclosure. A more complete reference is Burns et al., 1990. To illustrate the concepts and computational aspects, we deal with prismatic surfaces, which are infinite in the third dimension. Thus, they can mathematically be described in two dimensions only.
We follow particles from ``birth'' (emission) to ``death'' (absorption or extinction), through possibly many intermediate interactions (reflections) with surfaces. As we directly simulate physical objects (particles), this is often termed the Direct Simulation Monte Carlo method.
Here, between surfaces, particles travel in straight lines and do not interact. Extensions to trajectories other than straight lines are conceptually straightforward, but can be vexing in the difficulty of implementation. Where particles do interact, this may introduce significant additional complexity. Our approach is representative of the transport of photons, neutrons, electrons and molecules in situations where there is no participating medium---where volumetric interactions do not occur. A variety of application areas including thermal radiative transport, neutron damage and molecular sputter are well modelled under these restrictive assumptions.