James S. Warsa

Rylan C. Paye, Dmitriy Y. Anistratov, Jim E. Morel et al.

In this paper, new implicit methods with reduced memory are developed for solving the time-dependent Boltzmann transport equation (BTE). One-group transport problems in 1D slab geometry are considered. The reduced-memory methods are formulated for the BTE discretized with the linear-discontinuous scheme in space and backward-Euler time integration method. Numerical results are presented to demonstrate performance of the proposed numerical methods.

Dmitriy Y. Anistratov, Joseph M. Coale, James S. Warsa et al.

This paper presents multilevel iterative schemes for solving the multigroup Boltzmann transport equations (BTEs) with parallel calculation of group equations. They are formulated with multigroup and grey low-order equations of the Second-Moment (SM) method. The group high-order BTEs and low-order SM (LOSM) equations are solved in parallel. To further improve convergence and increase computational efficiency of algorithms Anderson acceleration is applied to inner iterations for solving the system of multigroup LOSM equations. Numerical results are presented to demonstrate performance of the multilevel iterative methods.

Samuel Olivier, James S. Warsa, HyeongKae Park

Thermal radiative transfer (TRT) presents significant computational challenges due to the stiff, nonlinear coupling between radiation and material energy, particularly in multigroup, high-fidelity transport models. In this work, we develop an efficient nonlinear acceleration framework for TRT based on the Second Moment (SM) method. Our approach couples high-order discrete ordinates transport to a gray, diffusion-based low-order system that implicitly resolves the stiff absorption-emission physics, isolating this stiffness from the high-order system. The resulting algorithm alternates between transport sweeps and a Newton-type solution of the coupled low-order and material energy balance equations, utilizing nonlinear temperature elimination for improved robustness. Crucially, our approach is the first moment-based TRT algorithm with a symmetric and positive definite (SPD) low-order system enabling scalable linear solves via algebraic multigrid-preconditioned conjugate gradient. We investigate both consistent and independent low-order discretizations within a discontinuous Galerkin framework and assess their performance on one and two-dimensional gray and multigroup benchmark problems.