Joint asymptotic error analysis for angular and spatial discretizations in discrete ordinates transport

Determine the asymptotic error introduced by angular discretization in the discrete ordinates approximation of the linear Boltzmann equation (including the Radiative Transfer Equation), and establish a joint asymptotic analysis that rigorously couples spatial and angular discretizations, applicable to formulations such as the ADO-Nodal method and other discrete ordinates schemes.

Background

The paper studies analytical and semi-analytical solutions for the linear Boltzmann/transport equation via the Analytical Discrete Ordinates (ADO) method, including its ADO-Nodal extension for two-dimensional problems. Prior work by the authors has analyzed spatial discretization errors using Richardson extrapolation and investigated the impact of angular quadrature schemes on convergence and ray effects.

Despite these advances, the authors identify the need for a rigorous treatment of the asymptotic error due to angular discretization, specifically in combination with spatial discretization. This joint analysis is essential for understanding convergence behavior of discrete ordinates solutions and for guiding the choice of quadrature schemes and mesh refinement in highly anisotropic scattering media.