Improved anisotropic linear source formulation for multiphysics problems

This work seeks to extend an existing formulation of the method of characteristics with linear source approximation for problems with dynamic cross sections. The previous formulation eliminated cross section dependence of precomputed coefficients for systems with an isotropic source. The method is extended to include a formulation for spatially flat anisotropic scattering that eliminates cross section dependence of precomputed coefficients without adding additional operations; increasing efficiency in multiphysics simulations where cross sections can be subject to change. The new formulation is implemented in the MPACT code and tested on two problems: 3D transport assembly calculations using MPACT's 2D/1D method and a 3D assembly with T/H feedback using MPACT's 2D/1D method coupled with COBRA-TF. This work demonstrates that the new linear source formulation allows for the number of mesh elements to be significantly reduced while maintaining accuracy, leading to shorter run-times for 3D cases with fixed cross sections, and substantial reduction of memory usage for 3D cases with fixed cross sections. The multiphysics calculations show similar runtimes for the same accuracy with significant reduction of memory. For similar accuracy, the method proved effective in reducing memory usage by, on average, 30% for 3D problems and 21% for multiphysics problems.