Solution of Pure Scattering Radiation Transport Equation using Finite Difference Method

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 processes. Equations of radiative transfer have application in a wide variety of subjects including optics, astrophysics, atmospheric science, and remote sensing. Analytic solutions to the radiative transfer equation (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 behaviour 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, diffusive form of RTE will be discretized using Finite Difference Method Forward Time Central Space (FTCS) method and solved in MATLAB®. The results reveal that the penetration intensity of the photons and validate the inverse-square law.