  Thermal Radiative Transfer (TRT) is the dominant energy transfer mechanism in
high-energy density physics with applications in inertial confinement fusion
and astrophysics. The stiff interactions between the material and radiation
fields make TRT problems challenging to model. In this study, we propose a
multi-dimensional extension of the deterministic particle (DP) method. The DP
method combines aspects from both particle and deterministic methods. If the
emission source is known \apriori, and no physical scattering is present, the
intensity of a particle can be integrated analytically. This introduces no
statistical noise compared to Monte-Carlo methods, while maintaining the
flexibility of particle methods. The method is closely related to the popular
method of long characteristics. The combination of the DP-method with a
discretely-consistent, nonlinear, gray low-order system enables an efficient
solution algorithm for multi-frequency TRT problems. We demonstrate with
numerical examples that the use of a linear-source approximation based on
spatial moments improves the behavior of our method in the thick diffusion
limit significantly.
