ABSTRACT

A hybrid finite volume/finite element method was recently developed to solve the radiative transfer equation (RTE). In this method, the radiation intensity is approximated as a linear combination of basis functions, dependent only on the angular direction. The coefficients of the approximation are unknown functions of the spatial coordinates. The spatial discretization is carried out using the finite volume method, transforming the differential equations into algebraic equations. The angular discretization is accomplished using a methodology similar to that employed in the finite element method. The Galerkin-like approximation of the radiation intensity is introduced into the RTE, which is multiplied by the nth basis function and integrated over all directions. The basis functions are taken as bilinear basis functions, and a classical polar/azimuthal discretization is carried out, as in the finite volume and discrete transfer methods. However, while in these methods the radiation intensity is constant over a control angle or a solid angle, respectively, in the present method the radiation intensity is a continuously varying function. Previous development and application of the method was limited to Cartesian coordinates. In the present work, the method is extended to complex geometries using a structured body-fitted mesh. Radiative transfer is calculated for several two-dimensional enclosures containing emitting-absorbing, scattering, gray media, and the predicted results are compared with benchmark solutions published in the literature. It was found that the results are in good agreement with reference solutions, demonstrating the ability of the present method to handle complex geometries.