Radiative transfer by the YIX method in nonhomogeneous, scattering, and nongray media

Abstract

A numerical solution of the integral equation of radiative heat transfer using the YIX method involving a mixture of highly anisotropic scattering particles and a nongray absorbing gas is presented. To validate the three-dimensional calculation, bench mark solutions are established on a model problem using a high-order accuracy method, the product integration method (PIM). Various effects, e.g., the discrete ordinates sets, first integration point of the YIX quadrature, optical thickness of the medium, grid sizes, and spectral resolution on the accuracy of the three-dimensional calculation are discussed. Results for three-dimensional calculations are presented. For all cases, the pressure variation has less significant effect on the results than those by particle density or temperature variations. The three-dimensional nonhomogeneous cases have different trends of variation in radiative flux and divergence due to their nonuniform particle density distribution and nonisothermal participating medium. The use of the YIX method with discrete ordinates for the multidimensional calculations of highly anisotropic scattering and spectrally-dependent medium is shown to be accurate and flexible.