Coupled Space-Angle Adaptivity for Radiation Transport Calculations

This paper describes the development of a coupled space-angle a posteriori error analysis and adaptive method for radiation transport calculations based on the second-order, even-parity form of the transport equation discretized by a variational finite element-spherical harmonics method (FE-P_N). Rigorous a posteriori error estimates for the global L₂ norm in the even-parity angular flux are derived by utilizing duality arguments. Separate error components for the spatial and angular discretizations are obtained by the adaptive algorithm by first seeking convergence in the spatial variable and then by projecting the spatially converged solution onto the higher-order P_N equation to estimate the angular truncation error. The validity of the developed coupled space-angle adaptive refinement strategy is assessed by comparing the developed error indicator with the true error for representative problems in one and two dimensions. The method of manufactured solutions and alternative transport solution methods are used to provide the true error. Comparisons indicate that the space-angle adaptivity framework is capable of guiding the FE-P_N method toward the true solution.