Monte Carlo simulation of radiative transfer in a medium with varying refractive index specified at discrete points

Abstract

• Monte Carlo simulation for radiative transfer in refractive media is presented. • Discrete ray tracing using scattered discrete refractive indices is developed. • Refractive-index values and gradients are retreived by a moving least square method. • Ray-tracing results for various irregularly-spaced refractive indices are examined. A Monte Carlo method with discrete ray tracing is developed to simulate radiative transfer in a medium with a spatially varying refractive-index distribution available merely at a set of arbitrary discrete points. We solve the ray equation by a Runge−Kutta Dormand−Prince method to carry out the numerical ray tracing. To retrieve the refractive-index values and gradients needed in the discrete ray tracing, we apply cubic spline interpolation for one-dimensional simulation and a moving least square (MLS) method for two-dimensional simulation. The influence of the basis vectors and the numbers of sampled data used by the MLS method on ray tracing based on the retrieved refractive-index values and gradients has been examined. The results of radiative equilibrium in a planar medium and radiative transfer in two-dimensional media with different geometries and conditions obtained by the present methods are compared with those obtained by solving the integral equations of radiative transfer and the discrete ordinates method. The comparisons show that the present methods generate accurate results for radiative transfer with various geometries, parameters and refractive-index distributions specified at discrete points.