Solution of Pure Scattering Radiation Transport Equation (RTE) Using Finite Difference Method (FDM)

Abstract

Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering. Radiative Transfer Equation (RTE) have been applied in a many subjects including optics, astrophysics, atmospheric science, remote sensing, etc. Analytic solutions for RTE exist for simple cases, but, for more realistic media with complex multiple scattering effects, numerical methods are required. In the RTE, six different independent variables define the radiance at any spatial and temporal point. By making appropriate assumptions about the behavior of photons in a scattering medium, the number of independent variables can be reduced. These assumptions lead to the diffusion theory (or diffusion equation) for photon transport. In this work, the diffusive form of RTE is discretized, using a Forward-Time Central-Space (FTCS) Finite Difference Method (FDM). The results reveal the radiance penetration according to Beer-Lambert law.